TSTP Solution File: SEU165+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU165+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:07:28 EDT 2022
% Result : Theorem 1.19s 1.61s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 135
% Syntax : Number of formulae : 2363 (1238 unt; 40 typ; 0 def)
% Number of atoms : 15582 (6187 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 33821 (6235 ~;5454 |; 270 &;21731 @)
% ( 71 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 73 ( 73 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 9 con; 0-4 aty)
% Number of variables : 7058 ( 0 ^7044 !; 14 ?;7058 :)
% 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_C,type,
sK10_C: $i > $i > $i ).
thf(tp_sK11_SY201,type,
sK11_SY201: $i > $i > $i ).
thf(tp_sK12_D,type,
sK12_D: $i > $i > $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_E,type,
sK14_E: $i > $i > $i > $i > $i ).
thf(tp_sK15_SY202,type,
sK15_SY202: $i > $i > $i > $i > $i ).
thf(tp_sK16_D,type,
sK16_D: $i > $i > $i > $i ).
thf(tp_sK17_SY205,type,
sK17_SY205: $i > $i > $i > $i ).
thf(tp_sK18_SY207,type,
sK18_SY207: $i > $i > $i > $i ).
thf(tp_sK19_D,type,
sK19_D: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_D,type,
sK20_D: $i > $i > $i > $i ).
thf(tp_sK21_C,type,
sK21_C: $i > $i > $i ).
thf(tp_sK22_B,type,
sK22_B: $i > $i ).
thf(tp_sK23_C,type,
sK23_C: $i > $i > $i ).
thf(tp_sK24_C,type,
sK24_C: $i > $i > $i ).
thf(tp_sK25_C,type,
sK25_C: $i > $i > $i ).
thf(tp_sK2_SY194,type,
sK2_SY194: $i ).
thf(tp_sK3_SY197,type,
sK3_SY197: $i ).
thf(tp_sK4_SY199,type,
sK4_SY199: $i ).
thf(tp_sK5_C,type,
sK5_C: $i > $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_D,type,
sK8_D: $i > $i > $i > $i ).
thf(tp_sK9_D,type,
sK9_D: $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(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(5,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_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(7,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(8,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(11,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(12,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(19,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
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(31,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
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(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
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(44,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_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] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(52,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(53,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(54,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(55,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(57,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(59,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(60,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(66,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(67,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(68,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(73,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(75,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(76,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(78,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(79,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(80,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(81,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(82,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(87,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(88,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(89,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(92,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(93,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(94,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(95,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(96,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[95]) ).
thf(97,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[96]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(100,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(101,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(102,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(104,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(105,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(106,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(108,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(109,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(115,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(116,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(117,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(118,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(119,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(120,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(121,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(122,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(123,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(124,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(125,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(126,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(127,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(128,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(130,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(131,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(132,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(133,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(134,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(135,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(136,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(137,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(138,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(139,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(141,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(142,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(143,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(144,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(145,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(146,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(147,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(148,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(149,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(150,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)],[53]) ).
thf(151,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(152,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(153,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(154,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(155,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(156,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(157,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(158,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(159,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(160,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(161,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(162,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(163,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(164,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)],[67]) ).
thf(165,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(166,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(167,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(168,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(169,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(170,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(171,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(172,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)],[75]) ).
thf(173,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(174,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(175,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)],[78]) ).
thf(176,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(177,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(178,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)],[81]) ).
thf(179,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(180,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(181,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(182,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(183,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(184,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(185,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)],[88]) ).
thf(186,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(187,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(188,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(191,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(192,plain,
( ( ! [SY194: $i,SY195: $i,SY196: $i] :
( ( in @ ( ordered_pair @ sK1_A @ SY194 ) @ ( cartesian_product2 @ SY195 @ SY196 ) )
<=> ( ( in @ sK1_A @ SY195 )
& ( in @ SY194 @ SY196 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[97]) ).
thf(193,plain,
( ( ! [SY197: $i,SY198: $i] :
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ SY197 @ SY198 ) )
<=> ( ( in @ sK1_A @ SY197 )
& ( in @ sK2_SY194 @ SY198 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[192]) ).
thf(194,plain,
( ( ! [SY199: $i] :
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ SY199 ) )
<=> ( ( in @ sK1_A @ sK3_SY197 )
& ( in @ sK2_SY194 @ SY199 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[193]) ).
thf(195,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) )
<=> ( ( in @ sK1_A @ sK3_SY197 )
& ( in @ sK2_SY194 @ sK4_SY199 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[194]) ).
thf(196,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) )
=> ( ( in @ sK1_A @ sK3_SY197 )
& ( in @ sK2_SY194 @ sK4_SY199 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[195]) ).
thf(197,plain,
( ( ( ( in @ sK1_A @ sK3_SY197 )
& ( in @ sK2_SY194 @ sK4_SY199 ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[195]) ).
thf(198,plain,
( ( ~ ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) )
=> ( ( in @ sK1_A @ sK3_SY197 )
& ( in @ sK2_SY194 @ sK4_SY199 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[196]) ).
thf(199,plain,
( ( ~ ( ( ( in @ sK1_A @ sK3_SY197 )
& ( in @ sK2_SY194 @ sK4_SY199 ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[197]) ).
thf(200,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) )
& ( ~ ( in @ sK1_A @ sK3_SY197 )
| ~ ( in @ sK2_SY194 @ sK4_SY199 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[198]) ).
thf(201,plain,
( ( ( in @ sK1_A @ sK3_SY197 )
& ( in @ sK2_SY194 @ sK4_SY199 )
& ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[199]) ).
thf(202,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(203,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(204,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(205,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_C @ B @ A ) @ A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(206,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(207,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(208,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(209,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(210,plain,
( ( ! [A: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(211,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(212,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[112]) ).
thf(213,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(214,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(215,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[127]) ).
thf(216,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(217,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK8_D @ C @ B @ A ) @ A )
| ( in @ ( sK8_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK8_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK8_D @ C @ B @ A ) @ A )
| ( in @ ( sK8_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK8_D @ C @ B @ A ) @ B )
| ( in @ ( sK8_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(218,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY200: $i] :
( ~ ( in @ ( sK10_C @ B @ A ) @ SY200 )
| ~ ( in @ SY200 @ A ) )
| ~ ( in @ ( sK10_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK10_C @ B @ A ) @ ( sK11_SY201 @ B @ A ) )
& ( in @ ( sK11_SY201 @ B @ A ) @ A ) )
| ( in @ ( sK10_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK9_D @ C @ B @ A ) )
& ( in @ ( sK9_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(219,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK12_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK12_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK12_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK12_D @ C @ B @ A ) @ A )
| ( in @ ( sK12_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK12_D @ C @ B @ A ) @ B )
| ( in @ ( sK12_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(220,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK13_C @ B @ A ) @ A )
& ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[133]) ).
thf(221,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY203: $i,SY204: $i] :
( ~ ( in @ SY203 @ A )
| ~ ( in @ SY204 @ B )
| ( ( sK16_D @ C @ B @ A )
!= ( ordered_pair @ SY203 @ SY204 ) ) )
| ~ ( in @ ( sK16_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK17_SY205 @ C @ B @ A ) @ A )
& ( in @ ( sK18_SY207 @ C @ B @ A ) @ B )
& ( ( sK16_D @ C @ B @ A )
= ( ordered_pair @ ( sK17_SY205 @ C @ B @ A ) @ ( sK18_SY207 @ C @ B @ A ) ) ) )
| ( in @ ( sK16_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK14_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK15_SY202 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK14_E @ D @ C @ B @ A ) @ ( sK15_SY202 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[134]) ).
thf(222,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK19_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK19_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK19_D @ C @ B @ A ) @ C )
| ( in @ ( sK19_D @ C @ B @ A ) @ A )
| ( in @ ( sK19_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[135]) ).
thf(223,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK20_D @ C @ B @ A ) @ C )
| ( ( sK20_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK20_D @ C @ B @ A ) @ C )
| ( ( sK20_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK20_D @ C @ B @ A ) @ C )
| ( ( sK20_D @ C @ B @ A )
= A )
| ( ( sK20_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[136]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK21_C @ B @ A ) @ B )
| ~ ( subset @ ( sK21_C @ B @ A ) @ A ) )
& ( ( in @ ( sK21_C @ B @ A ) @ B )
| ( subset @ ( sK21_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[137]) ).
thf(225,plain,
( ( ! [A: $i] :
( ( in @ ( sK22_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[138]) ).
thf(226,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK23_C @ B @ A )
!= A )
| ~ ( in @ ( sK23_C @ B @ A ) @ B ) )
& ( ( ( sK23_C @ B @ A )
= A )
| ( in @ ( sK23_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(227,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[140]) ).
thf(228,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(230,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(231,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(232,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(233,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(234,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(235,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[155]) ).
thf(237,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[156]) ).
thf(238,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(239,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK24_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(240,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(241,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(242,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(243,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK25_C @ B @ A ) @ A )
& ( in @ ( sK25_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[165]) ).
thf(245,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(246,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(247,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(248,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[171]) ).
thf(249,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(250,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(251,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(252,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(253,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(254,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[180]) ).
thf(255,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(256,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[182]) ).
thf(257,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[183]) ).
thf(258,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[184]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[185]) ).
thf(260,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(261,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[187]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[188]) ).
thf(263,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[189]) ).
thf(264,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[190]) ).
thf(265,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[191]) ).
thf(266,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(267,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(268,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(269,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(270,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(271,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(272,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(273,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(274,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(276,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(277,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(278,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(279,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(280,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(281,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(282,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(283,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(284,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(285,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(286,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(287,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(288,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(289,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(290,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(291,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(292,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(293,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK25_C @ B @ A ) @ A )
& ( in @ ( sK25_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(294,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(295,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(296,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(297,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(298,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(299,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK24_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(301,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(302,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(303,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(304,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(305,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(306,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(307,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(308,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(309,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(310,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(311,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(312,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(313,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(314,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(315,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(316,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(317,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(318,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK23_C @ B @ A )
!= A )
| ~ ( in @ ( sK23_C @ B @ A ) @ B ) )
& ( ( ( sK23_C @ B @ A )
= A )
| ( in @ ( sK23_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(319,plain,
( ( ! [A: $i] :
( ( in @ ( sK22_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(320,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK21_C @ B @ A ) @ B )
| ~ ( subset @ ( sK21_C @ B @ A ) @ A ) )
& ( ( in @ ( sK21_C @ B @ A ) @ B )
| ( subset @ ( sK21_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(321,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK20_D @ C @ B @ A ) @ C )
| ( ( sK20_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK20_D @ C @ B @ A ) @ C )
| ( ( sK20_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK20_D @ C @ B @ A ) @ C )
| ( ( sK20_D @ C @ B @ A )
= A )
| ( ( sK20_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(322,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK19_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK19_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK19_D @ C @ B @ A ) @ C )
| ( in @ ( sK19_D @ C @ B @ A ) @ A )
| ( in @ ( sK19_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(323,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY203: $i,SY204: $i] :
( ~ ( in @ SY203 @ A )
| ~ ( in @ SY204 @ B )
| ( ( sK16_D @ C @ B @ A )
!= ( ordered_pair @ SY203 @ SY204 ) ) )
| ~ ( in @ ( sK16_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK17_SY205 @ C @ B @ A ) @ A )
& ( in @ ( sK18_SY207 @ C @ B @ A ) @ B )
& ( ( sK16_D @ C @ B @ A )
= ( ordered_pair @ ( sK17_SY205 @ C @ B @ A ) @ ( sK18_SY207 @ C @ B @ A ) ) ) )
| ( in @ ( sK16_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK14_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK15_SY202 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK14_E @ D @ C @ B @ A ) @ ( sK15_SY202 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(324,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK13_C @ B @ A ) @ A )
& ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(325,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK12_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK12_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK12_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK12_D @ C @ B @ A ) @ A )
| ( in @ ( sK12_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK12_D @ C @ B @ A ) @ B )
| ( in @ ( sK12_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(326,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY200: $i] :
( ~ ( in @ ( sK10_C @ B @ A ) @ SY200 )
| ~ ( in @ SY200 @ A ) )
| ~ ( in @ ( sK10_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK10_C @ B @ A ) @ ( sK11_SY201 @ B @ A ) )
& ( in @ ( sK11_SY201 @ B @ A ) @ A ) )
| ( in @ ( sK10_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK9_D @ C @ B @ A ) )
& ( in @ ( sK9_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(327,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK8_D @ C @ B @ A ) @ A )
| ( in @ ( sK8_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK8_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK8_D @ C @ B @ A ) @ A )
| ( in @ ( sK8_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK8_D @ C @ B @ A ) @ B )
| ( in @ ( sK8_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(328,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(329,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(330,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(331,plain,
$true = $true,
inference(copy,[status(thm)],[126]) ).
thf(332,plain,
$true = $true,
inference(copy,[status(thm)],[125]) ).
thf(333,plain,
$true = $true,
inference(copy,[status(thm)],[124]) ).
thf(334,plain,
$true = $true,
inference(copy,[status(thm)],[123]) ).
thf(335,plain,
$true = $true,
inference(copy,[status(thm)],[122]) ).
thf(336,plain,
$true = $true,
inference(copy,[status(thm)],[121]) ).
thf(337,plain,
$true = $true,
inference(copy,[status(thm)],[120]) ).
thf(338,plain,
$true = $true,
inference(copy,[status(thm)],[119]) ).
thf(339,plain,
$true = $true,
inference(copy,[status(thm)],[118]) ).
thf(340,plain,
$true = $true,
inference(copy,[status(thm)],[117]) ).
thf(341,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(342,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(343,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(344,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(345,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(346,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(347,plain,
( ( ! [A: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(348,plain,
( ( empty @ sK7_A )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(349,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(350,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(351,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(352,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(353,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(354,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_C @ B @ A ) @ A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(355,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(356,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(357,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(358,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(359,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(360,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) )
& ( ~ ( in @ sK1_A @ sK3_SY197 )
| ~ ( in @ sK2_SY194 @ sK4_SY199 ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(361,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(362,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(363,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(364,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK24_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(365,plain,
( ( ~ ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) )
| ~ ( ~ ( in @ sK1_A @ sK3_SY197 )
| ~ ( in @ sK2_SY194 @ sK4_SY199 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(366,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(367,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(368,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(369,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK22_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(370,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(371,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(372,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(373,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK16_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK18_SY207 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK16_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK17_SY205 @ SX2 @ SX1 @ SX0 ) @ ( sK18_SY207 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i,SX5: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK15_SY202 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK14_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY202 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(374,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(375,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK23_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK23_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(376,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(377,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(378,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK20_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK20_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK20_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK20_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK20_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK20_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(379,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(380,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(381,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(382,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(383,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(384,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(385,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(386,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY201 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK11_SY201 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK9_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(387,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(388,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(389,plain,
! [SV1: $i] :
( ( ( ( singleton @ SV1 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(390,plain,
! [SV2: $i] :
( ( ! [SY208: $i] :
( ~ ( in @ SV2 @ SY208 )
| ( ( set_union2 @ ( singleton @ SV2 ) @ SY208 )
= SY208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(391,plain,
! [SV3: $i] :
( ( ! [SY209: $i] :
( ~ ( disjoint @ ( singleton @ SV3 ) @ SY209 )
| ~ ( in @ SV3 @ SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(392,plain,
! [SV4: $i] :
( ( ! [SY210: $i] :
( ( in @ SV4 @ SY210 )
| ( disjoint @ ( singleton @ SV4 ) @ SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(393,plain,
! [SV5: $i] :
( ( ! [SY211: $i] :
( ~ ( subset @ SV5 @ SY211 )
| ! [SY212: $i] :
( ( in @ SY212 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SY211 @ ( singleton @ SY212 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(394,plain,
! [SV6: $i] :
( ( ! [SY213: $i] :
( ~ ( in @ SV6 @ SY213 )
| ( subset @ SV6 @ ( union @ SY213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(395,plain,
! [SV7: $i] :
( ( ! [SY214: $i,SY215: $i,SY216: $i] :
( ( SV7 = SY216 )
| ( SV7 = SY215 )
| ( ( unordered_pair @ SV7 @ SY214 )
!= ( unordered_pair @ SY215 @ SY216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(396,plain,
! [SV8: $i] :
( ( ! [SY217: $i] :
( ~ ( subset @ SV8 @ SY217 )
| ( ( set_union2 @ SV8 @ SY217 )
= SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(397,plain,
! [SV9: $i] :
( ( ! [SY218: $i] : ( subset @ ( set_intersection2 @ SV9 @ SY218 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(398,plain,
! [SV10: $i] :
( ( ! [SY219: $i,SY220: $i] :
( ~ ( subset @ SV10 @ SY219 )
| ~ ( subset @ SV10 @ SY220 )
| ( subset @ SV10 @ ( set_intersection2 @ SY219 @ SY220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(399,plain,
! [SV11: $i] :
( ( ! [SY221: $i,SY222: $i] :
( ~ ( subset @ SV11 @ SY221 )
| ~ ( subset @ SY221 @ SY222 )
| ( subset @ SV11 @ SY222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(400,plain,
! [SV12: $i] :
( ( ! [SY223: $i] :
( ~ ( subset @ SV12 @ SY223 )
| ! [SY224: $i] : ( subset @ ( set_intersection2 @ SV12 @ SY224 ) @ ( set_intersection2 @ SY223 @ SY224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(401,plain,
! [SV13: $i] :
( ( ! [SY225: $i] :
( ~ ( subset @ SV13 @ SY225 )
| ( ( set_intersection2 @ SV13 @ SY225 )
= SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(402,plain,
! [SV14: $i] :
( ( subset @ empty_set @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(403,plain,
! [SV15: $i] :
( ( ! [SY226: $i] :
( ~ ( subset @ SV15 @ SY226 )
| ! [SY227: $i] : ( subset @ ( set_difference @ SV15 @ SY227 ) @ ( set_difference @ SY226 @ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(404,plain,
! [SV16: $i] :
( ( ! [SY228: $i] : ( subset @ ( set_difference @ SV16 @ SY228 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(405,plain,
! [SV17: $i] :
( ( ! [SY229: $i] :
( ( set_union2 @ SV17 @ ( set_difference @ SY229 @ SV17 ) )
= ( set_union2 @ SV17 @ SY229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(406,plain,
! [SV18: $i] :
( ( ~ ( subset @ SV18 @ empty_set )
| ( SV18 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(407,plain,
! [SV19: $i] :
( ( ! [SY230: $i] :
( ( set_difference @ ( set_union2 @ SV19 @ SY230 ) @ SY230 )
= ( set_difference @ SV19 @ SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(408,plain,
! [SV20: $i] :
( ( ! [SY231: $i] :
( ~ ( subset @ SV20 @ SY231 )
| ( SY231
= ( set_union2 @ SV20 @ ( set_difference @ SY231 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(409,plain,
! [SV21: $i] :
( ( ! [SY232: $i] :
( ~ ( in @ SV21 @ SY232 )
| ( ( set_union2 @ ( singleton @ SV21 ) @ SY232 )
= SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(410,plain,
! [SV22: $i] :
( ( ! [SY233: $i] :
( ( set_difference @ SV22 @ ( set_difference @ SV22 @ SY233 ) )
= ( set_intersection2 @ SV22 @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(411,plain,
! [SV23: $i] :
( ( ! [SY234: $i] :
( ~ ( proper_subset @ SY234 @ SV23 )
| ~ ( subset @ SV23 @ SY234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(412,plain,
! [SV24: $i] :
( ( ! [SY235: $i,SY236: $i] :
( ~ ( disjoint @ SY235 @ SY236 )
| ~ ( subset @ SV24 @ SY235 )
| ( disjoint @ SV24 @ SY236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(413,plain,
! [SV25: $i] :
( ( ( unordered_pair @ SV25 @ SV25 )
= ( singleton @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(414,plain,
! [SV26: $i] :
( ( ! [SY237: $i] :
( ~ ( subset @ ( singleton @ SV26 ) @ ( singleton @ SY237 ) )
| ( SV26 = SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(415,plain,
! [SV27: $i] :
( ( ! [SY238: $i] : ( subset @ SV27 @ ( set_union2 @ SV27 @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(416,plain,
! [SV28: $i] :
( ( ! [SY239: $i,SY240: $i] :
( ~ ( subset @ SV28 @ SY239 )
| ~ ( subset @ SY240 @ SY239 )
| ( subset @ ( set_union2 @ SV28 @ SY240 ) @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(417,plain,
! [SV29: $i] :
( ( ! [SY241: $i] :
( ! [SY242: $i] :
( ( singleton @ SV29 )
!= ( unordered_pair @ SY241 @ SY242 ) )
| ( SV29 = SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(418,plain,
! [SV30: $i] :
( ( ! [SY243: $i] :
( ~ ( in @ SV30 @ SY243 )
| ( subset @ SV30 @ ( union @ SY243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(419,plain,
! [SV31: $i] :
( ( ( union @ ( powerset @ SV31 ) )
= SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(420,plain,
! [SV32: $i] :
( ( ! [SY244: $i,SY245: $i] :
( ( ( singleton @ SV32 )
!= ( unordered_pair @ SY244 @ SY245 ) )
| ( SY244 = SY245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(421,plain,
! [SV33: $i] :
( ( ! [SY246: $i] :
( ~ ( in @ SV33 @ SY246 )
| ~ ( in @ SY246 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(422,plain,
! [SV34: $i] :
( ( ! [SY247: $i] :
( ~ ( proper_subset @ SV34 @ SY247 )
| ~ ( proper_subset @ SY247 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(423,plain,
! [SV35: $i] :
( ( ! [SY248: $i] :
( ( unordered_pair @ SV35 @ SY248 )
= ( unordered_pair @ SY248 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(424,plain,
! [SV36: $i] :
( ( ! [SY249: $i] :
( ( set_union2 @ SV36 @ SY249 )
= ( set_union2 @ SY249 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(425,plain,
! [SV37: $i] :
( ( ! [SY250: $i] :
( ( set_intersection2 @ SV37 @ SY250 )
= ( set_intersection2 @ SY250 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(426,plain,
! [SV38: $i] :
( ( ! [SY251: $i] :
( ( ordered_pair @ SV38 @ SY251 )
= ( unordered_pair @ ( unordered_pair @ SV38 @ SY251 ) @ ( singleton @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(427,plain,
! [SV39: $i] :
( ( ! [SY252: $i] :
~ ( empty @ ( ordered_pair @ SV39 @ SY252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(428,plain,
! [SV40: $i] :
( ( ( empty @ SV40 )
| ! [SY253: $i] :
~ ( empty @ ( set_union2 @ SV40 @ SY253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(429,plain,
! [SV41: $i] :
( ( ( empty @ SV41 )
| ! [SY254: $i] :
~ ( empty @ ( set_union2 @ SY254 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(430,plain,
! [SV42: $i] :
( ( ( set_union2 @ SV42 @ SV42 )
= SV42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(431,plain,
! [SV43: $i] :
( ( ( set_intersection2 @ SV43 @ SV43 )
= SV43 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(432,plain,
! [SV44: $i] :
( ( ~ ( proper_subset @ SV44 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(433,plain,
( ( empty @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(434,plain,
! [SV45: $i] :
( ( subset @ SV45 @ SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(435,plain,
! [SV46: $i] :
( ( ! [SY255: $i] :
( ~ ( disjoint @ SV46 @ SY255 )
| ( disjoint @ SY255 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(436,plain,
! [SV47: $i] :
( ( ( set_union2 @ SV47 @ empty_set )
= SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(437,plain,
! [SV48: $i] :
( ( ( set_intersection2 @ SV48 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(438,plain,
! [SV49: $i] :
( ( ( set_difference @ SV49 @ empty_set )
= SV49 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(439,plain,
! [SV50: $i] :
( ( ( set_difference @ empty_set @ SV50 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(440,plain,
! [SV51: $i] :
( ( ~ ( empty @ SV51 )
| ( SV51 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(441,plain,
! [SV52: $i] :
( ( ! [SY256: $i] :
( ~ ( empty @ SY256 )
| ~ ( in @ SV52 @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(442,plain,
! [SV53: $i] :
( ( ! [SY257: $i] :
( ( SV53 = SY257 )
| ~ ( empty @ SV53 )
| ~ ( empty @ SY257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(443,plain,
! [SV54: $i] :
( ( ~ ( ~ ! [SY258: $i,SY259: $i] :
( ~ ( in @ SV54 @ SY259 )
| ~ ( in @ SY258 @ SY259 )
| ( subset @ ( unordered_pair @ SV54 @ SY258 ) @ SY259 ) )
| ~ ~ ( ~ ! [SY260: $i,SY261: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY260 ) @ SY261 )
| ( in @ SV54 @ SY261 ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY262 ) @ SY263 )
| ( in @ SY262 @ SY263 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(444,plain,
! [SV55: $i] :
( ( ~ ( ~ ! [SY264: $i,SY265: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY264 )
| ~ ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY265 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY265 ) )
| ~ ( ~ ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY264 )
| ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY265 ) ) ) )
| ( SY265
= ( set_difference @ SV55 @ SY264 ) ) )
| ~ ! [SY266: $i,SY267: $i] :
( ( SY267
!= ( set_difference @ SV55 @ SY266 ) )
| ~ ( ~ ! [SY268: $i] :
( ~ ( in @ SY268 @ SV55 )
| ( in @ SY268 @ SY266 )
| ( in @ SY268 @ SY267 ) )
| ~ ~ ( ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ SY267 )
| ( in @ SY269 @ SV55 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY267 )
| ~ ( in @ SX3 @ SY266 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(445,plain,
! [SV56: $i] :
( ( ~ ( ~ ! [SY271: $i,SY272: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY272 )
| ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY272 )
| ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY271 ) ) )
| ~ ( ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY272 )
| ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SV56 )
| ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY271 ) ) )
| ( SY272
= ( set_union2 @ SV56 @ SY271 ) ) )
| ~ ! [SY273: $i,SY274: $i] :
( ( SY274
!= ( set_union2 @ SV56 @ SY273 ) )
| ~ ( ~ ! [SY275: $i] :
( ~ ( in @ SY275 @ SY274 )
| ( in @ SY275 @ SV56 )
| ( in @ SY275 @ SY273 ) )
| ~ ~ ( ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SV56 )
| ( in @ SY276 @ SY274 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY273 )
| ( in @ SX3 @ SY274 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(446,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK24_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(447,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) )
| ~ ( ~ ( in @ sK1_A @ sK3_SY197 )
| ~ ( in @ sK2_SY194 @ sK4_SY199 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(448,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(449,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(450,plain,
! [SV57: $i] :
( ( ~ ( ~ ! [SY278: $i,SY279: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SV57 )
| ~ ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY278 )
| ~ ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY279 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY279 ) )
| ~ ( ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY278 )
| ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY279 ) ) ) )
| ( SY279
= ( set_intersection2 @ SV57 @ SY278 ) ) )
| ~ ! [SY280: $i,SY281: $i] :
( ( SY281
!= ( set_intersection2 @ SV57 @ SY280 ) )
| ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ SV57 )
| ~ ( in @ SY282 @ SY280 )
| ( in @ SY282 @ SY281 ) )
| ~ ~ ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SY281 )
| ( in @ SY283 @ SV57 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY281 )
| ( in @ SX3 @ SY280 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(451,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK22_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(452,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(453,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(454,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(455,plain,
! [SV58: $i] :
( ( ~ ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( ~ ( ! [SY287: $i,SY288: $i] :
( ~ ( in @ SY287 @ SV58 )
| ~ ( in @ SY288 @ SY285 )
| ( ( sK16_D @ SY286 @ SY285 @ SV58 )
!= ( ordered_pair @ SY287 @ SY288 ) ) )
| ~ ( in @ ( sK16_D @ SY286 @ SY285 @ SV58 ) @ SY286 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SY286 @ SY285 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SY286 @ SY285 @ SV58 ) @ SY285 ) )
| ( ( sK16_D @ SY286 @ SY285 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SY286 @ SY285 @ SV58 ) @ ( sK18_SY207 @ SY286 @ SY285 @ SV58 ) ) ) )
| ( in @ ( sK16_D @ SY286 @ SY285 @ SV58 ) @ SY286 ) ) )
| ( SY286
= ( cartesian_product2 @ SV58 @ SY285 ) ) )
| ~ ! [SY289: $i,SY290: $i] :
( ( SY290
!= ( cartesian_product2 @ SV58 @ SY289 ) )
| ~ ( ~ ! [SY291: $i] :
( ! [SY292: $i,SY293: $i] :
( ~ ( in @ SY292 @ SV58 )
| ~ ( in @ SY293 @ SY289 )
| ( SY291
!= ( ordered_pair @ SY292 @ SY293 ) ) )
| ( in @ SY291 @ SY290 ) )
| ~ ! [SY294: $i] :
( ~ ( in @ SY294 @ SY290 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY294 @ SY290 @ SY289 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SY294 @ SY290 @ SY289 @ SV58 ) @ SY289 ) )
| ( SY294
!= ( ordered_pair @ ( sK14_E @ SY294 @ SY290 @ SY289 @ SV58 ) @ ( sK15_SY202 @ SY294 @ SY290 @ SY289 @ SV58 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(456,plain,
! [SV59: $i] :
( ( ! [SY295: $i] :
~ ( ~ ! [SY296: $i,SY297: $i] :
( ~ ( in @ SV59 @ SY296 )
| ~ ( in @ SY295 @ SY297 )
| ( in @ ( ordered_pair @ SV59 @ SY295 ) @ ( cartesian_product2 @ SY296 @ SY297 ) ) )
| ~ ~ ( ~ ! [SY298: $i] :
( ! [SY299: $i] :
~ ( in @ ( ordered_pair @ SV59 @ SY295 ) @ ( cartesian_product2 @ SY298 @ SY299 ) )
| ( in @ SV59 @ SY298 ) )
| ~ ! [SY300: $i,SY301: $i] :
( ~ ( in @ ( ordered_pair @ SV59 @ SY295 ) @ ( cartesian_product2 @ SY300 @ SY301 ) )
| ( in @ SY295 @ SY301 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(457,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK23_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK23_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(458,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(459,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(460,plain,
! [SV60: $i] :
( ( ~ ( ~ ! [SY302: $i,SY303: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SY303 @ SY302 @ SV60 ) @ SY303 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
!= SV60 ) )
| ~ ( ~ ( in @ ( sK20_D @ SY303 @ SY302 @ SV60 ) @ SY303 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
!= SY302 ) ) )
| ~ ( ( in @ ( sK20_D @ SY303 @ SY302 @ SV60 ) @ SY303 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
= SV60 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
= SY302 ) ) )
| ( SY303
= ( unordered_pair @ SV60 @ SY302 ) ) )
| ~ ! [SY304: $i,SY305: $i] :
( ( SY305
!= ( unordered_pair @ SV60 @ SY304 ) )
| ~ ( ~ ! [SY306: $i] :
( ~ ( in @ SY306 @ SY305 )
| ( SY306 = SV60 )
| ( SY306 = SY304 ) )
| ~ ~ ( ~ ! [SY307: $i] :
( ( SY307 != SV60 )
| ( in @ SY307 @ SY305 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY304 )
| ( in @ SX3 @ SY305 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(461,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(462,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(463,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(464,plain,
! [SV61: $i] :
( ( ! [SY309: $i] :
~ ( ~ ! [SY310: $i] :
( ! [SY311: $i] :
( ( ordered_pair @ SV61 @ SY309 )
!= ( ordered_pair @ SY310 @ SY311 ) )
| ( SV61 = SY310 ) )
| ~ ! [SY312: $i,SY313: $i] :
( ( ( ordered_pair @ SV61 @ SY309 )
!= ( ordered_pair @ SY312 @ SY313 ) )
| ( SY309 = SY313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(465,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(466,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(467,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(468,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY201 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK11_SY201 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK9_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(469,plain,
! [SV62: $i] :
( ( ! [SY314: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_C @ SY314 @ SV62 ) @ SV62 )
| ~ ( in @ ( sK5_C @ SY314 @ SV62 ) @ SY314 ) )
| ~ ( ( in @ ( sK5_C @ SY314 @ SV62 ) @ SV62 )
| ( in @ ( sK5_C @ SY314 @ SV62 ) @ SY314 ) ) )
| ( SV62 = SY314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(470,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(471,plain,
! [SV1: $i] :
( ( ( singleton @ SV1 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(472,plain,
! [SV63: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV63 )
| ( ( set_union2 @ ( singleton @ SV2 ) @ SV63 )
= SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(473,plain,
! [SV64: $i,SV3: $i] :
( ( ~ ( disjoint @ ( singleton @ SV3 ) @ SV64 )
| ~ ( in @ SV3 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(474,plain,
! [SV65: $i,SV4: $i] :
( ( ( in @ SV4 @ SV65 )
| ( disjoint @ ( singleton @ SV4 ) @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(475,plain,
! [SV66: $i,SV5: $i] :
( ( ~ ( subset @ SV5 @ SV66 )
| ! [SY315: $i] :
( ( in @ SY315 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV66 @ ( singleton @ SY315 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(476,plain,
! [SV67: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV67 )
| ( subset @ SV6 @ ( union @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(477,plain,
! [SV68: $i,SV7: $i] :
( ( ! [SY316: $i,SY317: $i] :
( ( SV7 = SY317 )
| ( SV7 = SY316 )
| ( ( unordered_pair @ SV7 @ SV68 )
!= ( unordered_pair @ SY316 @ SY317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(478,plain,
! [SV69: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ SV69 )
| ( ( set_union2 @ SV8 @ SV69 )
= SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(479,plain,
! [SV70: $i,SV9: $i] :
( ( subset @ ( set_intersection2 @ SV9 @ SV70 ) @ SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(480,plain,
! [SV71: $i,SV10: $i] :
( ( ! [SY318: $i] :
( ~ ( subset @ SV10 @ SV71 )
| ~ ( subset @ SV10 @ SY318 )
| ( subset @ SV10 @ ( set_intersection2 @ SV71 @ SY318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(481,plain,
! [SV72: $i,SV11: $i] :
( ( ! [SY319: $i] :
( ~ ( subset @ SV11 @ SV72 )
| ~ ( subset @ SV72 @ SY319 )
| ( subset @ SV11 @ SY319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(482,plain,
! [SV73: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV73 )
| ! [SY320: $i] : ( subset @ ( set_intersection2 @ SV12 @ SY320 ) @ ( set_intersection2 @ SV73 @ SY320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(483,plain,
! [SV74: $i,SV13: $i] :
( ( ~ ( subset @ SV13 @ SV74 )
| ( ( set_intersection2 @ SV13 @ SV74 )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(484,plain,
! [SV75: $i,SV15: $i] :
( ( ~ ( subset @ SV15 @ SV75 )
| ! [SY321: $i] : ( subset @ ( set_difference @ SV15 @ SY321 ) @ ( set_difference @ SV75 @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(485,plain,
! [SV76: $i,SV16: $i] :
( ( subset @ ( set_difference @ SV16 @ SV76 ) @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(486,plain,
! [SV77: $i,SV17: $i] :
( ( ( set_union2 @ SV17 @ ( set_difference @ SV77 @ SV17 ) )
= ( set_union2 @ SV17 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(487,plain,
! [SV18: $i] :
( ( ( ~ ( subset @ SV18 @ empty_set ) )
= $true )
| ( ( SV18 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(488,plain,
! [SV78: $i,SV19: $i] :
( ( ( set_difference @ ( set_union2 @ SV19 @ SV78 ) @ SV78 )
= ( set_difference @ SV19 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(489,plain,
! [SV79: $i,SV20: $i] :
( ( ~ ( subset @ SV20 @ SV79 )
| ( SV79
= ( set_union2 @ SV20 @ ( set_difference @ SV79 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(490,plain,
! [SV80: $i,SV21: $i] :
( ( ~ ( in @ SV21 @ SV80 )
| ( ( set_union2 @ ( singleton @ SV21 ) @ SV80 )
= SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(491,plain,
! [SV81: $i,SV22: $i] :
( ( ( set_difference @ SV22 @ ( set_difference @ SV22 @ SV81 ) )
= ( set_intersection2 @ SV22 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(492,plain,
! [SV23: $i,SV82: $i] :
( ( ~ ( proper_subset @ SV82 @ SV23 )
| ~ ( subset @ SV23 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(493,plain,
! [SV24: $i,SV83: $i] :
( ( ! [SY322: $i] :
( ~ ( disjoint @ SV83 @ SY322 )
| ~ ( subset @ SV24 @ SV83 )
| ( disjoint @ SV24 @ SY322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(494,plain,
! [SV84: $i,SV26: $i] :
( ( ~ ( subset @ ( singleton @ SV26 ) @ ( singleton @ SV84 ) )
| ( SV26 = SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(495,plain,
! [SV85: $i,SV27: $i] :
( ( subset @ SV27 @ ( set_union2 @ SV27 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(496,plain,
! [SV86: $i,SV28: $i] :
( ( ! [SY323: $i] :
( ~ ( subset @ SV28 @ SV86 )
| ~ ( subset @ SY323 @ SV86 )
| ( subset @ ( set_union2 @ SV28 @ SY323 ) @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(497,plain,
! [SV87: $i,SV29: $i] :
( ( ! [SY324: $i] :
( ( singleton @ SV29 )
!= ( unordered_pair @ SV87 @ SY324 ) )
| ( SV29 = SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(498,plain,
! [SV88: $i,SV30: $i] :
( ( ~ ( in @ SV30 @ SV88 )
| ( subset @ SV30 @ ( union @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(499,plain,
! [SV89: $i,SV32: $i] :
( ( ! [SY325: $i] :
( ( ( singleton @ SV32 )
!= ( unordered_pair @ SV89 @ SY325 ) )
| ( SV89 = SY325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(500,plain,
! [SV90: $i,SV33: $i] :
( ( ~ ( in @ SV33 @ SV90 )
| ~ ( in @ SV90 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(501,plain,
! [SV91: $i,SV34: $i] :
( ( ~ ( proper_subset @ SV34 @ SV91 )
| ~ ( proper_subset @ SV91 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(502,plain,
! [SV92: $i,SV35: $i] :
( ( ( unordered_pair @ SV35 @ SV92 )
= ( unordered_pair @ SV92 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(503,plain,
! [SV93: $i,SV36: $i] :
( ( ( set_union2 @ SV36 @ SV93 )
= ( set_union2 @ SV93 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(504,plain,
! [SV94: $i,SV37: $i] :
( ( ( set_intersection2 @ SV37 @ SV94 )
= ( set_intersection2 @ SV94 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(505,plain,
! [SV95: $i,SV38: $i] :
( ( ( ordered_pair @ SV38 @ SV95 )
= ( unordered_pair @ ( unordered_pair @ SV38 @ SV95 ) @ ( singleton @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(506,plain,
! [SV96: $i,SV39: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV39 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(507,plain,
! [SV40: $i] :
( ( ( empty @ SV40 )
= $true )
| ( ( ! [SY253: $i] :
~ ( empty @ ( set_union2 @ SV40 @ SY253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(508,plain,
! [SV41: $i] :
( ( ( empty @ SV41 )
= $true )
| ( ( ! [SY254: $i] :
~ ( empty @ ( set_union2 @ SY254 @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(509,plain,
! [SV44: $i] :
( ( proper_subset @ SV44 @ SV44 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(510,plain,
! [SV97: $i,SV46: $i] :
( ( ~ ( disjoint @ SV46 @ SV97 )
| ( disjoint @ SV97 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(511,plain,
! [SV51: $i] :
( ( ( ~ ( empty @ SV51 ) )
= $true )
| ( ( SV51 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(512,plain,
! [SV52: $i,SV98: $i] :
( ( ~ ( empty @ SV98 )
| ~ ( in @ SV52 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(513,plain,
! [SV99: $i,SV53: $i] :
( ( ( SV53 = SV99 )
| ~ ( empty @ SV53 )
| ~ ( empty @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(514,plain,
! [SV54: $i] :
( ( ~ ! [SY258: $i,SY259: $i] :
( ~ ( in @ SV54 @ SY259 )
| ~ ( in @ SY258 @ SY259 )
| ( subset @ ( unordered_pair @ SV54 @ SY258 ) @ SY259 ) )
| ~ ~ ( ~ ! [SY260: $i,SY261: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY260 ) @ SY261 )
| ( in @ SV54 @ SY261 ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY262 ) @ SY263 )
| ( in @ SY262 @ SY263 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(515,plain,
! [SV55: $i] :
( ( ~ ! [SY264: $i,SY265: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY264 )
| ~ ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY265 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY265 ) )
| ~ ( ~ ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY264 )
| ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY265 ) ) ) )
| ( SY265
= ( set_difference @ SV55 @ SY264 ) ) )
| ~ ! [SY266: $i,SY267: $i] :
( ( SY267
!= ( set_difference @ SV55 @ SY266 ) )
| ~ ( ~ ! [SY268: $i] :
( ~ ( in @ SY268 @ SV55 )
| ( in @ SY268 @ SY266 )
| ( in @ SY268 @ SY267 ) )
| ~ ~ ( ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ SY267 )
| ( in @ SY269 @ SV55 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY267 )
| ~ ( in @ SX3 @ SY266 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(516,plain,
! [SV56: $i] :
( ( ~ ! [SY271: $i,SY272: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY272 )
| ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY272 )
| ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY271 ) ) )
| ~ ( ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY272 )
| ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SV56 )
| ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY271 ) ) )
| ( SY272
= ( set_union2 @ SV56 @ SY271 ) ) )
| ~ ! [SY273: $i,SY274: $i] :
( ( SY274
!= ( set_union2 @ SV56 @ SY273 ) )
| ~ ( ~ ! [SY275: $i] :
( ~ ( in @ SY275 @ SY274 )
| ( in @ SY275 @ SV56 )
| ( in @ SY275 @ SY273 ) )
| ~ ~ ( ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SV56 )
| ( in @ SY276 @ SY274 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY273 )
| ( in @ SX3 @ SY274 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(517,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK24_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[446]) ).
thf(518,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[446]) ).
thf(519,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(520,plain,
( ( ~ ( ~ ( in @ sK1_A @ sK3_SY197 )
| ~ ( in @ sK2_SY194 @ sK4_SY199 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(521,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(522,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(523,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[449]) ).
thf(524,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[449]) ).
thf(525,plain,
! [SV57: $i] :
( ( ~ ! [SY278: $i,SY279: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SV57 )
| ~ ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY278 )
| ~ ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY279 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY279 ) )
| ~ ( ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY278 )
| ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY279 ) ) ) )
| ( SY279
= ( set_intersection2 @ SV57 @ SY278 ) ) )
| ~ ! [SY280: $i,SY281: $i] :
( ( SY281
!= ( set_intersection2 @ SV57 @ SY280 ) )
| ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ SV57 )
| ~ ( in @ SY282 @ SY280 )
| ( in @ SY282 @ SY281 ) )
| ~ ~ ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SY281 )
| ( in @ SY283 @ SV57 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY281 )
| ( in @ SX3 @ SY280 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(526,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK22_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(527,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(528,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(529,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(530,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(531,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(532,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(533,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(534,plain,
! [SV58: $i] :
( ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( ~ ( ! [SY287: $i,SY288: $i] :
( ~ ( in @ SY287 @ SV58 )
| ~ ( in @ SY288 @ SY285 )
| ( ( sK16_D @ SY286 @ SY285 @ SV58 )
!= ( ordered_pair @ SY287 @ SY288 ) ) )
| ~ ( in @ ( sK16_D @ SY286 @ SY285 @ SV58 ) @ SY286 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SY286 @ SY285 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SY286 @ SY285 @ SV58 ) @ SY285 ) )
| ( ( sK16_D @ SY286 @ SY285 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SY286 @ SY285 @ SV58 ) @ ( sK18_SY207 @ SY286 @ SY285 @ SV58 ) ) ) )
| ( in @ ( sK16_D @ SY286 @ SY285 @ SV58 ) @ SY286 ) ) )
| ( SY286
= ( cartesian_product2 @ SV58 @ SY285 ) ) )
| ~ ! [SY289: $i,SY290: $i] :
( ( SY290
!= ( cartesian_product2 @ SV58 @ SY289 ) )
| ~ ( ~ ! [SY291: $i] :
( ! [SY292: $i,SY293: $i] :
( ~ ( in @ SY292 @ SV58 )
| ~ ( in @ SY293 @ SY289 )
| ( SY291
!= ( ordered_pair @ SY292 @ SY293 ) ) )
| ( in @ SY291 @ SY290 ) )
| ~ ! [SY294: $i] :
( ~ ( in @ SY294 @ SY290 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY294 @ SY290 @ SY289 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SY294 @ SY290 @ SY289 @ SV58 ) @ SY289 ) )
| ( SY294
!= ( ordered_pair @ ( sK14_E @ SY294 @ SY290 @ SY289 @ SV58 ) @ ( sK15_SY202 @ SY294 @ SY290 @ SY289 @ SV58 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(535,plain,
! [SV100: $i,SV59: $i] :
( ( ~ ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( in @ SV59 @ SY326 )
| ~ ( in @ SV100 @ SY327 )
| ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY326 @ SY327 ) ) )
| ~ ~ ( ~ ! [SY328: $i] :
( ! [SY329: $i] :
~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY328 @ SY329 ) )
| ( in @ SV59 @ SY328 ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY330 @ SY331 ) )
| ( in @ SV100 @ SY331 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(536,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK23_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK23_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(537,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(538,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(539,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[458]) ).
thf(540,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(541,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(542,plain,
! [SV60: $i] :
( ( ~ ! [SY302: $i,SY303: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SY303 @ SY302 @ SV60 ) @ SY303 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
!= SV60 ) )
| ~ ( ~ ( in @ ( sK20_D @ SY303 @ SY302 @ SV60 ) @ SY303 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
!= SY302 ) ) )
| ~ ( ( in @ ( sK20_D @ SY303 @ SY302 @ SV60 ) @ SY303 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
= SV60 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
= SY302 ) ) )
| ( SY303
= ( unordered_pair @ SV60 @ SY302 ) ) )
| ~ ! [SY304: $i,SY305: $i] :
( ( SY305
!= ( unordered_pair @ SV60 @ SY304 ) )
| ~ ( ~ ! [SY306: $i] :
( ~ ( in @ SY306 @ SY305 )
| ( SY306 = SV60 )
| ( SY306 = SY304 ) )
| ~ ~ ( ~ ! [SY307: $i] :
( ( SY307 != SV60 )
| ( in @ SY307 @ SY305 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY304 )
| ( in @ SX3 @ SY305 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(543,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(544,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(545,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(546,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[462]) ).
thf(547,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(548,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(549,plain,
! [SV101: $i,SV61: $i] :
( ( ~ ( ~ ! [SY332: $i] :
( ! [SY333: $i] :
( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SY332 @ SY333 ) )
| ( SV61 = SY332 ) )
| ~ ! [SY334: $i,SY335: $i] :
( ( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SY334 @ SY335 ) )
| ( SV101 = SY335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(550,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(551,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(552,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[466]) ).
thf(553,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[466]) ).
thf(554,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(555,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(556,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY201 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK11_SY201 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(557,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK9_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(558,plain,
! [SV62: $i,SV102: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
| ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 ) )
| ~ ( ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
| ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 ) ) )
| ( SV62 = SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(559,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(560,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(561,plain,
! [SV63: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV63 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV2 ) @ SV63 )
= SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(562,plain,
! [SV64: $i,SV3: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV3 ) @ SV64 ) )
= $true )
| ( ( ~ ( in @ SV3 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(563,plain,
! [SV65: $i,SV4: $i] :
( ( ( in @ SV4 @ SV65 )
= $true )
| ( ( disjoint @ ( singleton @ SV4 ) @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(564,plain,
! [SV66: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ SV66 ) )
= $true )
| ( ( ! [SY315: $i] :
( ( in @ SY315 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV66 @ ( singleton @ SY315 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(565,plain,
! [SV67: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV67 ) )
= $true )
| ( ( subset @ SV6 @ ( union @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(566,plain,
! [SV68: $i,SV103: $i,SV7: $i] :
( ( ! [SY336: $i] :
( ( SV7 = SY336 )
| ( SV7 = SV103 )
| ( ( unordered_pair @ SV7 @ SV68 )
!= ( unordered_pair @ SV103 @ SY336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(567,plain,
! [SV69: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV69 ) )
= $true )
| ( ( ( set_union2 @ SV8 @ SV69 )
= SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(568,plain,
! [SV104: $i,SV71: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV71 )
| ~ ( subset @ SV10 @ SV104 )
| ( subset @ SV10 @ ( set_intersection2 @ SV71 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(569,plain,
! [SV105: $i,SV72: $i,SV11: $i] :
( ( ~ ( subset @ SV11 @ SV72 )
| ~ ( subset @ SV72 @ SV105 )
| ( subset @ SV11 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(570,plain,
! [SV73: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV73 ) )
= $true )
| ( ( ! [SY320: $i] : ( subset @ ( set_intersection2 @ SV12 @ SY320 ) @ ( set_intersection2 @ SV73 @ SY320 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(571,plain,
! [SV74: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV74 ) )
= $true )
| ( ( ( set_intersection2 @ SV13 @ SV74 )
= SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(572,plain,
! [SV75: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV75 ) )
= $true )
| ( ( ! [SY321: $i] : ( subset @ ( set_difference @ SV15 @ SY321 ) @ ( set_difference @ SV75 @ SY321 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(573,plain,
! [SV18: $i] :
( ( ( subset @ SV18 @ empty_set )
= $false )
| ( ( SV18 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(574,plain,
! [SV79: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV79 ) )
= $true )
| ( ( SV79
= ( set_union2 @ SV20 @ ( set_difference @ SV79 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(575,plain,
! [SV80: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV80 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV21 ) @ SV80 )
= SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(576,plain,
! [SV23: $i,SV82: $i] :
( ( ( ~ ( proper_subset @ SV82 @ SV23 ) )
= $true )
| ( ( ~ ( subset @ SV23 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(577,plain,
! [SV24: $i,SV106: $i,SV83: $i] :
( ( ~ ( disjoint @ SV83 @ SV106 )
| ~ ( subset @ SV24 @ SV83 )
| ( disjoint @ SV24 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(578,plain,
! [SV84: $i,SV26: $i] :
( ( ( ~ ( subset @ ( singleton @ SV26 ) @ ( singleton @ SV84 ) ) )
= $true )
| ( ( SV26 = SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(579,plain,
! [SV107: $i,SV86: $i,SV28: $i] :
( ( ~ ( subset @ SV28 @ SV86 )
| ~ ( subset @ SV107 @ SV86 )
| ( subset @ ( set_union2 @ SV28 @ SV107 ) @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(580,plain,
! [SV87: $i,SV29: $i] :
( ( ( ! [SY324: $i] :
( ( singleton @ SV29 )
!= ( unordered_pair @ SV87 @ SY324 ) ) )
= $true )
| ( ( SV29 = SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(581,plain,
! [SV88: $i,SV30: $i] :
( ( ( ~ ( in @ SV30 @ SV88 ) )
= $true )
| ( ( subset @ SV30 @ ( union @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(582,plain,
! [SV108: $i,SV89: $i,SV32: $i] :
( ( ( ( singleton @ SV32 )
!= ( unordered_pair @ SV89 @ SV108 ) )
| ( SV89 = SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(583,plain,
! [SV90: $i,SV33: $i] :
( ( ( ~ ( in @ SV33 @ SV90 ) )
= $true )
| ( ( ~ ( in @ SV90 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(584,plain,
! [SV91: $i,SV34: $i] :
( ( ( ~ ( proper_subset @ SV34 @ SV91 ) )
= $true )
| ( ( ~ ( proper_subset @ SV91 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(585,plain,
! [SV96: $i,SV39: $i] :
( ( empty @ ( ordered_pair @ SV39 @ SV96 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(586,plain,
! [SV109: $i,SV40: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV40 @ SV109 ) ) )
= $true )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(587,plain,
! [SV41: $i,SV110: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV110 @ SV41 ) ) )
= $true )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(588,plain,
! [SV97: $i,SV46: $i] :
( ( ( ~ ( disjoint @ SV46 @ SV97 ) )
= $true )
| ( ( disjoint @ SV97 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(589,plain,
! [SV51: $i] :
( ( ( empty @ SV51 )
= $false )
| ( ( SV51 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(590,plain,
! [SV52: $i,SV98: $i] :
( ( ( ~ ( empty @ SV98 ) )
= $true )
| ( ( ~ ( in @ SV52 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(591,plain,
! [SV99: $i,SV53: $i] :
( ( ( ( SV53 = SV99 )
| ~ ( empty @ SV53 ) )
= $true )
| ( ( ~ ( empty @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(592,plain,
! [SV54: $i] :
( ( ~ ! [SY258: $i,SY259: $i] :
( ~ ( in @ SV54 @ SY259 )
| ~ ( in @ SY258 @ SY259 )
| ( subset @ ( unordered_pair @ SV54 @ SY258 ) @ SY259 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(593,plain,
! [SV54: $i] :
( ( ~ ~ ( ~ ! [SY260: $i,SY261: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY260 ) @ SY261 )
| ( in @ SV54 @ SY261 ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY262 ) @ SY263 )
| ( in @ SY262 @ SY263 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(594,plain,
! [SV55: $i] :
( ( ~ ! [SY264: $i,SY265: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY264 )
| ~ ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY265 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY265 ) )
| ~ ( ~ ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY264 )
| ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY265 ) ) ) )
| ( SY265
= ( set_difference @ SV55 @ SY264 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(595,plain,
! [SV55: $i] :
( ( ~ ! [SY266: $i,SY267: $i] :
( ( SY267
!= ( set_difference @ SV55 @ SY266 ) )
| ~ ( ~ ! [SY268: $i] :
( ~ ( in @ SY268 @ SV55 )
| ( in @ SY268 @ SY266 )
| ( in @ SY268 @ SY267 ) )
| ~ ~ ( ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ SY267 )
| ( in @ SY269 @ SV55 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY267 )
| ~ ( in @ SX3 @ SY266 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[515]) ).
thf(596,plain,
! [SV56: $i] :
( ( ~ ! [SY271: $i,SY272: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY272 )
| ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY272 )
| ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY271 ) ) )
| ~ ( ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY272 )
| ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SV56 )
| ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY271 ) ) )
| ( SY272
= ( set_union2 @ SV56 @ SY271 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(597,plain,
! [SV56: $i] :
( ( ~ ! [SY273: $i,SY274: $i] :
( ( SY274
!= ( set_union2 @ SV56 @ SY273 ) )
| ~ ( ~ ! [SY275: $i] :
( ~ ( in @ SY275 @ SY274 )
| ( in @ SY275 @ SV56 )
| ( in @ SY275 @ SY273 ) )
| ~ ~ ( ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SV56 )
| ( in @ SY276 @ SY274 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY273 )
| ( in @ SX3 @ SY274 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(598,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK24_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(599,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(600,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(601,plain,
( ( ~ ( in @ sK1_A @ sK3_SY197 )
| ~ ( in @ sK2_SY194 @ sK4_SY199 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(602,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(603,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(604,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(605,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(606,plain,
! [SV57: $i] :
( ( ~ ! [SY278: $i,SY279: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SV57 )
| ~ ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY278 )
| ~ ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY279 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY279 ) )
| ~ ( ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY278 )
| ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY279 ) ) ) )
| ( SY279
= ( set_intersection2 @ SV57 @ SY278 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(607,plain,
! [SV57: $i] :
( ( ~ ! [SY280: $i,SY281: $i] :
( ( SY281
!= ( set_intersection2 @ SV57 @ SY280 ) )
| ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ SV57 )
| ~ ( in @ SY282 @ SY280 )
| ( in @ SY282 @ SY281 ) )
| ~ ~ ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SY281 )
| ( in @ SY283 @ SV57 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY281 )
| ( in @ SX3 @ SY280 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[525]) ).
thf(608,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK22_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(609,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(610,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(611,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(612,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(613,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(614,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(615,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(616,plain,
! [SV58: $i] :
( ( ~ ! [SY285: $i,SY286: $i] :
( ~ ( ~ ( ! [SY287: $i,SY288: $i] :
( ~ ( in @ SY287 @ SV58 )
| ~ ( in @ SY288 @ SY285 )
| ( ( sK16_D @ SY286 @ SY285 @ SV58 )
!= ( ordered_pair @ SY287 @ SY288 ) ) )
| ~ ( in @ ( sK16_D @ SY286 @ SY285 @ SV58 ) @ SY286 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SY286 @ SY285 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SY286 @ SY285 @ SV58 ) @ SY285 ) )
| ( ( sK16_D @ SY286 @ SY285 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SY286 @ SY285 @ SV58 ) @ ( sK18_SY207 @ SY286 @ SY285 @ SV58 ) ) ) )
| ( in @ ( sK16_D @ SY286 @ SY285 @ SV58 ) @ SY286 ) ) )
| ( SY286
= ( cartesian_product2 @ SV58 @ SY285 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(617,plain,
! [SV58: $i] :
( ( ~ ! [SY289: $i,SY290: $i] :
( ( SY290
!= ( cartesian_product2 @ SV58 @ SY289 ) )
| ~ ( ~ ! [SY291: $i] :
( ! [SY292: $i,SY293: $i] :
( ~ ( in @ SY292 @ SV58 )
| ~ ( in @ SY293 @ SY289 )
| ( SY291
!= ( ordered_pair @ SY292 @ SY293 ) ) )
| ( in @ SY291 @ SY290 ) )
| ~ ! [SY294: $i] :
( ~ ( in @ SY294 @ SY290 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY294 @ SY290 @ SY289 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SY294 @ SY290 @ SY289 @ SV58 ) @ SY289 ) )
| ( SY294
!= ( ordered_pair @ ( sK14_E @ SY294 @ SY290 @ SY289 @ SV58 ) @ ( sK15_SY202 @ SY294 @ SY290 @ SY289 @ SV58 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(618,plain,
! [SV100: $i,SV59: $i] :
( ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( in @ SV59 @ SY326 )
| ~ ( in @ SV100 @ SY327 )
| ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY326 @ SY327 ) ) )
| ~ ~ ( ~ ! [SY328: $i] :
( ! [SY329: $i] :
~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY328 @ SY329 ) )
| ( in @ SV59 @ SY328 ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY330 @ SY331 ) )
| ( in @ SV100 @ SY331 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(619,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK23_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK23_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(620,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(621,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(622,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(623,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(624,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(625,plain,
! [SV60: $i] :
( ( ~ ! [SY302: $i,SY303: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SY303 @ SY302 @ SV60 ) @ SY303 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
!= SV60 ) )
| ~ ( ~ ( in @ ( sK20_D @ SY303 @ SY302 @ SV60 ) @ SY303 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
!= SY302 ) ) )
| ~ ( ( in @ ( sK20_D @ SY303 @ SY302 @ SV60 ) @ SY303 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
= SV60 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
= SY302 ) ) )
| ( SY303
= ( unordered_pair @ SV60 @ SY302 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(626,plain,
! [SV60: $i] :
( ( ~ ! [SY304: $i,SY305: $i] :
( ( SY305
!= ( unordered_pair @ SV60 @ SY304 ) )
| ~ ( ~ ! [SY306: $i] :
( ~ ( in @ SY306 @ SY305 )
| ( SY306 = SV60 )
| ( SY306 = SY304 ) )
| ~ ~ ( ~ ! [SY307: $i] :
( ( SY307 != SV60 )
| ( in @ SY307 @ SY305 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY304 )
| ( in @ SX3 @ SY305 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(627,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(628,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(629,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(630,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(631,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(632,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(633,plain,
! [SV101: $i,SV61: $i] :
( ( ~ ! [SY332: $i] :
( ! [SY333: $i] :
( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SY332 @ SY333 ) )
| ( SV61 = SY332 ) )
| ~ ! [SY334: $i,SY335: $i] :
( ( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SY334 @ SY335 ) )
| ( SV101 = SY335 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(634,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(635,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(636,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(637,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(638,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(639,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(640,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY201 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK11_SY201 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(641,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK9_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(642,plain,
! [SV62: $i,SV102: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
| ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 ) )
| ~ ( ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
| ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 ) ) ) )
= $true )
| ( ( SV62 = SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(643,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(644,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(645,plain,
! [SV63: $i,SV2: $i] :
( ( ( in @ SV2 @ SV63 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV2 ) @ SV63 )
= SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(646,plain,
! [SV64: $i,SV3: $i] :
( ( ( disjoint @ ( singleton @ SV3 ) @ SV64 )
= $false )
| ( ( ~ ( in @ SV3 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(647,plain,
! [SV66: $i,SV5: $i] :
( ( ( subset @ SV5 @ SV66 )
= $false )
| ( ( ! [SY315: $i] :
( ( in @ SY315 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV66 @ ( singleton @ SY315 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(648,plain,
! [SV67: $i,SV6: $i] :
( ( ( in @ SV6 @ SV67 )
= $false )
| ( ( subset @ SV6 @ ( union @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(649,plain,
! [SV68: $i,SV103: $i,SV111: $i,SV7: $i] :
( ( ( SV7 = SV111 )
| ( SV7 = SV103 )
| ( ( unordered_pair @ SV7 @ SV68 )
!= ( unordered_pair @ SV103 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(650,plain,
! [SV69: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV69 )
= $false )
| ( ( ( set_union2 @ SV8 @ SV69 )
= SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(651,plain,
! [SV104: $i,SV71: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV71 )
| ~ ( subset @ SV10 @ SV104 ) )
= $true )
| ( ( subset @ SV10 @ ( set_intersection2 @ SV71 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(652,plain,
! [SV105: $i,SV72: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV72 )
| ~ ( subset @ SV72 @ SV105 ) )
= $true )
| ( ( subset @ SV11 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(653,plain,
! [SV73: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV73 )
= $false )
| ( ( ! [SY320: $i] : ( subset @ ( set_intersection2 @ SV12 @ SY320 ) @ ( set_intersection2 @ SV73 @ SY320 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(654,plain,
! [SV74: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV74 )
= $false )
| ( ( ( set_intersection2 @ SV13 @ SV74 )
= SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(655,plain,
! [SV75: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV75 )
= $false )
| ( ( ! [SY321: $i] : ( subset @ ( set_difference @ SV15 @ SY321 ) @ ( set_difference @ SV75 @ SY321 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(656,plain,
! [SV79: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV79 )
= $false )
| ( ( SV79
= ( set_union2 @ SV20 @ ( set_difference @ SV79 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(657,plain,
! [SV80: $i,SV21: $i] :
( ( ( in @ SV21 @ SV80 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV21 ) @ SV80 )
= SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(658,plain,
! [SV23: $i,SV82: $i] :
( ( ( proper_subset @ SV82 @ SV23 )
= $false )
| ( ( ~ ( subset @ SV23 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(659,plain,
! [SV24: $i,SV106: $i,SV83: $i] :
( ( ( ~ ( disjoint @ SV83 @ SV106 )
| ~ ( subset @ SV24 @ SV83 ) )
= $true )
| ( ( disjoint @ SV24 @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(660,plain,
! [SV84: $i,SV26: $i] :
( ( ( subset @ ( singleton @ SV26 ) @ ( singleton @ SV84 ) )
= $false )
| ( ( SV26 = SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(661,plain,
! [SV107: $i,SV86: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV86 )
| ~ ( subset @ SV107 @ SV86 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV28 @ SV107 ) @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(662,plain,
! [SV112: $i,SV87: $i,SV29: $i] :
( ( ( ( ( singleton @ SV29 )
!= ( unordered_pair @ SV87 @ SV112 ) ) )
= $true )
| ( ( SV29 = SV87 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(663,plain,
! [SV88: $i,SV30: $i] :
( ( ( in @ SV30 @ SV88 )
= $false )
| ( ( subset @ SV30 @ ( union @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(664,plain,
! [SV108: $i,SV89: $i,SV32: $i] :
( ( ( ( ( singleton @ SV32 )
!= ( unordered_pair @ SV89 @ SV108 ) ) )
= $true )
| ( ( SV89 = SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(665,plain,
! [SV90: $i,SV33: $i] :
( ( ( in @ SV33 @ SV90 )
= $false )
| ( ( ~ ( in @ SV90 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(666,plain,
! [SV91: $i,SV34: $i] :
( ( ( proper_subset @ SV34 @ SV91 )
= $false )
| ( ( ~ ( proper_subset @ SV91 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(667,plain,
! [SV109: $i,SV40: $i] :
( ( ( empty @ ( set_union2 @ SV40 @ SV109 ) )
= $false )
| ( ( empty @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(668,plain,
! [SV41: $i,SV110: $i] :
( ( ( empty @ ( set_union2 @ SV110 @ SV41 ) )
= $false )
| ( ( empty @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(669,plain,
! [SV97: $i,SV46: $i] :
( ( ( disjoint @ SV46 @ SV97 )
= $false )
| ( ( disjoint @ SV97 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(670,plain,
! [SV52: $i,SV98: $i] :
( ( ( empty @ SV98 )
= $false )
| ( ( ~ ( in @ SV52 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(671,plain,
! [SV99: $i,SV53: $i] :
( ( ( SV53 = SV99 )
= $true )
| ( ( ~ ( empty @ SV53 ) )
= $true )
| ( ( ~ ( empty @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(672,plain,
! [SV54: $i] :
( ( ! [SY258: $i,SY259: $i] :
( ~ ( in @ SV54 @ SY259 )
| ~ ( in @ SY258 @ SY259 )
| ( subset @ ( unordered_pair @ SV54 @ SY258 ) @ SY259 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(673,plain,
! [SV54: $i] :
( ( ~ ( ~ ! [SY260: $i,SY261: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY260 ) @ SY261 )
| ( in @ SV54 @ SY261 ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY262 ) @ SY263 )
| ( in @ SY262 @ SY263 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(674,plain,
! [SV55: $i] :
( ( ! [SY264: $i,SY265: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY264 )
| ~ ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY265 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY265 ) )
| ~ ( ~ ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY264 )
| ( in @ ( sK8_D @ SY265 @ SY264 @ SV55 ) @ SY265 ) ) ) )
| ( SY265
= ( set_difference @ SV55 @ SY264 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[594]) ).
thf(675,plain,
! [SV55: $i] :
( ( ! [SY266: $i,SY267: $i] :
( ( SY267
!= ( set_difference @ SV55 @ SY266 ) )
| ~ ( ~ ! [SY268: $i] :
( ~ ( in @ SY268 @ SV55 )
| ( in @ SY268 @ SY266 )
| ( in @ SY268 @ SY267 ) )
| ~ ~ ( ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ SY267 )
| ( in @ SY269 @ SV55 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY267 )
| ~ ( in @ SX3 @ SY266 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(676,plain,
! [SV56: $i] :
( ( ! [SY271: $i,SY272: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY272 )
| ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY272 )
| ~ ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY271 ) ) )
| ~ ( ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY272 )
| ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SV56 )
| ( in @ ( sK19_D @ SY272 @ SY271 @ SV56 ) @ SY271 ) ) )
| ( SY272
= ( set_union2 @ SV56 @ SY271 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(677,plain,
! [SV56: $i] :
( ( ! [SY273: $i,SY274: $i] :
( ( SY274
!= ( set_union2 @ SV56 @ SY273 ) )
| ~ ( ~ ! [SY275: $i] :
( ~ ( in @ SY275 @ SY274 )
| ( in @ SY275 @ SV56 )
| ( in @ SY275 @ SY273 ) )
| ~ ~ ( ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SV56 )
| ( in @ SY276 @ SY274 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY273 )
| ( in @ SX3 @ SY274 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(678,plain,
! [SV113: $i] :
( ( ! [SY337: $i] :
( ( disjoint @ SV113 @ SY337 )
| ( in @ ( sK24_C @ SY337 @ SV113 ) @ ( set_intersection2 @ SV113 @ SY337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(679,plain,
! [SV114: $i] :
( ( ! [SY338: $i] :
( ! [SY339: $i] :
~ ( in @ SY339 @ ( set_intersection2 @ SV114 @ SY338 ) )
| ~ ( disjoint @ SV114 @ SY338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(680,plain,
( ( ( ~ ( in @ sK1_A @ sK3_SY197 ) )
= $true )
| ( ( ~ ( in @ sK2_SY194 @ sK4_SY199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(681,plain,
! [SV115: $i] :
( ( ! [SY340: $i] :
( ( ( set_difference @ SV115 @ SY340 )
!= empty_set )
| ( subset @ SV115 @ SY340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(682,plain,
! [SV116: $i] :
( ( ! [SY341: $i] :
( ~ ( subset @ SV116 @ SY341 )
| ( ( set_difference @ SV116 @ SY341 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(683,plain,
! [SV117: $i] :
( ( ! [SY342: $i] :
( ( ( set_intersection2 @ SV117 @ SY342 )
!= empty_set )
| ( disjoint @ SV117 @ SY342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(684,plain,
! [SV118: $i] :
( ( ! [SY343: $i] :
( ~ ( disjoint @ SV118 @ SY343 )
| ( ( set_intersection2 @ SV118 @ SY343 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(685,plain,
! [SV57: $i] :
( ( ! [SY278: $i,SY279: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SV57 )
| ~ ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY278 )
| ~ ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY279 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY279 ) )
| ~ ( ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY278 )
| ( in @ ( sK12_D @ SY279 @ SY278 @ SV57 ) @ SY279 ) ) ) )
| ( SY279
= ( set_intersection2 @ SV57 @ SY278 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(686,plain,
! [SV57: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ( SY281
!= ( set_intersection2 @ SV57 @ SY280 ) )
| ~ ( ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ SV57 )
| ~ ( in @ SY282 @ SY280 )
| ( in @ SY282 @ SY281 ) )
| ~ ~ ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SY281 )
| ( in @ SY283 @ SV57 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY281 )
| ( in @ SX3 @ SY280 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(687,plain,
! [SV119: $i] :
( ( ( in @ ( sK22_B @ SV119 ) @ SV119 )
| ( SV119 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(688,plain,
! [SV120: $i] :
( ( ( SV120 != empty_set )
| ! [SY344: $i] :
~ ( in @ SY344 @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(689,plain,
! [SV121: $i] :
( ( ! [SY345: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_C @ SY345 @ SV121 ) @ SY345 )
| ~ ( subset @ ( sK21_C @ SY345 @ SV121 ) @ SV121 ) )
| ~ ( ( in @ ( sK21_C @ SY345 @ SV121 ) @ SY345 )
| ( subset @ ( sK21_C @ SY345 @ SV121 ) @ SV121 ) ) )
| ( SY345
= ( powerset @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(690,plain,
! [SV122: $i] :
( ( ! [SY346: $i] :
( ( SY346
!= ( powerset @ SV122 ) )
| ~ ( ~ ! [SY347: $i] :
( ~ ( in @ SY347 @ SY346 )
| ( subset @ SY347 @ SV122 ) )
| ~ ! [SY348: $i] :
( ~ ( subset @ SY348 @ SV122 )
| ( in @ SY348 @ SY346 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(691,plain,
! [SV123: $i] :
( ( ! [SY349: $i] :
( ( ( set_difference @ SV123 @ SY349 )
!= empty_set )
| ( subset @ SV123 @ SY349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(692,plain,
! [SV124: $i] :
( ( ! [SY350: $i] :
( ~ ( subset @ SV124 @ SY350 )
| ( ( set_difference @ SV124 @ SY350 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(693,plain,
! [SV125: $i] :
( ( ! [SY351: $i] :
( ( ( set_difference @ SV125 @ SY351 )
!= SV125 )
| ( disjoint @ SV125 @ SY351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(694,plain,
! [SV126: $i] :
( ( ! [SY352: $i] :
( ~ ( disjoint @ SV126 @ SY352 )
| ( ( set_difference @ SV126 @ SY352 )
= SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(695,plain,
! [SV58: $i] :
( ( ! [SY285: $i,SY286: $i] :
( ~ ( ~ ( ! [SY287: $i,SY288: $i] :
( ~ ( in @ SY287 @ SV58 )
| ~ ( in @ SY288 @ SY285 )
| ( ( sK16_D @ SY286 @ SY285 @ SV58 )
!= ( ordered_pair @ SY287 @ SY288 ) ) )
| ~ ( in @ ( sK16_D @ SY286 @ SY285 @ SV58 ) @ SY286 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SY286 @ SY285 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SY286 @ SY285 @ SV58 ) @ SY285 ) )
| ( ( sK16_D @ SY286 @ SY285 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SY286 @ SY285 @ SV58 ) @ ( sK18_SY207 @ SY286 @ SY285 @ SV58 ) ) ) )
| ( in @ ( sK16_D @ SY286 @ SY285 @ SV58 ) @ SY286 ) ) )
| ( SY286
= ( cartesian_product2 @ SV58 @ SY285 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[616]) ).
thf(696,plain,
! [SV58: $i] :
( ( ! [SY289: $i,SY290: $i] :
( ( SY290
!= ( cartesian_product2 @ SV58 @ SY289 ) )
| ~ ( ~ ! [SY291: $i] :
( ! [SY292: $i,SY293: $i] :
( ~ ( in @ SY292 @ SV58 )
| ~ ( in @ SY293 @ SY289 )
| ( SY291
!= ( ordered_pair @ SY292 @ SY293 ) ) )
| ( in @ SY291 @ SY290 ) )
| ~ ! [SY294: $i] :
( ~ ( in @ SY294 @ SY290 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY294 @ SY290 @ SY289 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SY294 @ SY290 @ SY289 @ SV58 ) @ SY289 ) )
| ( SY294
!= ( ordered_pair @ ( sK14_E @ SY294 @ SY290 @ SY289 @ SV58 ) @ ( sK15_SY202 @ SY294 @ SY290 @ SY289 @ SV58 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[617]) ).
thf(697,plain,
! [SV100: $i,SV59: $i] :
( ( ~ ! [SY326: $i,SY327: $i] :
( ~ ( in @ SV59 @ SY326 )
| ~ ( in @ SV100 @ SY327 )
| ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY326 @ SY327 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(698,plain,
! [SV100: $i,SV59: $i] :
( ( ~ ~ ( ~ ! [SY328: $i] :
( ! [SY329: $i] :
~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY328 @ SY329 ) )
| ( in @ SV59 @ SY328 ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY330 @ SY331 ) )
| ( in @ SV100 @ SY331 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[618]) ).
thf(699,plain,
! [SV127: $i] :
( ( ! [SY353: $i] :
( ~ ( ~ ( ( ( sK23_C @ SY353 @ SV127 )
!= SV127 )
| ~ ( in @ ( sK23_C @ SY353 @ SV127 ) @ SY353 ) )
| ~ ( ( ( sK23_C @ SY353 @ SV127 )
= SV127 )
| ( in @ ( sK23_C @ SY353 @ SV127 ) @ SY353 ) ) )
| ( SY353
= ( singleton @ SV127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(700,plain,
! [SV128: $i] :
( ( ! [SY354: $i] :
( ( SY354
!= ( singleton @ SV128 ) )
| ~ ( ~ ! [SY355: $i] :
( ( SY355 != SV128 )
| ( in @ SY355 @ SY354 ) )
| ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ SY354 )
| ( SY356 = SV128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(701,plain,
! [SV129: $i] :
( ( ! [SY357: $i] :
( ~ ( ~ ( in @ ( sK13_C @ SY357 @ SV129 ) @ SV129 )
| ~ ~ ( in @ ( sK13_C @ SY357 @ SV129 ) @ SY357 ) )
| ( subset @ SV129 @ SY357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(702,plain,
! [SV130: $i] :
( ( ! [SY358: $i] :
( ~ ( subset @ SV130 @ SY358 )
| ! [SY359: $i] :
( ~ ( in @ SY359 @ SV130 )
| ( in @ SY359 @ SY358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(703,plain,
! [SV131: $i] :
( ( ! [SY360: $i] :
( ( disjoint @ SV131 @ SY360 )
| ~ ( ~ ( in @ ( sK25_C @ SY360 @ SV131 ) @ SV131 )
| ~ ( in @ ( sK25_C @ SY360 @ SV131 ) @ SY360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(704,plain,
! [SV132: $i] :
( ( ! [SY361: $i] :
( ! [SY362: $i] :
( ~ ( in @ SY362 @ SV132 )
| ~ ( in @ SY362 @ SY361 ) )
| ~ ( disjoint @ SV132 @ SY361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(705,plain,
! [SV60: $i] :
( ( ! [SY302: $i,SY303: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SY303 @ SY302 @ SV60 ) @ SY303 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
!= SV60 ) )
| ~ ( ~ ( in @ ( sK20_D @ SY303 @ SY302 @ SV60 ) @ SY303 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
!= SY302 ) ) )
| ~ ( ( in @ ( sK20_D @ SY303 @ SY302 @ SV60 ) @ SY303 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
= SV60 )
| ( ( sK20_D @ SY303 @ SY302 @ SV60 )
= SY302 ) ) )
| ( SY303
= ( unordered_pair @ SV60 @ SY302 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(706,plain,
! [SV60: $i] :
( ( ! [SY304: $i,SY305: $i] :
( ( SY305
!= ( unordered_pair @ SV60 @ SY304 ) )
| ~ ( ~ ! [SY306: $i] :
( ~ ( in @ SY306 @ SY305 )
| ( SY306 = SV60 )
| ( SY306 = SY304 ) )
| ~ ~ ( ~ ! [SY307: $i] :
( ( SY307 != SV60 )
| ( in @ SY307 @ SY305 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY304 )
| ( in @ SX3 @ SY305 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(707,plain,
! [SV133: $i] :
( ( ! [SY363: $i] :
( ~ ( subset @ SV133 @ ( singleton @ SY363 ) )
| ( SV133 = empty_set )
| ( SV133
= ( singleton @ SY363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(708,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(709,plain,
! [SV134: $i] :
( ( ! [SY364: $i] :
( ~ ( in @ SV134 @ SY364 )
| ( subset @ ( singleton @ SV134 ) @ SY364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(710,plain,
! [SV135: $i] :
( ( ! [SY365: $i] :
( ~ ( subset @ ( singleton @ SV135 ) @ SY365 )
| ( in @ SV135 @ SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(711,plain,
! [SV136: $i] :
( ( ! [SY366: $i] :
( ~ ( subset @ SV136 @ ( singleton @ SY366 ) )
| ( SV136 = empty_set )
| ( SV136
= ( singleton @ SY366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(712,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(713,plain,
! [SV101: $i,SV61: $i] :
( ( ~ ! [SY332: $i] :
( ! [SY333: $i] :
( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SY332 @ SY333 ) )
| ( SV61 = SY332 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(714,plain,
! [SV101: $i,SV61: $i] :
( ( ~ ! [SY334: $i,SY335: $i] :
( ( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SY334 @ SY335 ) )
| ( SV101 = SY335 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(715,plain,
! [SV137: $i] :
( ( ! [SY367: $i] :
( ~ ( subset @ SV137 @ SY367 )
| ~ ( subset @ SY367 @ SV137 )
| ( SV137 = SY367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(716,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(717,plain,
! [SV138: $i] :
( ( ! [SY368: $i] :
( ( SV138 = SY368 )
| ~ ( subset @ SV138 @ SY368 )
| ( proper_subset @ SV138 @ SY368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(718,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(719,plain,
! [SV139: $i] :
( ( ! [SY369: $i] :
( ~ ( in @ SV139 @ SY369 )
| ( subset @ ( singleton @ SV139 ) @ SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(720,plain,
! [SV140: $i] :
( ( ! [SY370: $i] :
( ~ ( subset @ ( singleton @ SV140 ) @ SY370 )
| ( in @ SV140 @ SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(721,plain,
! [SV141: $i] :
( ( ! [SY371: $i] :
( ~ ( ~ ( ! [SY372: $i] :
( ~ ( in @ ( sK10_C @ SY371 @ SV141 ) @ SY372 )
| ~ ( in @ SY372 @ SV141 ) )
| ~ ( in @ ( sK10_C @ SY371 @ SV141 ) @ SY371 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SY371 @ SV141 ) @ ( sK11_SY201 @ SY371 @ SV141 ) )
| ~ ( in @ ( sK11_SY201 @ SY371 @ SV141 ) @ SV141 ) )
| ( in @ ( sK10_C @ SY371 @ SV141 ) @ SY371 ) ) )
| ( SY371
= ( union @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(722,plain,
! [SV142: $i] :
( ( ! [SY373: $i] :
( ( SY373
!= ( union @ SV142 ) )
| ~ ( ~ ! [SY374: $i] :
( ! [SY375: $i] :
( ~ ( in @ SY374 @ SY375 )
| ~ ( in @ SY375 @ SV142 ) )
| ( in @ SY374 @ SY373 ) )
| ~ ! [SY376: $i] :
( ~ ( in @ SY376 @ SY373 )
| ~ ( ~ ( in @ SY376 @ ( sK9_D @ SY376 @ SY373 @ SV142 ) )
| ~ ( in @ ( sK9_D @ SY376 @ SY373 @ SV142 ) @ SV142 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(723,plain,
! [SV62: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
| ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 ) )
| ~ ( ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
| ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 ) ) )
= $false )
| ( ( SV62 = SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(724,plain,
! [SV143: $i] :
( ( ! [SY377: $i] :
( ( ( set_difference @ SV143 @ ( singleton @ SY377 ) )
!= SV143 )
| ~ ( in @ SY377 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(725,plain,
! [SV144: $i] :
( ( ! [SY378: $i] :
( ( in @ SY378 @ SV144 )
| ( ( set_difference @ SV144 @ ( singleton @ SY378 ) )
= SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(726,plain,
! [SV64: $i,SV3: $i] :
( ( ( in @ SV3 @ SV64 )
= $false )
| ( ( disjoint @ ( singleton @ SV3 ) @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(727,plain,
! [SV66: $i,SV5: $i,SV145: $i] :
( ( ( ( in @ SV145 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV66 @ ( singleton @ SV145 ) ) ) )
= $true )
| ( ( subset @ SV5 @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(728,plain,
! [SV68: $i,SV103: $i,SV111: $i,SV7: $i] :
( ( ( SV7 = SV111 )
= $true )
| ( ( ( SV7 = SV103 )
| ( ( unordered_pair @ SV7 @ SV68 )
!= ( unordered_pair @ SV103 @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(729,plain,
! [SV104: $i,SV71: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV71 ) )
= $true )
| ( ( ~ ( subset @ SV10 @ SV104 ) )
= $true )
| ( ( subset @ SV10 @ ( set_intersection2 @ SV71 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(730,plain,
! [SV105: $i,SV72: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV72 ) )
= $true )
| ( ( ~ ( subset @ SV72 @ SV105 ) )
= $true )
| ( ( subset @ SV11 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(731,plain,
! [SV73: $i,SV146: $i,SV12: $i] :
( ( ( subset @ ( set_intersection2 @ SV12 @ SV146 ) @ ( set_intersection2 @ SV73 @ SV146 ) )
= $true )
| ( ( subset @ SV12 @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(732,plain,
! [SV75: $i,SV147: $i,SV15: $i] :
( ( ( subset @ ( set_difference @ SV15 @ SV147 ) @ ( set_difference @ SV75 @ SV147 ) )
= $true )
| ( ( subset @ SV15 @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(733,plain,
! [SV82: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV82 )
= $false )
| ( ( proper_subset @ SV82 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(734,plain,
! [SV24: $i,SV106: $i,SV83: $i] :
( ( ( ~ ( disjoint @ SV83 @ SV106 ) )
= $true )
| ( ( ~ ( subset @ SV24 @ SV83 ) )
= $true )
| ( ( disjoint @ SV24 @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(735,plain,
! [SV107: $i,SV86: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV86 ) )
= $true )
| ( ( ~ ( subset @ SV107 @ SV86 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV28 @ SV107 ) @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(736,plain,
! [SV112: $i,SV87: $i,SV29: $i] :
( ( ( ( singleton @ SV29 )
= ( unordered_pair @ SV87 @ SV112 ) )
= $false )
| ( ( SV29 = SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(737,plain,
! [SV108: $i,SV89: $i,SV32: $i] :
( ( ( ( singleton @ SV32 )
= ( unordered_pair @ SV89 @ SV108 ) )
= $false )
| ( ( SV89 = SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(738,plain,
! [SV33: $i,SV90: $i] :
( ( ( in @ SV90 @ SV33 )
= $false )
| ( ( in @ SV33 @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(739,plain,
! [SV34: $i,SV91: $i] :
( ( ( proper_subset @ SV91 @ SV34 )
= $false )
| ( ( proper_subset @ SV34 @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(740,plain,
! [SV98: $i,SV52: $i] :
( ( ( in @ SV52 @ SV98 )
= $false )
| ( ( empty @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(741,plain,
! [SV99: $i,SV53: $i] :
( ( ( empty @ SV53 )
= $false )
| ( ( SV53 = SV99 )
= $true )
| ( ( ~ ( empty @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(742,plain,
! [SV148: $i,SV54: $i] :
( ( ! [SY379: $i] :
( ~ ( in @ SV54 @ SY379 )
| ~ ( in @ SV148 @ SY379 )
| ( subset @ ( unordered_pair @ SV54 @ SV148 ) @ SY379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(743,plain,
! [SV54: $i] :
( ( ~ ! [SY260: $i,SY261: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY260 ) @ SY261 )
| ( in @ SV54 @ SY261 ) )
| ~ ! [SY262: $i,SY263: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY262 ) @ SY263 )
| ( in @ SY262 @ SY263 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(744,plain,
! [SV55: $i,SV149: $i] :
( ( ! [SY380: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_D @ SY380 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SY380 @ SV149 @ SV55 ) @ SV149 )
| ~ ( in @ ( sK8_D @ SY380 @ SV149 @ SV55 ) @ SY380 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SY380 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SY380 @ SV149 @ SV55 ) @ SY380 ) )
| ~ ( ~ ( in @ ( sK8_D @ SY380 @ SV149 @ SV55 ) @ SV149 )
| ( in @ ( sK8_D @ SY380 @ SV149 @ SV55 ) @ SY380 ) ) ) )
| ( SY380
= ( set_difference @ SV55 @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(745,plain,
! [SV150: $i,SV55: $i] :
( ( ! [SY381: $i] :
( ( SY381
!= ( set_difference @ SV55 @ SV150 ) )
| ~ ( ~ ! [SY382: $i] :
( ~ ( in @ SY382 @ SV55 )
| ( in @ SY382 @ SV150 )
| ( in @ SY382 @ SY381 ) )
| ~ ~ ( ~ ! [SY269: $i] :
( ~ ( in @ SY269 @ SY381 )
| ( in @ SY269 @ SV55 ) )
| ~ ! [SY384: $i] :
( ~ ( in @ SY384 @ SY381 )
| ~ ( in @ SY384 @ SV150 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(746,plain,
! [SV56: $i,SV151: $i] :
( ( ! [SY385: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SY385 @ SV151 @ SV56 ) @ SY385 )
| ~ ( in @ ( sK19_D @ SY385 @ SV151 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK19_D @ SY385 @ SV151 @ SV56 ) @ SY385 )
| ~ ( in @ ( sK19_D @ SY385 @ SV151 @ SV56 ) @ SV151 ) ) )
| ~ ( ( in @ ( sK19_D @ SY385 @ SV151 @ SV56 ) @ SY385 )
| ( in @ ( sK19_D @ SY385 @ SV151 @ SV56 ) @ SV56 )
| ( in @ ( sK19_D @ SY385 @ SV151 @ SV56 ) @ SV151 ) ) )
| ( SY385
= ( set_union2 @ SV56 @ SV151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(747,plain,
! [SV152: $i,SV56: $i] :
( ( ! [SY386: $i] :
( ( SY386
!= ( set_union2 @ SV56 @ SV152 ) )
| ~ ( ~ ! [SY387: $i] :
( ~ ( in @ SY387 @ SY386 )
| ( in @ SY387 @ SV56 )
| ( in @ SY387 @ SV152 ) )
| ~ ~ ( ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SV56 )
| ( in @ SY276 @ SY386 ) )
| ~ ! [SY389: $i] :
( ~ ( in @ SY389 @ SV152 )
| ( in @ SY389 @ SY386 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(748,plain,
! [SV153: $i,SV113: $i] :
( ( ( disjoint @ SV113 @ SV153 )
| ( in @ ( sK24_C @ SV153 @ SV113 ) @ ( set_intersection2 @ SV113 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(749,plain,
! [SV154: $i,SV114: $i] :
( ( ! [SY390: $i] :
~ ( in @ SY390 @ ( set_intersection2 @ SV114 @ SV154 ) )
| ~ ( disjoint @ SV114 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(750,plain,
( ( ( in @ sK1_A @ sK3_SY197 )
= $false )
| ( ( ~ ( in @ sK2_SY194 @ sK4_SY199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(751,plain,
! [SV155: $i,SV115: $i] :
( ( ( ( set_difference @ SV115 @ SV155 )
!= empty_set )
| ( subset @ SV115 @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(752,plain,
! [SV156: $i,SV116: $i] :
( ( ~ ( subset @ SV116 @ SV156 )
| ( ( set_difference @ SV116 @ SV156 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(753,plain,
! [SV157: $i,SV117: $i] :
( ( ( ( set_intersection2 @ SV117 @ SV157 )
!= empty_set )
| ( disjoint @ SV117 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(754,plain,
! [SV158: $i,SV118: $i] :
( ( ~ ( disjoint @ SV118 @ SV158 )
| ( ( set_intersection2 @ SV118 @ SV158 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(755,plain,
! [SV57: $i,SV159: $i] :
( ( ! [SY391: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY391 @ SV159 @ SV57 ) @ SV57 )
| ~ ( in @ ( sK12_D @ SY391 @ SV159 @ SV57 ) @ SV159 )
| ~ ( in @ ( sK12_D @ SY391 @ SV159 @ SV57 ) @ SY391 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY391 @ SV159 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SY391 @ SV159 @ SV57 ) @ SY391 ) )
| ~ ( ( in @ ( sK12_D @ SY391 @ SV159 @ SV57 ) @ SV159 )
| ( in @ ( sK12_D @ SY391 @ SV159 @ SV57 ) @ SY391 ) ) ) )
| ( SY391
= ( set_intersection2 @ SV57 @ SV159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(756,plain,
! [SV160: $i,SV57: $i] :
( ( ! [SY392: $i] :
( ( SY392
!= ( set_intersection2 @ SV57 @ SV160 ) )
| ~ ( ~ ! [SY393: $i] :
( ~ ( in @ SY393 @ SV57 )
| ~ ( in @ SY393 @ SV160 )
| ( in @ SY393 @ SY392 ) )
| ~ ~ ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SY392 )
| ( in @ SY283 @ SV57 ) )
| ~ ! [SY395: $i] :
( ~ ( in @ SY395 @ SY392 )
| ( in @ SY395 @ SV160 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(757,plain,
! [SV119: $i] :
( ( ( in @ ( sK22_B @ SV119 ) @ SV119 )
= $true )
| ( ( SV119 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(758,plain,
! [SV120: $i] :
( ( ( ( SV120 != empty_set ) )
= $true )
| ( ( ! [SY344: $i] :
~ ( in @ SY344 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(759,plain,
! [SV121: $i,SV161: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
| ~ ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 ) )
| ~ ( ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
| ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 ) ) )
| ( SV161
= ( powerset @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(760,plain,
! [SV122: $i,SV162: $i] :
( ( ( SV162
!= ( powerset @ SV122 ) )
| ~ ( ~ ! [SY396: $i] :
( ~ ( in @ SY396 @ SV162 )
| ( subset @ SY396 @ SV122 ) )
| ~ ! [SY397: $i] :
( ~ ( subset @ SY397 @ SV122 )
| ( in @ SY397 @ SV162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(761,plain,
! [SV163: $i,SV123: $i] :
( ( ( ( set_difference @ SV123 @ SV163 )
!= empty_set )
| ( subset @ SV123 @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(762,plain,
! [SV164: $i,SV124: $i] :
( ( ~ ( subset @ SV124 @ SV164 )
| ( ( set_difference @ SV124 @ SV164 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(763,plain,
! [SV165: $i,SV125: $i] :
( ( ( ( set_difference @ SV125 @ SV165 )
!= SV125 )
| ( disjoint @ SV125 @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(764,plain,
! [SV166: $i,SV126: $i] :
( ( ~ ( disjoint @ SV126 @ SV166 )
| ( ( set_difference @ SV126 @ SV166 )
= SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(765,plain,
! [SV167: $i,SV58: $i] :
( ( ! [SY398: $i] :
( ~ ( ~ ( ! [SY399: $i,SY400: $i] :
( ~ ( in @ SY399 @ SV58 )
| ~ ( in @ SY400 @ SV167 )
| ( ( sK16_D @ SY398 @ SV167 @ SV58 )
!= ( ordered_pair @ SY399 @ SY400 ) ) )
| ~ ( in @ ( sK16_D @ SY398 @ SV167 @ SV58 ) @ SY398 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SY398 @ SV167 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SY398 @ SV167 @ SV58 ) @ SV167 ) )
| ( ( sK16_D @ SY398 @ SV167 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SY398 @ SV167 @ SV58 ) @ ( sK18_SY207 @ SY398 @ SV167 @ SV58 ) ) ) )
| ( in @ ( sK16_D @ SY398 @ SV167 @ SV58 ) @ SY398 ) ) )
| ( SY398
= ( cartesian_product2 @ SV58 @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(766,plain,
! [SV168: $i,SV58: $i] :
( ( ! [SY401: $i] :
( ( SY401
!= ( cartesian_product2 @ SV58 @ SV168 ) )
| ~ ( ~ ! [SY402: $i] :
( ! [SY403: $i,SY404: $i] :
( ~ ( in @ SY403 @ SV58 )
| ~ ( in @ SY404 @ SV168 )
| ( SY402
!= ( ordered_pair @ SY403 @ SY404 ) ) )
| ( in @ SY402 @ SY401 ) )
| ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SY401 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY405 @ SY401 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SY405 @ SY401 @ SV168 @ SV58 ) @ SV168 ) )
| ( SY405
!= ( ordered_pair @ ( sK14_E @ SY405 @ SY401 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SY405 @ SY401 @ SV168 @ SV58 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(767,plain,
! [SV100: $i,SV59: $i] :
( ( ! [SY326: $i,SY327: $i] :
( ~ ( in @ SV59 @ SY326 )
| ~ ( in @ SV100 @ SY327 )
| ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY326 @ SY327 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[697]) ).
thf(768,plain,
! [SV100: $i,SV59: $i] :
( ( ~ ( ~ ! [SY328: $i] :
( ! [SY329: $i] :
~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY328 @ SY329 ) )
| ( in @ SV59 @ SY328 ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY330 @ SY331 ) )
| ( in @ SV100 @ SY331 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(769,plain,
! [SV127: $i,SV169: $i] :
( ( ~ ( ~ ( ( ( sK23_C @ SV169 @ SV127 )
!= SV127 )
| ~ ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 ) )
| ~ ( ( ( sK23_C @ SV169 @ SV127 )
= SV127 )
| ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 ) ) )
| ( SV169
= ( singleton @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(770,plain,
! [SV128: $i,SV170: $i] :
( ( ( SV170
!= ( singleton @ SV128 ) )
| ~ ( ~ ! [SY406: $i] :
( ( SY406 != SV128 )
| ( in @ SY406 @ SV170 ) )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV170 )
| ( SY407 = SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(771,plain,
! [SV129: $i,SV171: $i] :
( ( ~ ( ~ ( in @ ( sK13_C @ SV171 @ SV129 ) @ SV129 )
| ~ ~ ( in @ ( sK13_C @ SV171 @ SV129 ) @ SV171 ) )
| ( subset @ SV129 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(772,plain,
! [SV172: $i,SV130: $i] :
( ( ~ ( subset @ SV130 @ SV172 )
| ! [SY408: $i] :
( ~ ( in @ SY408 @ SV130 )
| ( in @ SY408 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(773,plain,
! [SV173: $i,SV131: $i] :
( ( ( disjoint @ SV131 @ SV173 )
| ~ ( ~ ( in @ ( sK25_C @ SV173 @ SV131 ) @ SV131 )
| ~ ( in @ ( sK25_C @ SV173 @ SV131 ) @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(774,plain,
! [SV174: $i,SV132: $i] :
( ( ! [SY409: $i] :
( ~ ( in @ SY409 @ SV132 )
| ~ ( in @ SY409 @ SV174 ) )
| ~ ( disjoint @ SV132 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(775,plain,
! [SV60: $i,SV175: $i] :
( ( ! [SY410: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SY410 @ SV175 @ SV60 ) @ SY410 )
| ( ( sK20_D @ SY410 @ SV175 @ SV60 )
!= SV60 ) )
| ~ ( ~ ( in @ ( sK20_D @ SY410 @ SV175 @ SV60 ) @ SY410 )
| ( ( sK20_D @ SY410 @ SV175 @ SV60 )
!= SV175 ) ) )
| ~ ( ( in @ ( sK20_D @ SY410 @ SV175 @ SV60 ) @ SY410 )
| ( ( sK20_D @ SY410 @ SV175 @ SV60 )
= SV60 )
| ( ( sK20_D @ SY410 @ SV175 @ SV60 )
= SV175 ) ) )
| ( SY410
= ( unordered_pair @ SV60 @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(776,plain,
! [SV176: $i,SV60: $i] :
( ( ! [SY411: $i] :
( ( SY411
!= ( unordered_pair @ SV60 @ SV176 ) )
| ~ ( ~ ! [SY412: $i] :
( ~ ( in @ SY412 @ SY411 )
| ( SY412 = SV60 )
| ( SY412 = SV176 ) )
| ~ ~ ( ~ ! [SY307: $i] :
( ( SY307 != SV60 )
| ( in @ SY307 @ SY411 ) )
| ~ ! [SY414: $i] :
( ( SY414 != SV176 )
| ( in @ SY414 @ SY411 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(777,plain,
! [SV177: $i,SV133: $i] :
( ( ~ ( subset @ SV133 @ ( singleton @ SV177 ) )
| ( SV133 = empty_set )
| ( SV133
= ( singleton @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(778,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(779,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[708]) ).
thf(780,plain,
! [SV178: $i,SV134: $i] :
( ( ~ ( in @ SV134 @ SV178 )
| ( subset @ ( singleton @ SV134 ) @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(781,plain,
! [SV179: $i,SV135: $i] :
( ( ~ ( subset @ ( singleton @ SV135 ) @ SV179 )
| ( in @ SV135 @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(782,plain,
! [SV180: $i,SV136: $i] :
( ( ~ ( subset @ SV136 @ ( singleton @ SV180 ) )
| ( SV136 = empty_set )
| ( SV136
= ( singleton @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(783,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(784,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[712]) ).
thf(785,plain,
! [SV101: $i,SV61: $i] :
( ( ! [SY332: $i] :
( ! [SY333: $i] :
( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SY332 @ SY333 ) )
| ( SV61 = SY332 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[713]) ).
thf(786,plain,
! [SV101: $i,SV61: $i] :
( ( ! [SY334: $i,SY335: $i] :
( ( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SY334 @ SY335 ) )
| ( SV101 = SY335 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[714]) ).
thf(787,plain,
! [SV181: $i,SV137: $i] :
( ( ~ ( subset @ SV137 @ SV181 )
| ~ ( subset @ SV181 @ SV137 )
| ( SV137 = SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(788,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(789,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(790,plain,
! [SV182: $i,SV138: $i] :
( ( ( SV138 = SV182 )
| ~ ( subset @ SV138 @ SV182 )
| ( proper_subset @ SV138 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(791,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[718]) ).
thf(792,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[718]) ).
thf(793,plain,
! [SV183: $i,SV139: $i] :
( ( ~ ( in @ SV139 @ SV183 )
| ( subset @ ( singleton @ SV139 ) @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(794,plain,
! [SV184: $i,SV140: $i] :
( ( ~ ( subset @ ( singleton @ SV140 ) @ SV184 )
| ( in @ SV140 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(795,plain,
! [SV141: $i,SV185: $i] :
( ( ~ ( ~ ( ! [SY415: $i] :
( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SY415 )
| ~ ( in @ SY415 @ SV141 ) )
| ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ ( sK11_SY201 @ SV185 @ SV141 ) )
| ~ ( in @ ( sK11_SY201 @ SV185 @ SV141 ) @ SV141 ) )
| ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) ) )
| ( SV185
= ( union @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(796,plain,
! [SV142: $i,SV186: $i] :
( ( ( SV186
!= ( union @ SV142 ) )
| ~ ( ~ ! [SY416: $i] :
( ! [SY375: $i] :
( ~ ( in @ SY416 @ SY375 )
| ~ ( in @ SY375 @ SV142 ) )
| ( in @ SY416 @ SV186 ) )
| ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV186 )
| ~ ( ~ ( in @ SY418 @ ( sK9_D @ SY418 @ SV186 @ SV142 ) )
| ~ ( in @ ( sK9_D @ SY418 @ SV186 @ SV142 ) @ SV142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(797,plain,
! [SV62: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
| ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 ) ) )
= $false )
| ( ( SV62 = SV102 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(798,plain,
! [SV62: $i,SV102: $i] :
( ( ( ~ ( ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
| ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 ) ) )
= $false )
| ( ( SV62 = SV102 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[723]) ).
thf(799,plain,
! [SV187: $i,SV143: $i] :
( ( ( ( set_difference @ SV143 @ ( singleton @ SV187 ) )
!= SV143 )
| ~ ( in @ SV187 @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(800,plain,
! [SV144: $i,SV188: $i] :
( ( ( in @ SV188 @ SV144 )
| ( ( set_difference @ SV144 @ ( singleton @ SV188 ) )
= SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(801,plain,
! [SV66: $i,SV5: $i,SV145: $i] :
( ( ( in @ SV145 @ SV5 )
= $true )
| ( ( subset @ SV5 @ ( set_difference @ SV66 @ ( singleton @ SV145 ) ) )
= $true )
| ( ( subset @ SV5 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(802,plain,
! [SV111: $i,SV68: $i,SV103: $i,SV7: $i] :
( ( ( SV7 = SV103 )
= $true )
| ( ( ( ( unordered_pair @ SV7 @ SV68 )
!= ( unordered_pair @ SV103 @ SV111 ) ) )
= $true )
| ( ( SV7 = SV111 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(803,plain,
! [SV104: $i,SV71: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV71 )
= $false )
| ( ( ~ ( subset @ SV10 @ SV104 ) )
= $true )
| ( ( subset @ SV10 @ ( set_intersection2 @ SV71 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(804,plain,
! [SV105: $i,SV72: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV72 )
= $false )
| ( ( ~ ( subset @ SV72 @ SV105 ) )
= $true )
| ( ( subset @ SV11 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(805,plain,
! [SV24: $i,SV106: $i,SV83: $i] :
( ( ( disjoint @ SV83 @ SV106 )
= $false )
| ( ( ~ ( subset @ SV24 @ SV83 ) )
= $true )
| ( ( disjoint @ SV24 @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(806,plain,
! [SV107: $i,SV86: $i,SV28: $i] :
( ( ( subset @ SV28 @ SV86 )
= $false )
| ( ( ~ ( subset @ SV107 @ SV86 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV28 @ SV107 ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(807,plain,
! [SV53: $i,SV99: $i] :
( ( ( empty @ SV99 )
= $false )
| ( ( SV53 = SV99 )
= $true )
| ( ( empty @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(808,plain,
! [SV148: $i,SV189: $i,SV54: $i] :
( ( ~ ( in @ SV54 @ SV189 )
| ~ ( in @ SV148 @ SV189 )
| ( subset @ ( unordered_pair @ SV54 @ SV148 ) @ SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(809,plain,
! [SV54: $i] :
( ( ~ ! [SY260: $i,SY261: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY260 ) @ SY261 )
| ( in @ SV54 @ SY261 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[743]) ).
thf(810,plain,
! [SV54: $i] :
( ( ~ ! [SY262: $i,SY263: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY262 ) @ SY263 )
| ( in @ SY262 @ SY263 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[743]) ).
thf(811,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
| ~ ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) ) ) )
| ( SV190
= ( set_difference @ SV55 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(812,plain,
! [SV150: $i,SV55: $i,SV191: $i] :
( ( ( SV191
!= ( set_difference @ SV55 @ SV150 ) )
| ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV55 )
| ( in @ SY419 @ SV150 )
| ( in @ SY419 @ SV191 ) )
| ~ ~ ( ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV191 )
| ( in @ SY420 @ SV55 ) )
| ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV191 )
| ~ ( in @ SY421 @ SV150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(813,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) ) )
| ~ ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 )
| ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) ) )
| ( SV192
= ( set_union2 @ SV56 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(814,plain,
! [SV152: $i,SV56: $i,SV193: $i] :
( ( ( SV193
!= ( set_union2 @ SV56 @ SV152 ) )
| ~ ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV193 )
| ( in @ SY422 @ SV56 )
| ( in @ SY422 @ SV152 ) )
| ~ ~ ( ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV56 )
| ( in @ SY423 @ SV193 ) )
| ~ ! [SY424: $i] :
( ~ ( in @ SY424 @ SV152 )
| ( in @ SY424 @ SV193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(815,plain,
! [SV153: $i,SV113: $i] :
( ( ( disjoint @ SV113 @ SV153 )
= $true )
| ( ( in @ ( sK24_C @ SV153 @ SV113 ) @ ( set_intersection2 @ SV113 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(816,plain,
! [SV154: $i,SV114: $i] :
( ( ( ! [SY390: $i] :
~ ( in @ SY390 @ ( set_intersection2 @ SV114 @ SV154 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV114 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(817,plain,
( ( ( in @ sK2_SY194 @ sK4_SY199 )
= $false )
| ( ( in @ sK1_A @ sK3_SY197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(818,plain,
! [SV155: $i,SV115: $i] :
( ( ( ( ( set_difference @ SV115 @ SV155 )
!= empty_set ) )
= $true )
| ( ( subset @ SV115 @ SV155 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(819,plain,
! [SV156: $i,SV116: $i] :
( ( ( ~ ( subset @ SV116 @ SV156 ) )
= $true )
| ( ( ( set_difference @ SV116 @ SV156 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(820,plain,
! [SV157: $i,SV117: $i] :
( ( ( ( ( set_intersection2 @ SV117 @ SV157 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV117 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(821,plain,
! [SV158: $i,SV118: $i] :
( ( ( ~ ( disjoint @ SV118 @ SV158 ) )
= $true )
| ( ( ( set_intersection2 @ SV118 @ SV158 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(822,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
| ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) ) ) )
| ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(823,plain,
! [SV160: $i,SV57: $i,SV195: $i] :
( ( ( SV195
!= ( set_intersection2 @ SV57 @ SV160 ) )
| ~ ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SV57 )
| ~ ( in @ SY425 @ SV160 )
| ( in @ SY425 @ SV195 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV195 )
| ( in @ SY426 @ SV57 ) )
| ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV195 )
| ( in @ SY427 @ SV160 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(824,plain,
! [SV120: $i] :
( ( ( SV120 = empty_set )
= $false )
| ( ( ! [SY344: $i] :
~ ( in @ SY344 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(825,plain,
! [SV121: $i,SV161: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
| ~ ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 ) )
| ~ ( ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
| ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 ) ) ) )
= $true )
| ( ( SV161
= ( powerset @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(826,plain,
! [SV122: $i,SV162: $i] :
( ( ( ( SV162
!= ( powerset @ SV122 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY396: $i] :
( ~ ( in @ SY396 @ SV162 )
| ( subset @ SY396 @ SV122 ) )
| ~ ! [SY397: $i] :
( ~ ( subset @ SY397 @ SV122 )
| ( in @ SY397 @ SV162 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(827,plain,
! [SV163: $i,SV123: $i] :
( ( ( ( ( set_difference @ SV123 @ SV163 )
!= empty_set ) )
= $true )
| ( ( subset @ SV123 @ SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(828,plain,
! [SV164: $i,SV124: $i] :
( ( ( ~ ( subset @ SV124 @ SV164 ) )
= $true )
| ( ( ( set_difference @ SV124 @ SV164 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(829,plain,
! [SV165: $i,SV125: $i] :
( ( ( ( ( set_difference @ SV125 @ SV165 )
!= SV125 ) )
= $true )
| ( ( disjoint @ SV125 @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(830,plain,
! [SV166: $i,SV126: $i] :
( ( ( ~ ( disjoint @ SV126 @ SV166 ) )
= $true )
| ( ( ( set_difference @ SV126 @ SV166 )
= SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(831,plain,
! [SV196: $i,SV167: $i,SV58: $i] :
( ( ~ ( ~ ( ! [SY428: $i,SY429: $i] :
( ~ ( in @ SY428 @ SV58 )
| ~ ( in @ SY429 @ SV167 )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ SY428 @ SY429 ) ) )
| ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) @ SV167 ) )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) ) ) )
| ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) ) )
| ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(832,plain,
! [SV168: $i,SV58: $i,SV197: $i] :
( ( ( SV197
!= ( cartesian_product2 @ SV58 @ SV168 ) )
| ~ ( ~ ! [SY430: $i] :
( ! [SY403: $i,SY404: $i] :
( ~ ( in @ SY403 @ SV58 )
| ~ ( in @ SY404 @ SV168 )
| ( SY430
!= ( ordered_pair @ SY403 @ SY404 ) ) )
| ( in @ SY430 @ SV197 ) )
| ~ ! [SY433: $i] :
( ~ ( in @ SY433 @ SV197 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY433 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SY433 @ SV197 @ SV168 @ SV58 ) @ SV168 ) )
| ( SY433
!= ( ordered_pair @ ( sK14_E @ SY433 @ SV197 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SY433 @ SV197 @ SV168 @ SV58 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(833,plain,
! [SV100: $i,SV198: $i,SV59: $i] :
( ( ! [SY434: $i] :
( ~ ( in @ SV59 @ SV198 )
| ~ ( in @ SV100 @ SY434 )
| ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV198 @ SY434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(834,plain,
! [SV100: $i,SV59: $i] :
( ( ~ ! [SY328: $i] :
( ! [SY329: $i] :
~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY328 @ SY329 ) )
| ( in @ SV59 @ SY328 ) )
| ~ ! [SY330: $i,SY331: $i] :
( ~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY330 @ SY331 ) )
| ( in @ SV100 @ SY331 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(835,plain,
! [SV127: $i,SV169: $i] :
( ( ( ~ ( ~ ( ( ( sK23_C @ SV169 @ SV127 )
!= SV127 )
| ~ ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 ) )
| ~ ( ( ( sK23_C @ SV169 @ SV127 )
= SV127 )
| ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 ) ) ) )
= $true )
| ( ( SV169
= ( singleton @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(836,plain,
! [SV128: $i,SV170: $i] :
( ( ( ( SV170
!= ( singleton @ SV128 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY406: $i] :
( ( SY406 != SV128 )
| ( in @ SY406 @ SV170 ) )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV170 )
| ( SY407 = SV128 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(837,plain,
! [SV129: $i,SV171: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_C @ SV171 @ SV129 ) @ SV129 )
| ~ ~ ( in @ ( sK13_C @ SV171 @ SV129 ) @ SV171 ) ) )
= $true )
| ( ( subset @ SV129 @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(838,plain,
! [SV172: $i,SV130: $i] :
( ( ( ~ ( subset @ SV130 @ SV172 ) )
= $true )
| ( ( ! [SY408: $i] :
( ~ ( in @ SY408 @ SV130 )
| ( in @ SY408 @ SV172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(839,plain,
! [SV173: $i,SV131: $i] :
( ( ( disjoint @ SV131 @ SV173 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK25_C @ SV173 @ SV131 ) @ SV131 )
| ~ ( in @ ( sK25_C @ SV173 @ SV131 ) @ SV173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(840,plain,
! [SV174: $i,SV132: $i] :
( ( ( ! [SY409: $i] :
( ~ ( in @ SY409 @ SV132 )
| ~ ( in @ SY409 @ SV174 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV132 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(841,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV60 ) )
| ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV175 ) ) )
| ~ ( ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV60 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV175 ) ) )
| ( SV199
= ( unordered_pair @ SV60 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(842,plain,
! [SV176: $i,SV60: $i,SV200: $i] :
( ( ( SV200
!= ( unordered_pair @ SV60 @ SV176 ) )
| ~ ( ~ ! [SY435: $i] :
( ~ ( in @ SY435 @ SV200 )
| ( SY435 = SV60 )
| ( SY435 = SV176 ) )
| ~ ~ ( ~ ! [SY436: $i] :
( ( SY436 != SV60 )
| ( in @ SY436 @ SV200 ) )
| ~ ! [SY437: $i] :
( ( SY437 != SV176 )
| ( in @ SY437 @ SV200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(843,plain,
! [SV177: $i,SV133: $i] :
( ( ( ~ ( subset @ SV133 @ ( singleton @ SV177 ) ) )
= $true )
| ( ( ( SV133 = empty_set )
| ( SV133
= ( singleton @ SV177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(844,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[778]) ).
thf(845,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[779]) ).
thf(846,plain,
! [SV178: $i,SV134: $i] :
( ( ( ~ ( in @ SV134 @ SV178 ) )
= $true )
| ( ( subset @ ( singleton @ SV134 ) @ SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(847,plain,
! [SV179: $i,SV135: $i] :
( ( ( ~ ( subset @ ( singleton @ SV135 ) @ SV179 ) )
= $true )
| ( ( in @ SV135 @ SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[781]) ).
thf(848,plain,
! [SV180: $i,SV136: $i] :
( ( ( ~ ( subset @ SV136 @ ( singleton @ SV180 ) ) )
= $true )
| ( ( ( SV136 = empty_set )
| ( SV136
= ( singleton @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[782]) ).
thf(849,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(850,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(851,plain,
! [SV201: $i,SV101: $i,SV61: $i] :
( ( ! [SY438: $i] :
( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SV201 @ SY438 ) )
| ( SV61 = SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(852,plain,
! [SV202: $i,SV101: $i,SV61: $i] :
( ( ! [SY439: $i] :
( ( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SV202 @ SY439 ) )
| ( SV101 = SY439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(853,plain,
! [SV181: $i,SV137: $i] :
( ( ( ~ ( subset @ SV137 @ SV181 )
| ~ ( subset @ SV181 @ SV137 ) )
= $true )
| ( ( SV137 = SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(854,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[788]) ).
thf(855,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(856,plain,
! [SV182: $i,SV138: $i] :
( ( ( ( SV138 = SV182 )
| ~ ( subset @ SV138 @ SV182 ) )
= $true )
| ( ( proper_subset @ SV138 @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(857,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(858,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(859,plain,
! [SV183: $i,SV139: $i] :
( ( ( ~ ( in @ SV139 @ SV183 ) )
= $true )
| ( ( subset @ ( singleton @ SV139 ) @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(860,plain,
! [SV184: $i,SV140: $i] :
( ( ( ~ ( subset @ ( singleton @ SV140 ) @ SV184 ) )
= $true )
| ( ( in @ SV140 @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(861,plain,
! [SV141: $i,SV185: $i] :
( ( ( ~ ( ~ ( ! [SY415: $i] :
( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SY415 )
| ~ ( in @ SY415 @ SV141 ) )
| ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ ( sK11_SY201 @ SV185 @ SV141 ) )
| ~ ( in @ ( sK11_SY201 @ SV185 @ SV141 ) @ SV141 ) )
| ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) ) ) )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(862,plain,
! [SV142: $i,SV186: $i] :
( ( ( ( SV186
!= ( union @ SV142 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY416: $i] :
( ! [SY375: $i] :
( ~ ( in @ SY416 @ SY375 )
| ~ ( in @ SY375 @ SV142 ) )
| ( in @ SY416 @ SV186 ) )
| ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV186 )
| ~ ( ~ ( in @ SY418 @ ( sK9_D @ SY418 @ SV186 @ SV142 ) )
| ~ ( in @ ( sK9_D @ SY418 @ SV186 @ SV142 ) @ SV142 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(863,plain,
! [SV62: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
| ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 ) )
= $true )
| ( ( SV62 = SV102 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(864,plain,
! [SV62: $i,SV102: $i] :
( ( ( ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
| ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 ) )
= $true )
| ( ( SV62 = SV102 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(865,plain,
! [SV187: $i,SV143: $i] :
( ( ( ( ( set_difference @ SV143 @ ( singleton @ SV187 ) )
!= SV143 ) )
= $true )
| ( ( ~ ( in @ SV187 @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(866,plain,
! [SV144: $i,SV188: $i] :
( ( ( in @ SV188 @ SV144 )
= $true )
| ( ( ( set_difference @ SV144 @ ( singleton @ SV188 ) )
= SV144 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(867,plain,
! [SV111: $i,SV103: $i,SV68: $i,SV7: $i] :
( ( ( ( unordered_pair @ SV7 @ SV68 )
= ( unordered_pair @ SV103 @ SV111 ) )
= $false )
| ( ( SV7 = SV103 )
= $true )
| ( ( SV7 = SV111 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(868,plain,
! [SV71: $i,SV104: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV104 )
= $false )
| ( ( subset @ SV10 @ SV71 )
= $false )
| ( ( subset @ SV10 @ ( set_intersection2 @ SV71 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(869,plain,
! [SV11: $i,SV105: $i,SV72: $i] :
( ( ( subset @ SV72 @ SV105 )
= $false )
| ( ( subset @ SV11 @ SV72 )
= $false )
| ( ( subset @ SV11 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(870,plain,
! [SV106: $i,SV83: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV83 )
= $false )
| ( ( disjoint @ SV83 @ SV106 )
= $false )
| ( ( disjoint @ SV24 @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(871,plain,
! [SV28: $i,SV86: $i,SV107: $i] :
( ( ( subset @ SV107 @ SV86 )
= $false )
| ( ( subset @ SV28 @ SV86 )
= $false )
| ( ( subset @ ( set_union2 @ SV28 @ SV107 ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(872,plain,
! [SV148: $i,SV189: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV189 )
| ~ ( in @ SV148 @ SV189 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV54 @ SV148 ) @ SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(873,plain,
! [SV54: $i] :
( ( ! [SY260: $i,SY261: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY260 ) @ SY261 )
| ( in @ SV54 @ SY261 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(874,plain,
! [SV54: $i] :
( ( ! [SY262: $i,SY263: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SY262 ) @ SY263 )
| ( in @ SY262 @ SY263 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(875,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
| ~ ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) ) ) ) )
= $true )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(876,plain,
! [SV150: $i,SV55: $i,SV191: $i] :
( ( ( ( SV191
!= ( set_difference @ SV55 @ SV150 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV55 )
| ( in @ SY419 @ SV150 )
| ( in @ SY419 @ SV191 ) )
| ~ ~ ( ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV191 )
| ( in @ SY420 @ SV55 ) )
| ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV191 )
| ~ ( in @ SY421 @ SV150 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(877,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) ) )
| ~ ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 )
| ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) ) ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(878,plain,
! [SV152: $i,SV56: $i,SV193: $i] :
( ( ( ( SV193
!= ( set_union2 @ SV56 @ SV152 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV193 )
| ( in @ SY422 @ SV56 )
| ( in @ SY422 @ SV152 ) )
| ~ ~ ( ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV56 )
| ( in @ SY423 @ SV193 ) )
| ~ ! [SY424: $i] :
( ~ ( in @ SY424 @ SV152 )
| ( in @ SY424 @ SV193 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(879,plain,
! [SV154: $i,SV114: $i,SV203: $i] :
( ( ( ~ ( in @ SV203 @ ( set_intersection2 @ SV114 @ SV154 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV114 @ SV154 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(880,plain,
! [SV155: $i,SV115: $i] :
( ( ( ( set_difference @ SV115 @ SV155 )
= empty_set )
= $false )
| ( ( subset @ SV115 @ SV155 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(881,plain,
! [SV156: $i,SV116: $i] :
( ( ( subset @ SV116 @ SV156 )
= $false )
| ( ( ( set_difference @ SV116 @ SV156 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(882,plain,
! [SV157: $i,SV117: $i] :
( ( ( ( set_intersection2 @ SV117 @ SV157 )
= empty_set )
= $false )
| ( ( disjoint @ SV117 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(883,plain,
! [SV158: $i,SV118: $i] :
( ( ( disjoint @ SV118 @ SV158 )
= $false )
| ( ( ( set_intersection2 @ SV118 @ SV158 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(884,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
| ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) ) ) ) )
= $true )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(885,plain,
! [SV160: $i,SV57: $i,SV195: $i] :
( ( ( ( SV195
!= ( set_intersection2 @ SV57 @ SV160 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SV57 )
| ~ ( in @ SY425 @ SV160 )
| ( in @ SY425 @ SV195 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV195 )
| ( in @ SY426 @ SV57 ) )
| ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV195 )
| ( in @ SY427 @ SV160 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(886,plain,
! [SV120: $i,SV204: $i] :
( ( ( ~ ( in @ SV204 @ SV120 ) )
= $true )
| ( ( SV120 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(887,plain,
! [SV121: $i,SV161: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
| ~ ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 ) )
| ~ ( ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
| ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 ) ) )
= $false )
| ( ( SV161
= ( powerset @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(888,plain,
! [SV122: $i,SV162: $i] :
( ( ( SV162
= ( powerset @ SV122 ) )
= $false )
| ( ( ~ ( ~ ! [SY396: $i] :
( ~ ( in @ SY396 @ SV162 )
| ( subset @ SY396 @ SV122 ) )
| ~ ! [SY397: $i] :
( ~ ( subset @ SY397 @ SV122 )
| ( in @ SY397 @ SV162 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[826]) ).
thf(889,plain,
! [SV163: $i,SV123: $i] :
( ( ( ( set_difference @ SV123 @ SV163 )
= empty_set )
= $false )
| ( ( subset @ SV123 @ SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(890,plain,
! [SV164: $i,SV124: $i] :
( ( ( subset @ SV124 @ SV164 )
= $false )
| ( ( ( set_difference @ SV124 @ SV164 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(891,plain,
! [SV165: $i,SV125: $i] :
( ( ( ( set_difference @ SV125 @ SV165 )
= SV125 )
= $false )
| ( ( disjoint @ SV125 @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(892,plain,
! [SV166: $i,SV126: $i] :
( ( ( disjoint @ SV126 @ SV166 )
= $false )
| ( ( ( set_difference @ SV126 @ SV166 )
= SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(893,plain,
! [SV196: $i,SV167: $i,SV58: $i] :
( ( ( ~ ( ~ ( ! [SY428: $i,SY429: $i] :
( ~ ( in @ SY428 @ SV58 )
| ~ ( in @ SY429 @ SV167 )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ SY428 @ SY429 ) ) )
| ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) @ SV167 ) )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) ) ) )
| ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) ) ) )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[831]) ).
thf(894,plain,
! [SV168: $i,SV58: $i,SV197: $i] :
( ( ( ( SV197
!= ( cartesian_product2 @ SV58 @ SV168 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY430: $i] :
( ! [SY403: $i,SY404: $i] :
( ~ ( in @ SY403 @ SV58 )
| ~ ( in @ SY404 @ SV168 )
| ( SY430
!= ( ordered_pair @ SY403 @ SY404 ) ) )
| ( in @ SY430 @ SV197 ) )
| ~ ! [SY433: $i] :
( ~ ( in @ SY433 @ SV197 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY433 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SY433 @ SV197 @ SV168 @ SV58 ) @ SV168 ) )
| ( SY433
!= ( ordered_pair @ ( sK14_E @ SY433 @ SV197 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SY433 @ SV197 @ SV168 @ SV58 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[832]) ).
thf(895,plain,
! [SV205: $i,SV100: $i,SV198: $i,SV59: $i] :
( ( ~ ( in @ SV59 @ SV198 )
| ~ ( in @ SV100 @ SV205 )
| ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV198 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(896,plain,
! [SV100: $i,SV59: $i] :
( ( ~ ! [SY328: $i] :
( ! [SY329: $i] :
~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY328 @ SY329 ) )
| ( in @ SV59 @ SY328 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[834]) ).
thf(897,plain,
! [SV100: $i,SV59: $i] :
( ( ~ ! [SY330: $i,SY331: $i] :
( ~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY330 @ SY331 ) )
| ( in @ SV100 @ SY331 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[834]) ).
thf(898,plain,
! [SV127: $i,SV169: $i] :
( ( ( ~ ( ( ( sK23_C @ SV169 @ SV127 )
!= SV127 )
| ~ ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 ) )
| ~ ( ( ( sK23_C @ SV169 @ SV127 )
= SV127 )
| ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 ) ) )
= $false )
| ( ( SV169
= ( singleton @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(899,plain,
! [SV128: $i,SV170: $i] :
( ( ( SV170
= ( singleton @ SV128 ) )
= $false )
| ( ( ~ ( ~ ! [SY406: $i] :
( ( SY406 != SV128 )
| ( in @ SY406 @ SV170 ) )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV170 )
| ( SY407 = SV128 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(900,plain,
! [SV129: $i,SV171: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV171 @ SV129 ) @ SV129 )
| ~ ~ ( in @ ( sK13_C @ SV171 @ SV129 ) @ SV171 ) )
= $false )
| ( ( subset @ SV129 @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(901,plain,
! [SV172: $i,SV130: $i] :
( ( ( subset @ SV130 @ SV172 )
= $false )
| ( ( ! [SY408: $i] :
( ~ ( in @ SY408 @ SV130 )
| ( in @ SY408 @ SV172 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(902,plain,
! [SV131: $i,SV173: $i] :
( ( ( ~ ( in @ ( sK25_C @ SV173 @ SV131 ) @ SV131 )
| ~ ( in @ ( sK25_C @ SV173 @ SV131 ) @ SV173 ) )
= $false )
| ( ( disjoint @ SV131 @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(903,plain,
! [SV174: $i,SV132: $i,SV206: $i] :
( ( ( ~ ( in @ SV206 @ SV132 )
| ~ ( in @ SV206 @ SV174 ) )
= $true )
| ( ( ~ ( disjoint @ SV132 @ SV174 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(904,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV60 ) )
| ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV175 ) ) )
| ~ ( ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV60 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV175 ) ) ) )
= $true )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(905,plain,
! [SV176: $i,SV60: $i,SV200: $i] :
( ( ( ( SV200
!= ( unordered_pair @ SV60 @ SV176 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY435: $i] :
( ~ ( in @ SY435 @ SV200 )
| ( SY435 = SV60 )
| ( SY435 = SV176 ) )
| ~ ~ ( ~ ! [SY436: $i] :
( ( SY436 != SV60 )
| ( in @ SY436 @ SV200 ) )
| ~ ! [SY437: $i] :
( ( SY437 != SV176 )
| ( in @ SY437 @ SV200 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(906,plain,
! [SV177: $i,SV133: $i] :
( ( ( subset @ SV133 @ ( singleton @ SV177 ) )
= $false )
| ( ( ( SV133 = empty_set )
| ( SV133
= ( singleton @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(907,plain,
! [SV207: $i] :
( ( ( SV207 != empty_set )
| ! [SY440: $i] : ( subset @ SV207 @ ( singleton @ SY440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(908,plain,
! [SV208: $i] :
( ( ! [SY441: $i] :
( ( SV208
!= ( singleton @ SY441 ) )
| ( subset @ SV208 @ ( singleton @ SY441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(909,plain,
! [SV178: $i,SV134: $i] :
( ( ( in @ SV134 @ SV178 )
= $false )
| ( ( subset @ ( singleton @ SV134 ) @ SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(910,plain,
! [SV179: $i,SV135: $i] :
( ( ( subset @ ( singleton @ SV135 ) @ SV179 )
= $false )
| ( ( in @ SV135 @ SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(911,plain,
! [SV180: $i,SV136: $i] :
( ( ( subset @ SV136 @ ( singleton @ SV180 ) )
= $false )
| ( ( ( SV136 = empty_set )
| ( SV136
= ( singleton @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(912,plain,
! [SV209: $i] :
( ( ( SV209 != empty_set )
| ! [SY442: $i] : ( subset @ SV209 @ ( singleton @ SY442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(913,plain,
! [SV210: $i] :
( ( ! [SY443: $i] :
( ( SV210
!= ( singleton @ SY443 ) )
| ( subset @ SV210 @ ( singleton @ SY443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(914,plain,
! [SV201: $i,SV101: $i,SV61: $i] :
( ( ( ! [SY438: $i] :
( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SV201 @ SY438 ) ) )
= $true )
| ( ( SV61 = SV201 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(915,plain,
! [SV211: $i,SV202: $i,SV101: $i,SV61: $i] :
( ( ( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SV202 @ SV211 ) )
| ( SV101 = SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(916,plain,
! [SV181: $i,SV137: $i] :
( ( ( ~ ( subset @ SV137 @ SV181 ) )
= $true )
| ( ( ~ ( subset @ SV181 @ SV137 ) )
= $true )
| ( ( SV137 = SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(917,plain,
! [SV212: $i] :
( ( ! [SY444: $i] :
( ( SV212 != SY444 )
| ( subset @ SV212 @ SY444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(918,plain,
! [SV213: $i] :
( ( ! [SY445: $i] :
( ( SV213 != SY445 )
| ( subset @ SY445 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(919,plain,
! [SV182: $i,SV138: $i] :
( ( ( SV138 = SV182 )
= $true )
| ( ( ~ ( subset @ SV138 @ SV182 ) )
= $true )
| ( ( proper_subset @ SV138 @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[856]) ).
thf(920,plain,
! [SV214: $i] :
( ( ! [SY446: $i] :
( ~ ( proper_subset @ SV214 @ SY446 )
| ( SV214 != SY446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(921,plain,
! [SV215: $i] :
( ( ! [SY447: $i] :
( ~ ( proper_subset @ SV215 @ SY447 )
| ( subset @ SV215 @ SY447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(922,plain,
! [SV183: $i,SV139: $i] :
( ( ( in @ SV139 @ SV183 )
= $false )
| ( ( subset @ ( singleton @ SV139 ) @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(923,plain,
! [SV184: $i,SV140: $i] :
( ( ( subset @ ( singleton @ SV140 ) @ SV184 )
= $false )
| ( ( in @ SV140 @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(924,plain,
! [SV141: $i,SV185: $i] :
( ( ( ~ ( ! [SY415: $i] :
( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SY415 )
| ~ ( in @ SY415 @ SV141 ) )
| ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ ( sK11_SY201 @ SV185 @ SV141 ) )
| ~ ( in @ ( sK11_SY201 @ SV185 @ SV141 ) @ SV141 ) )
| ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) ) )
= $false )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(925,plain,
! [SV142: $i,SV186: $i] :
( ( ( SV186
= ( union @ SV142 ) )
= $false )
| ( ( ~ ( ~ ! [SY416: $i] :
( ! [SY375: $i] :
( ~ ( in @ SY416 @ SY375 )
| ~ ( in @ SY375 @ SV142 ) )
| ( in @ SY416 @ SV186 ) )
| ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV186 )
| ~ ( ~ ( in @ SY418 @ ( sK9_D @ SY418 @ SV186 @ SV142 ) )
| ~ ( in @ ( sK9_D @ SY418 @ SV186 @ SV142 ) @ SV142 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(926,plain,
! [SV62: $i,SV102: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 ) )
= $true )
| ( ( ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 ) )
= $true )
| ( ( SV62 = SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(927,plain,
! [SV62: $i,SV102: $i] :
( ( ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
= $true )
| ( ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 )
= $true )
| ( ( SV62 = SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(928,plain,
! [SV187: $i,SV143: $i] :
( ( ( ( set_difference @ SV143 @ ( singleton @ SV187 ) )
= SV143 )
= $false )
| ( ( ~ ( in @ SV187 @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(929,plain,
! [SV148: $i,SV189: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV189 ) )
= $true )
| ( ( ~ ( in @ SV148 @ SV189 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV54 @ SV148 ) @ SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(930,plain,
! [SV216: $i,SV54: $i] :
( ( ! [SY448: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SV216 ) @ SY448 )
| ( in @ SV54 @ SY448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(931,plain,
! [SV217: $i,SV54: $i] :
( ( ! [SY449: $i] :
( ~ ( subset @ ( unordered_pair @ SV54 @ SV217 ) @ SY449 )
| ( in @ SV217 @ SY449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(932,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
| ~ ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) ) ) )
= $false )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[875]) ).
thf(933,plain,
! [SV150: $i,SV55: $i,SV191: $i] :
( ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false )
| ( ( ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV55 )
| ( in @ SY419 @ SV150 )
| ( in @ SY419 @ SV191 ) )
| ~ ~ ( ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV191 )
| ( in @ SY420 @ SV55 ) )
| ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV191 )
| ~ ( in @ SY421 @ SV150 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(934,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) ) )
| ~ ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 )
| ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) ) )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(935,plain,
! [SV152: $i,SV56: $i,SV193: $i] :
( ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false )
| ( ( ~ ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV193 )
| ( in @ SY422 @ SV56 )
| ( in @ SY422 @ SV152 ) )
| ~ ~ ( ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV56 )
| ( in @ SY423 @ SV193 ) )
| ~ ! [SY424: $i] :
( ~ ( in @ SY424 @ SV152 )
| ( in @ SY424 @ SV193 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(936,plain,
! [SV154: $i,SV114: $i,SV203: $i] :
( ( ( in @ SV203 @ ( set_intersection2 @ SV114 @ SV154 ) )
= $false )
| ( ( ~ ( disjoint @ SV114 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(937,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
| ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) ) ) )
= $false )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(938,plain,
! [SV160: $i,SV57: $i,SV195: $i] :
( ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false )
| ( ( ~ ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SV57 )
| ~ ( in @ SY425 @ SV160 )
| ( in @ SY425 @ SV195 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV195 )
| ( in @ SY426 @ SV57 ) )
| ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV195 )
| ( in @ SY427 @ SV160 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(939,plain,
! [SV120: $i,SV204: $i] :
( ( ( in @ SV204 @ SV120 )
= $false )
| ( ( SV120 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(940,plain,
! [SV121: $i,SV161: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
| ~ ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 ) ) )
= $false )
| ( ( SV161
= ( powerset @ SV121 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[887]) ).
thf(941,plain,
! [SV121: $i,SV161: $i] :
( ( ( ~ ( ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
| ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 ) ) )
= $false )
| ( ( SV161
= ( powerset @ SV121 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[887]) ).
thf(942,plain,
! [SV122: $i,SV162: $i] :
( ( ( ~ ! [SY396: $i] :
( ~ ( in @ SY396 @ SV162 )
| ( subset @ SY396 @ SV122 ) )
| ~ ! [SY397: $i] :
( ~ ( subset @ SY397 @ SV122 )
| ( in @ SY397 @ SV162 ) ) )
= $false )
| ( ( SV162
= ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(943,plain,
! [SV196: $i,SV167: $i,SV58: $i] :
( ( ( ~ ( ! [SY428: $i,SY429: $i] :
( ~ ( in @ SY428 @ SV58 )
| ~ ( in @ SY429 @ SV167 )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ SY428 @ SY429 ) ) )
| ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) @ SV167 ) )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) ) ) )
| ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) ) )
= $false )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(944,plain,
! [SV168: $i,SV58: $i,SV197: $i] :
( ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false )
| ( ( ~ ( ~ ! [SY430: $i] :
( ! [SY403: $i,SY404: $i] :
( ~ ( in @ SY403 @ SV58 )
| ~ ( in @ SY404 @ SV168 )
| ( SY430
!= ( ordered_pair @ SY403 @ SY404 ) ) )
| ( in @ SY430 @ SV197 ) )
| ~ ! [SY433: $i] :
( ~ ( in @ SY433 @ SV197 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY433 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SY433 @ SV197 @ SV168 @ SV58 ) @ SV168 ) )
| ( SY433
!= ( ordered_pair @ ( sK14_E @ SY433 @ SV197 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SY433 @ SV197 @ SV168 @ SV58 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(945,plain,
! [SV205: $i,SV100: $i,SV198: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV198 )
| ~ ( in @ SV100 @ SV205 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV198 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(946,plain,
! [SV100: $i,SV59: $i] :
( ( ! [SY328: $i] :
( ! [SY329: $i] :
~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY328 @ SY329 ) )
| ( in @ SV59 @ SY328 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(947,plain,
! [SV100: $i,SV59: $i] :
( ( ! [SY330: $i,SY331: $i] :
( ~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SY330 @ SY331 ) )
| ( in @ SV100 @ SY331 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[897]) ).
thf(948,plain,
! [SV127: $i,SV169: $i] :
( ( ( ~ ( ( ( sK23_C @ SV169 @ SV127 )
!= SV127 )
| ~ ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 ) ) )
= $false )
| ( ( SV169
= ( singleton @ SV127 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[898]) ).
thf(949,plain,
! [SV127: $i,SV169: $i] :
( ( ( ~ ( ( ( sK23_C @ SV169 @ SV127 )
= SV127 )
| ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 ) ) )
= $false )
| ( ( SV169
= ( singleton @ SV127 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[898]) ).
thf(950,plain,
! [SV170: $i,SV128: $i] :
( ( ( ~ ! [SY406: $i] :
( ( SY406 != SV128 )
| ( in @ SY406 @ SV170 ) )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV170 )
| ( SY407 = SV128 ) ) )
= $false )
| ( ( SV170
= ( singleton @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(951,plain,
! [SV129: $i,SV171: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV171 @ SV129 ) @ SV129 ) )
= $false )
| ( ( subset @ SV129 @ SV171 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[900]) ).
thf(952,plain,
! [SV129: $i,SV171: $i] :
( ( ( ~ ~ ( in @ ( sK13_C @ SV171 @ SV129 ) @ SV171 ) )
= $false )
| ( ( subset @ SV129 @ SV171 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[900]) ).
thf(953,plain,
! [SV172: $i,SV130: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ SV130 )
| ( in @ SV218 @ SV172 ) )
= $true )
| ( ( subset @ SV130 @ SV172 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(954,plain,
! [SV131: $i,SV173: $i] :
( ( ( ~ ( in @ ( sK25_C @ SV173 @ SV131 ) @ SV131 ) )
= $false )
| ( ( disjoint @ SV131 @ SV173 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(955,plain,
! [SV131: $i,SV173: $i] :
( ( ( ~ ( in @ ( sK25_C @ SV173 @ SV131 ) @ SV173 ) )
= $false )
| ( ( disjoint @ SV131 @ SV173 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(956,plain,
! [SV174: $i,SV132: $i,SV206: $i] :
( ( ( ~ ( in @ SV206 @ SV132 ) )
= $true )
| ( ( ~ ( in @ SV206 @ SV174 ) )
= $true )
| ( ( ~ ( disjoint @ SV132 @ SV174 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(957,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV60 ) )
| ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV175 ) ) )
| ~ ( ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV60 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV175 ) ) )
= $false )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(958,plain,
! [SV176: $i,SV60: $i,SV200: $i] :
( ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false )
| ( ( ~ ( ~ ! [SY435: $i] :
( ~ ( in @ SY435 @ SV200 )
| ( SY435 = SV60 )
| ( SY435 = SV176 ) )
| ~ ~ ( ~ ! [SY436: $i] :
( ( SY436 != SV60 )
| ( in @ SY436 @ SV200 ) )
| ~ ! [SY437: $i] :
( ( SY437 != SV176 )
| ( in @ SY437 @ SV200 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(959,plain,
! [SV177: $i,SV133: $i] :
( ( ( SV133 = empty_set )
= $true )
| ( ( SV133
= ( singleton @ SV177 ) )
= $true )
| ( ( subset @ SV133 @ ( singleton @ SV177 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(960,plain,
! [SV207: $i] :
( ( ( ( SV207 != empty_set ) )
= $true )
| ( ( ! [SY440: $i] : ( subset @ SV207 @ ( singleton @ SY440 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(961,plain,
! [SV219: $i,SV208: $i] :
( ( ( SV208
!= ( singleton @ SV219 ) )
| ( subset @ SV208 @ ( singleton @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(962,plain,
! [SV180: $i,SV136: $i] :
( ( ( SV136 = empty_set )
= $true )
| ( ( SV136
= ( singleton @ SV180 ) )
= $true )
| ( ( subset @ SV136 @ ( singleton @ SV180 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(963,plain,
! [SV209: $i] :
( ( ( ( SV209 != empty_set ) )
= $true )
| ( ( ! [SY442: $i] : ( subset @ SV209 @ ( singleton @ SY442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(964,plain,
! [SV220: $i,SV210: $i] :
( ( ( SV210
!= ( singleton @ SV220 ) )
| ( subset @ SV210 @ ( singleton @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(965,plain,
! [SV221: $i,SV201: $i,SV101: $i,SV61: $i] :
( ( ( ( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SV201 @ SV221 ) ) )
= $true )
| ( ( SV61 = SV201 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(966,plain,
! [SV211: $i,SV202: $i,SV101: $i,SV61: $i] :
( ( ( ( ( ordered_pair @ SV61 @ SV101 )
!= ( ordered_pair @ SV202 @ SV211 ) ) )
= $true )
| ( ( SV101 = SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(967,plain,
! [SV181: $i,SV137: $i] :
( ( ( subset @ SV137 @ SV181 )
= $false )
| ( ( ~ ( subset @ SV181 @ SV137 ) )
= $true )
| ( ( SV137 = SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(968,plain,
! [SV222: $i,SV212: $i] :
( ( ( SV212 != SV222 )
| ( subset @ SV212 @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(969,plain,
! [SV223: $i,SV213: $i] :
( ( ( SV213 != SV223 )
| ( subset @ SV223 @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(970,plain,
! [SV182: $i,SV138: $i] :
( ( ( subset @ SV138 @ SV182 )
= $false )
| ( ( SV138 = SV182 )
= $true )
| ( ( proper_subset @ SV138 @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(971,plain,
! [SV224: $i,SV214: $i] :
( ( ~ ( proper_subset @ SV214 @ SV224 )
| ( SV214 != SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(972,plain,
! [SV225: $i,SV215: $i] :
( ( ~ ( proper_subset @ SV215 @ SV225 )
| ( subset @ SV215 @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(973,plain,
! [SV141: $i,SV185: $i] :
( ( ( ~ ( ! [SY415: $i] :
( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SY415 )
| ~ ( in @ SY415 @ SV141 ) )
| ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) ) )
= $false )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(974,plain,
! [SV141: $i,SV185: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ ( sK11_SY201 @ SV185 @ SV141 ) )
| ~ ( in @ ( sK11_SY201 @ SV185 @ SV141 ) @ SV141 ) )
| ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) ) )
= $false )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(975,plain,
! [SV186: $i,SV142: $i] :
( ( ( ~ ! [SY416: $i] :
( ! [SY375: $i] :
( ~ ( in @ SY416 @ SY375 )
| ~ ( in @ SY375 @ SV142 ) )
| ( in @ SY416 @ SV186 ) )
| ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV186 )
| ~ ( ~ ( in @ SY418 @ ( sK9_D @ SY418 @ SV186 @ SV142 ) )
| ~ ( in @ ( sK9_D @ SY418 @ SV186 @ SV142 ) @ SV142 ) ) ) )
= $false )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(976,plain,
! [SV62: $i,SV102: $i] :
( ( ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
= $false )
| ( ( ~ ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 ) )
= $true )
| ( ( SV62 = SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(977,plain,
! [SV143: $i,SV187: $i] :
( ( ( in @ SV187 @ SV143 )
= $false )
| ( ( ( set_difference @ SV143 @ ( singleton @ SV187 ) )
= SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(978,plain,
! [SV148: $i,SV189: $i,SV54: $i] :
( ( ( in @ SV54 @ SV189 )
= $false )
| ( ( ~ ( in @ SV148 @ SV189 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV54 @ SV148 ) @ SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(979,plain,
! [SV226: $i,SV216: $i,SV54: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV54 @ SV216 ) @ SV226 )
| ( in @ SV54 @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(980,plain,
! [SV227: $i,SV217: $i,SV54: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV54 @ SV217 ) @ SV227 )
| ( in @ SV217 @ SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(981,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) ) )
= $false )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[932]) ).
thf(982,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
| ~ ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) ) ) )
= $false )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[932]) ).
thf(983,plain,
! [SV191: $i,SV150: $i,SV55: $i] :
( ( ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV55 )
| ( in @ SY419 @ SV150 )
| ( in @ SY419 @ SV191 ) )
| ~ ~ ( ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV191 )
| ( in @ SY420 @ SV55 ) )
| ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV191 )
| ~ ( in @ SY421 @ SV150 ) ) ) )
= $false )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(984,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) ) ) )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[934]) ).
thf(985,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 )
| ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) ) )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[934]) ).
thf(986,plain,
! [SV152: $i,SV56: $i,SV193: $i] :
( ( ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV193 )
| ( in @ SY422 @ SV56 )
| ( in @ SY422 @ SV152 ) )
| ~ ~ ( ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV56 )
| ( in @ SY423 @ SV193 ) )
| ~ ! [SY424: $i] :
( ~ ( in @ SY424 @ SV152 )
| ( in @ SY424 @ SV193 ) ) ) )
= $false )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(987,plain,
! [SV203: $i,SV154: $i,SV114: $i] :
( ( ( disjoint @ SV114 @ SV154 )
= $false )
| ( ( in @ SV203 @ ( set_intersection2 @ SV114 @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(988,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) ) )
= $false )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(989,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
| ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) ) ) )
= $false )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(990,plain,
! [SV195: $i,SV160: $i,SV57: $i] :
( ( ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SV57 )
| ~ ( in @ SY425 @ SV160 )
| ( in @ SY425 @ SV195 ) )
| ~ ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV195 )
| ( in @ SY426 @ SV57 ) )
| ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV195 )
| ( in @ SY427 @ SV160 ) ) ) )
= $false )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(991,plain,
! [SV121: $i,SV161: $i] :
( ( ( ~ ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
| ~ ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 ) )
= $true )
| ( ( SV161
= ( powerset @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[940]) ).
thf(992,plain,
! [SV121: $i,SV161: $i] :
( ( ( ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
| ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 ) )
= $true )
| ( ( SV161
= ( powerset @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(993,plain,
! [SV122: $i,SV162: $i] :
( ( ( ~ ! [SY396: $i] :
( ~ ( in @ SY396 @ SV162 )
| ( subset @ SY396 @ SV122 ) ) )
= $false )
| ( ( SV162
= ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(994,plain,
! [SV162: $i,SV122: $i] :
( ( ( ~ ! [SY397: $i] :
( ~ ( subset @ SY397 @ SV122 )
| ( in @ SY397 @ SV162 ) ) )
= $false )
| ( ( SV162
= ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(995,plain,
! [SV196: $i,SV167: $i,SV58: $i] :
( ( ( ~ ( ! [SY428: $i,SY429: $i] :
( ~ ( in @ SY428 @ SV58 )
| ~ ( in @ SY429 @ SV167 )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ SY428 @ SY429 ) ) )
| ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) ) )
= $false )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[943]) ).
thf(996,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) @ SV167 ) )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) ) ) )
| ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) ) )
= $false )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[943]) ).
thf(997,plain,
! [SV197: $i,SV168: $i,SV58: $i] :
( ( ( ~ ! [SY430: $i] :
( ! [SY403: $i,SY404: $i] :
( ~ ( in @ SY403 @ SV58 )
| ~ ( in @ SY404 @ SV168 )
| ( SY430
!= ( ordered_pair @ SY403 @ SY404 ) ) )
| ( in @ SY430 @ SV197 ) )
| ~ ! [SY433: $i] :
( ~ ( in @ SY433 @ SV197 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY433 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SY433 @ SV197 @ SV168 @ SV58 ) @ SV168 ) )
| ( SY433
!= ( ordered_pair @ ( sK14_E @ SY433 @ SV197 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SY433 @ SV197 @ SV168 @ SV58 ) ) ) ) ) )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(998,plain,
! [SV205: $i,SV100: $i,SV198: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV198 ) )
= $true )
| ( ( ~ ( in @ SV100 @ SV205 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV198 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(999,plain,
! [SV228: $i,SV100: $i,SV59: $i] :
( ( ! [SY450: $i] :
~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV228 @ SY450 ) )
| ( in @ SV59 @ SV228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1000,plain,
! [SV229: $i,SV100: $i,SV59: $i] :
( ( ! [SY451: $i] :
( ~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV229 @ SY451 ) )
| ( in @ SV100 @ SY451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1001,plain,
! [SV127: $i,SV169: $i] :
( ( ( ( ( sK23_C @ SV169 @ SV127 )
!= SV127 )
| ~ ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 ) )
= $true )
| ( ( SV169
= ( singleton @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[948]) ).
thf(1002,plain,
! [SV127: $i,SV169: $i] :
( ( ( ( ( sK23_C @ SV169 @ SV127 )
= SV127 )
| ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 ) )
= $true )
| ( ( SV169
= ( singleton @ SV127 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[949]) ).
thf(1003,plain,
! [SV170: $i,SV128: $i] :
( ( ( ~ ! [SY406: $i] :
( ( SY406 != SV128 )
| ( in @ SY406 @ SV170 ) ) )
= $false )
| ( ( SV170
= ( singleton @ SV128 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1004,plain,
! [SV128: $i,SV170: $i] :
( ( ( ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV170 )
| ( SY407 = SV128 ) ) )
= $false )
| ( ( SV170
= ( singleton @ SV128 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(1005,plain,
! [SV129: $i,SV171: $i] :
( ( ( in @ ( sK13_C @ SV171 @ SV129 ) @ SV129 )
= $true )
| ( ( subset @ SV129 @ SV171 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(1006,plain,
! [SV129: $i,SV171: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV171 @ SV129 ) @ SV171 ) )
= $true )
| ( ( subset @ SV129 @ SV171 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[952]) ).
thf(1007,plain,
! [SV172: $i,SV130: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ SV130 ) )
= $true )
| ( ( in @ SV218 @ SV172 )
= $true )
| ( ( subset @ SV130 @ SV172 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1008,plain,
! [SV131: $i,SV173: $i] :
( ( ( in @ ( sK25_C @ SV173 @ SV131 ) @ SV131 )
= $true )
| ( ( disjoint @ SV131 @ SV173 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[954]) ).
thf(1009,plain,
! [SV131: $i,SV173: $i] :
( ( ( in @ ( sK25_C @ SV173 @ SV131 ) @ SV173 )
= $true )
| ( ( disjoint @ SV131 @ SV173 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[955]) ).
thf(1010,plain,
! [SV174: $i,SV132: $i,SV206: $i] :
( ( ( in @ SV206 @ SV132 )
= $false )
| ( ( ~ ( in @ SV206 @ SV174 ) )
= $true )
| ( ( ~ ( disjoint @ SV132 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1011,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV60 ) )
| ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV175 ) ) ) )
= $false )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1012,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ~ ( ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV60 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV175 ) ) )
= $false )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[957]) ).
thf(1013,plain,
! [SV176: $i,SV60: $i,SV200: $i] :
( ( ( ~ ! [SY435: $i] :
( ~ ( in @ SY435 @ SV200 )
| ( SY435 = SV60 )
| ( SY435 = SV176 ) )
| ~ ~ ( ~ ! [SY436: $i] :
( ( SY436 != SV60 )
| ( in @ SY436 @ SV200 ) )
| ~ ! [SY437: $i] :
( ( SY437 != SV176 )
| ( in @ SY437 @ SV200 ) ) ) )
= $false )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[958]) ).
thf(1014,plain,
! [SV207: $i] :
( ( ( SV207 = empty_set )
= $false )
| ( ( ! [SY440: $i] : ( subset @ SV207 @ ( singleton @ SY440 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1015,plain,
! [SV219: $i,SV208: $i] :
( ( ( ( SV208
!= ( singleton @ SV219 ) ) )
= $true )
| ( ( subset @ SV208 @ ( singleton @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(1016,plain,
! [SV209: $i] :
( ( ( SV209 = empty_set )
= $false )
| ( ( ! [SY442: $i] : ( subset @ SV209 @ ( singleton @ SY442 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1017,plain,
! [SV220: $i,SV210: $i] :
( ( ( ( SV210
!= ( singleton @ SV220 ) ) )
= $true )
| ( ( subset @ SV210 @ ( singleton @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1018,plain,
! [SV221: $i,SV201: $i,SV101: $i,SV61: $i] :
( ( ( ( ordered_pair @ SV61 @ SV101 )
= ( ordered_pair @ SV201 @ SV221 ) )
= $false )
| ( ( SV61 = SV201 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1019,plain,
! [SV211: $i,SV202: $i,SV101: $i,SV61: $i] :
( ( ( ( ordered_pair @ SV61 @ SV101 )
= ( ordered_pair @ SV202 @ SV211 ) )
= $false )
| ( ( SV101 = SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1020,plain,
! [SV137: $i,SV181: $i] :
( ( ( subset @ SV181 @ SV137 )
= $false )
| ( ( subset @ SV137 @ SV181 )
= $false )
| ( ( SV137 = SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1021,plain,
! [SV222: $i,SV212: $i] :
( ( ( ( SV212 != SV222 ) )
= $true )
| ( ( subset @ SV212 @ SV222 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1022,plain,
! [SV223: $i,SV213: $i] :
( ( ( ( SV213 != SV223 ) )
= $true )
| ( ( subset @ SV223 @ SV213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1023,plain,
! [SV224: $i,SV214: $i] :
( ( ( ~ ( proper_subset @ SV214 @ SV224 ) )
= $true )
| ( ( ( SV214 != SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1024,plain,
! [SV225: $i,SV215: $i] :
( ( ( ~ ( proper_subset @ SV215 @ SV225 ) )
= $true )
| ( ( subset @ SV215 @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1025,plain,
! [SV141: $i,SV185: $i] :
( ( ( ! [SY415: $i] :
( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SY415 )
| ~ ( in @ SY415 @ SV141 ) )
| ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1026,plain,
! [SV141: $i,SV185: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ ( sK11_SY201 @ SV185 @ SV141 ) )
| ~ ( in @ ( sK11_SY201 @ SV185 @ SV141 ) @ SV141 ) )
| ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(1027,plain,
! [SV186: $i,SV142: $i] :
( ( ( ~ ! [SY416: $i] :
( ! [SY375: $i] :
( ~ ( in @ SY416 @ SY375 )
| ~ ( in @ SY375 @ SV142 ) )
| ( in @ SY416 @ SV186 ) ) )
= $false )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1028,plain,
! [SV142: $i,SV186: $i] :
( ( ( ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV186 )
| ~ ( ~ ( in @ SY418 @ ( sK9_D @ SY418 @ SV186 @ SV142 ) )
| ~ ( in @ ( sK9_D @ SY418 @ SV186 @ SV142 ) @ SV142 ) ) ) )
= $false )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1029,plain,
! [SV62: $i,SV102: $i] :
( ( ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV102 )
= $false )
| ( ( in @ ( sK5_C @ SV102 @ SV62 ) @ SV62 )
= $false )
| ( ( SV62 = SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1030,plain,
! [SV54: $i,SV189: $i,SV148: $i] :
( ( ( in @ SV148 @ SV189 )
= $false )
| ( ( in @ SV54 @ SV189 )
= $false )
| ( ( subset @ ( unordered_pair @ SV54 @ SV148 ) @ SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1031,plain,
! [SV226: $i,SV216: $i,SV54: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV54 @ SV216 ) @ SV226 ) )
= $true )
| ( ( in @ SV54 @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1032,plain,
! [SV227: $i,SV217: $i,SV54: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV54 @ SV217 ) @ SV227 ) )
= $true )
| ( ( in @ SV217 @ SV227 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1033,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[981]) ).
thf(1034,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
| ~ ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) ) ) )
= $true )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[982]) ).
thf(1035,plain,
! [SV191: $i,SV150: $i,SV55: $i] :
( ( ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV55 )
| ( in @ SY419 @ SV150 )
| ( in @ SY419 @ SV191 ) ) )
= $false )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1036,plain,
! [SV150: $i,SV55: $i,SV191: $i] :
( ( ( ~ ~ ( ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV191 )
| ( in @ SY420 @ SV55 ) )
| ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV191 )
| ~ ( in @ SY421 @ SV150 ) ) ) )
= $false )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1037,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) ) ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[984]) ).
thf(1038,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 )
| ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1039,plain,
! [SV152: $i,SV56: $i,SV193: $i] :
( ( ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV193 )
| ( in @ SY422 @ SV56 )
| ( in @ SY422 @ SV152 ) ) )
= $false )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1040,plain,
! [SV152: $i,SV193: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV56 )
| ( in @ SY423 @ SV193 ) )
| ~ ! [SY424: $i] :
( ~ ( in @ SY424 @ SV152 )
| ( in @ SY424 @ SV193 ) ) ) )
= $false )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[986]) ).
thf(1041,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
= $true )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1042,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
| ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) ) ) )
= $true )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1043,plain,
! [SV195: $i,SV160: $i,SV57: $i] :
( ( ( ~ ! [SY425: $i] :
( ~ ( in @ SY425 @ SV57 )
| ~ ( in @ SY425 @ SV160 )
| ( in @ SY425 @ SV195 ) ) )
= $false )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1044,plain,
! [SV160: $i,SV57: $i,SV195: $i] :
( ( ( ~ ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV195 )
| ( in @ SY426 @ SV57 ) )
| ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV195 )
| ( in @ SY427 @ SV160 ) ) ) )
= $false )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1045,plain,
! [SV121: $i,SV161: $i] :
( ( ( ~ ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 ) )
= $true )
| ( ( ~ ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 ) )
= $true )
| ( ( SV161
= ( powerset @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[991]) ).
thf(1046,plain,
! [SV121: $i,SV161: $i] :
( ( ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
= $true )
| ( ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 )
= $true )
| ( ( SV161
= ( powerset @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1047,plain,
! [SV122: $i,SV162: $i] :
( ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ SV162 )
| ( subset @ SY396 @ SV122 ) ) )
= $true )
| ( ( SV162
= ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1048,plain,
! [SV162: $i,SV122: $i] :
( ( ( ! [SY397: $i] :
( ~ ( subset @ SY397 @ SV122 )
| ( in @ SY397 @ SV162 ) ) )
= $true )
| ( ( SV162
= ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1049,plain,
! [SV196: $i,SV167: $i,SV58: $i] :
( ( ( ! [SY428: $i,SY429: $i] :
( ~ ( in @ SY428 @ SV58 )
| ~ ( in @ SY429 @ SV167 )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ SY428 @ SY429 ) ) )
| ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(1050,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) @ SV167 ) )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) ) ) )
| ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(1051,plain,
! [SV197: $i,SV168: $i,SV58: $i] :
( ( ( ~ ! [SY430: $i] :
( ! [SY403: $i,SY404: $i] :
( ~ ( in @ SY403 @ SV58 )
| ~ ( in @ SY404 @ SV168 )
| ( SY430
!= ( ordered_pair @ SY403 @ SY404 ) ) )
| ( in @ SY430 @ SV197 ) ) )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[997]) ).
thf(1052,plain,
! [SV58: $i,SV168: $i,SV197: $i] :
( ( ( ~ ! [SY433: $i] :
( ~ ( in @ SY433 @ SV197 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY433 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SY433 @ SV197 @ SV168 @ SV58 ) @ SV168 ) )
| ( SY433
!= ( ordered_pair @ ( sK14_E @ SY433 @ SV197 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SY433 @ SV197 @ SV168 @ SV58 ) ) ) ) ) )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[997]) ).
thf(1053,plain,
! [SV205: $i,SV100: $i,SV198: $i,SV59: $i] :
( ( ( in @ SV59 @ SV198 )
= $false )
| ( ( ~ ( in @ SV100 @ SV205 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV198 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1054,plain,
! [SV228: $i,SV100: $i,SV59: $i] :
( ( ( ! [SY450: $i] :
~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV228 @ SY450 ) ) )
= $true )
| ( ( in @ SV59 @ SV228 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1055,plain,
! [SV230: $i,SV229: $i,SV100: $i,SV59: $i] :
( ( ~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV229 @ SV230 ) )
| ( in @ SV100 @ SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1056,plain,
! [SV127: $i,SV169: $i] :
( ( ( ( ( sK23_C @ SV169 @ SV127 )
!= SV127 ) )
= $true )
| ( ( ~ ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 ) )
= $true )
| ( ( SV169
= ( singleton @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1057,plain,
! [SV127: $i,SV169: $i] :
( ( ( ( sK23_C @ SV169 @ SV127 )
= SV127 )
= $true )
| ( ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 )
= $true )
| ( ( SV169
= ( singleton @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1058,plain,
! [SV170: $i,SV128: $i] :
( ( ( ! [SY406: $i] :
( ( SY406 != SV128 )
| ( in @ SY406 @ SV170 ) ) )
= $true )
| ( ( SV170
= ( singleton @ SV128 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1059,plain,
! [SV128: $i,SV170: $i] :
( ( ( ! [SY407: $i] :
( ~ ( in @ SY407 @ SV170 )
| ( SY407 = SV128 ) ) )
= $true )
| ( ( SV170
= ( singleton @ SV128 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1060,plain,
! [SV129: $i,SV171: $i] :
( ( ( in @ ( sK13_C @ SV171 @ SV129 ) @ SV171 )
= $false )
| ( ( subset @ SV129 @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1061,plain,
! [SV172: $i,SV130: $i,SV218: $i] :
( ( ( in @ SV218 @ SV130 )
= $false )
| ( ( in @ SV218 @ SV172 )
= $true )
| ( ( subset @ SV130 @ SV172 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1062,plain,
! [SV132: $i,SV174: $i,SV206: $i] :
( ( ( in @ SV206 @ SV174 )
= $false )
| ( ( in @ SV206 @ SV132 )
= $false )
| ( ( ~ ( disjoint @ SV132 @ SV174 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1063,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV60 ) )
| ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV175 ) ) ) )
= $true )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1011]) ).
thf(1064,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV60 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV175 ) )
= $true )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1012]) ).
thf(1065,plain,
! [SV176: $i,SV60: $i,SV200: $i] :
( ( ( ~ ! [SY435: $i] :
( ~ ( in @ SY435 @ SV200 )
| ( SY435 = SV60 )
| ( SY435 = SV176 ) ) )
= $false )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1013]) ).
thf(1066,plain,
! [SV176: $i,SV200: $i,SV60: $i] :
( ( ( ~ ~ ( ~ ! [SY436: $i] :
( ( SY436 != SV60 )
| ( in @ SY436 @ SV200 ) )
| ~ ! [SY437: $i] :
( ( SY437 != SV176 )
| ( in @ SY437 @ SV200 ) ) ) )
= $false )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1013]) ).
thf(1067,plain,
! [SV231: $i,SV207: $i] :
( ( ( subset @ SV207 @ ( singleton @ SV231 ) )
= $true )
| ( ( SV207 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1068,plain,
! [SV219: $i,SV208: $i] :
( ( ( SV208
= ( singleton @ SV219 ) )
= $false )
| ( ( subset @ SV208 @ ( singleton @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1069,plain,
! [SV232: $i,SV209: $i] :
( ( ( subset @ SV209 @ ( singleton @ SV232 ) )
= $true )
| ( ( SV209 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1070,plain,
! [SV220: $i,SV210: $i] :
( ( ( SV210
= ( singleton @ SV220 ) )
= $false )
| ( ( subset @ SV210 @ ( singleton @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1071,plain,
! [SV222: $i,SV212: $i] :
( ( ( SV212 = SV222 )
= $false )
| ( ( subset @ SV212 @ SV222 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1072,plain,
! [SV223: $i,SV213: $i] :
( ( ( SV213 = SV223 )
= $false )
| ( ( subset @ SV223 @ SV213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1073,plain,
! [SV224: $i,SV214: $i] :
( ( ( proper_subset @ SV214 @ SV224 )
= $false )
| ( ( ( SV214 != SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1074,plain,
! [SV225: $i,SV215: $i] :
( ( ( proper_subset @ SV215 @ SV225 )
= $false )
| ( ( subset @ SV215 @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1075,plain,
! [SV141: $i,SV185: $i] :
( ( ( ! [SY415: $i] :
( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SY415 )
| ~ ( in @ SY415 @ SV141 ) ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1076,plain,
! [SV141: $i,SV185: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ ( sK11_SY201 @ SV185 @ SV141 ) )
| ~ ( in @ ( sK11_SY201 @ SV185 @ SV141 ) @ SV141 ) ) )
= $true )
| ( ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1077,plain,
! [SV186: $i,SV142: $i] :
( ( ( ! [SY416: $i] :
( ! [SY375: $i] :
( ~ ( in @ SY416 @ SY375 )
| ~ ( in @ SY375 @ SV142 ) )
| ( in @ SY416 @ SV186 ) ) )
= $true )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1078,plain,
! [SV142: $i,SV186: $i] :
( ( ( ! [SY418: $i] :
( ~ ( in @ SY418 @ SV186 )
| ~ ( ~ ( in @ SY418 @ ( sK9_D @ SY418 @ SV186 @ SV142 ) )
| ~ ( in @ ( sK9_D @ SY418 @ SV186 @ SV142 ) @ SV142 ) ) ) )
= $true )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1028]) ).
thf(1079,plain,
! [SV226: $i,SV216: $i,SV54: $i] :
( ( ( subset @ ( unordered_pair @ SV54 @ SV216 ) @ SV226 )
= $false )
| ( ( in @ SV54 @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1080,plain,
! [SV227: $i,SV217: $i,SV54: $i] :
( ( ( subset @ ( unordered_pair @ SV54 @ SV217 ) @ SV227 )
= $false )
| ( ( in @ SV217 @ SV227 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1081,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 ) )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1082,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
| ~ ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) ) )
= $false )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1034]) ).
thf(1083,plain,
! [SV191: $i,SV150: $i,SV55: $i] :
( ( ( ! [SY419: $i] :
( ~ ( in @ SY419 @ SV55 )
| ( in @ SY419 @ SV150 )
| ( in @ SY419 @ SV191 ) ) )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1035]) ).
thf(1084,plain,
! [SV150: $i,SV55: $i,SV191: $i] :
( ( ( ~ ( ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV191 )
| ( in @ SY420 @ SV55 ) )
| ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV191 )
| ~ ( in @ SY421 @ SV150 ) ) ) )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1036]) ).
thf(1085,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) ) )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1086,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
= $true )
| ( ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 )
| ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1087,plain,
! [SV152: $i,SV56: $i,SV193: $i] :
( ( ( ! [SY422: $i] :
( ~ ( in @ SY422 @ SV193 )
| ( in @ SY422 @ SV56 )
| ( in @ SY422 @ SV152 ) ) )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1039]) ).
thf(1088,plain,
! [SV152: $i,SV193: $i,SV56: $i] :
( ( ( ~ ( ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV56 )
| ( in @ SY423 @ SV193 ) )
| ~ ! [SY424: $i] :
( ~ ( in @ SY424 @ SV152 )
| ( in @ SY424 @ SV193 ) ) ) )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1089,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 ) )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
= $true )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1041]) ).
thf(1090,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
| ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) ) )
= $false )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1091,plain,
! [SV195: $i,SV160: $i,SV57: $i] :
( ( ( ! [SY425: $i] :
( ~ ( in @ SY425 @ SV57 )
| ~ ( in @ SY425 @ SV160 )
| ( in @ SY425 @ SV195 ) ) )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1092,plain,
! [SV160: $i,SV57: $i,SV195: $i] :
( ( ( ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV195 )
| ( in @ SY426 @ SV57 ) )
| ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV195 )
| ( in @ SY427 @ SV160 ) ) ) )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1044]) ).
thf(1093,plain,
! [SV121: $i,SV161: $i] :
( ( ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
= $false )
| ( ( ~ ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 ) )
= $true )
| ( ( SV161
= ( powerset @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1094,plain,
! [SV122: $i,SV162: $i,SV233: $i] :
( ( ( ~ ( in @ SV233 @ SV162 )
| ( subset @ SV233 @ SV122 ) )
= $true )
| ( ( SV162
= ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1095,plain,
! [SV162: $i,SV122: $i,SV234: $i] :
( ( ( ~ ( subset @ SV234 @ SV122 )
| ( in @ SV234 @ SV162 ) )
= $true )
| ( ( SV162
= ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1096,plain,
! [SV196: $i,SV167: $i,SV58: $i] :
( ( ( ! [SY428: $i,SY429: $i] :
( ~ ( in @ SY428 @ SV58 )
| ~ ( in @ SY429 @ SV167 )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ SY428 @ SY429 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1097,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) @ SV167 ) )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) ) ) ) )
= $true )
| ( ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1050]) ).
thf(1098,plain,
! [SV197: $i,SV168: $i,SV58: $i] :
( ( ( ! [SY430: $i] :
( ! [SY403: $i,SY404: $i] :
( ~ ( in @ SY403 @ SV58 )
| ~ ( in @ SY404 @ SV168 )
| ( SY430
!= ( ordered_pair @ SY403 @ SY404 ) ) )
| ( in @ SY430 @ SV197 ) ) )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1051]) ).
thf(1099,plain,
! [SV58: $i,SV168: $i,SV197: $i] :
( ( ( ! [SY433: $i] :
( ~ ( in @ SY433 @ SV197 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY433 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SY433 @ SV197 @ SV168 @ SV58 ) @ SV168 ) )
| ( SY433
!= ( ordered_pair @ ( sK14_E @ SY433 @ SV197 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SY433 @ SV197 @ SV168 @ SV58 ) ) ) ) ) )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1100,plain,
! [SV198: $i,SV59: $i,SV205: $i,SV100: $i] :
( ( ( in @ SV100 @ SV205 )
= $false )
| ( ( in @ SV59 @ SV198 )
= $false )
| ( ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV198 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1101,plain,
! [SV235: $i,SV228: $i,SV100: $i,SV59: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV228 @ SV235 ) ) )
= $true )
| ( ( in @ SV59 @ SV228 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1102,plain,
! [SV230: $i,SV229: $i,SV100: $i,SV59: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV229 @ SV230 ) ) )
= $true )
| ( ( in @ SV100 @ SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1103,plain,
! [SV127: $i,SV169: $i] :
( ( ( ( sK23_C @ SV169 @ SV127 )
= SV127 )
= $false )
| ( ( ~ ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 ) )
= $true )
| ( ( SV169
= ( singleton @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1104,plain,
! [SV170: $i,SV128: $i,SV236: $i] :
( ( ( ( SV236 != SV128 )
| ( in @ SV236 @ SV170 ) )
= $true )
| ( ( SV170
= ( singleton @ SV128 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1105,plain,
! [SV128: $i,SV170: $i,SV237: $i] :
( ( ( ~ ( in @ SV237 @ SV170 )
| ( SV237 = SV128 ) )
= $true )
| ( ( SV170
= ( singleton @ SV128 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1106,plain,
! [SV206: $i,SV174: $i,SV132: $i] :
( ( ( disjoint @ SV132 @ SV174 )
= $false )
| ( ( in @ SV206 @ SV132 )
= $false )
| ( ( in @ SV206 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1107,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV60 ) )
| ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV175 ) ) )
= $false )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1108,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
= $true )
| ( ( ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV60 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV175 ) )
= $true )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1109,plain,
! [SV176: $i,SV60: $i,SV200: $i] :
( ( ( ! [SY435: $i] :
( ~ ( in @ SY435 @ SV200 )
| ( SY435 = SV60 )
| ( SY435 = SV176 ) ) )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1065]) ).
thf(1110,plain,
! [SV176: $i,SV200: $i,SV60: $i] :
( ( ( ~ ( ~ ! [SY436: $i] :
( ( SY436 != SV60 )
| ( in @ SY436 @ SV200 ) )
| ~ ! [SY437: $i] :
( ( SY437 != SV176 )
| ( in @ SY437 @ SV200 ) ) ) )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1111,plain,
! [SV224: $i,SV214: $i] :
( ( ( SV214 = SV224 )
= $false )
| ( ( proper_subset @ SV214 @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1112,plain,
! [SV238: $i,SV141: $i,SV185: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV238 )
| ~ ( in @ SV238 @ SV141 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1113,plain,
! [SV141: $i,SV185: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ ( sK11_SY201 @ SV185 @ SV141 ) )
| ~ ( in @ ( sK11_SY201 @ SV185 @ SV141 ) @ SV141 ) )
= $false )
| ( ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1114,plain,
! [SV186: $i,SV142: $i,SV239: $i] :
( ( ( ! [SY452: $i] :
( ~ ( in @ SV239 @ SY452 )
| ~ ( in @ SY452 @ SV142 ) )
| ( in @ SV239 @ SV186 ) )
= $true )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1115,plain,
! [SV142: $i,SV186: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ SV186 )
| ~ ( ~ ( in @ SV240 @ ( sK9_D @ SV240 @ SV186 @ SV142 ) )
| ~ ( in @ ( sK9_D @ SV240 @ SV186 @ SV142 ) @ SV142 ) ) )
= $true )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1116,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 ) )
= $true )
| ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1117,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) ) )
= $false )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1118,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) ) )
= $false )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1119,plain,
! [SV191: $i,SV150: $i,SV55: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV55 )
| ( in @ SV241 @ SV150 )
| ( in @ SV241 @ SV191 ) )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1120,plain,
! [SV150: $i,SV55: $i,SV191: $i] :
( ( ( ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV191 )
| ( in @ SY420 @ SV55 ) )
| ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV191 )
| ~ ( in @ SY421 @ SV150 ) ) )
= $false )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1121,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 ) ) )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1085]) ).
thf(1122,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) ) )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1085]) ).
thf(1123,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 )
= $true )
| ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 )
= $true )
| ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1124,plain,
! [SV152: $i,SV56: $i,SV193: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV193 )
| ( in @ SV242 @ SV56 )
| ( in @ SV242 @ SV152 ) )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1125,plain,
! [SV152: $i,SV193: $i,SV56: $i] :
( ( ( ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV56 )
| ( in @ SY423 @ SV193 ) )
| ~ ! [SY424: $i] :
( ~ ( in @ SY424 @ SV152 )
| ( in @ SY424 @ SV193 ) ) )
= $false )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1126,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 ) )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 ) )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
= $true )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1127,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) ) )
= $false )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1128,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ~ ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) ) )
= $false )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1129,plain,
! [SV195: $i,SV160: $i,SV57: $i,SV243: $i] :
( ( ( ~ ( in @ SV243 @ SV57 )
| ~ ( in @ SV243 @ SV160 )
| ( in @ SV243 @ SV195 ) )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1130,plain,
! [SV160: $i,SV57: $i,SV195: $i] :
( ( ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV195 )
| ( in @ SY426 @ SV57 ) )
| ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV195 )
| ( in @ SY427 @ SV160 ) ) )
= $false )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1131,plain,
! [SV121: $i,SV161: $i] :
( ( ( subset @ ( sK21_C @ SV161 @ SV121 ) @ SV121 )
= $false )
| ( ( in @ ( sK21_C @ SV161 @ SV121 ) @ SV161 )
= $false )
| ( ( SV161
= ( powerset @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1132,plain,
! [SV122: $i,SV162: $i,SV233: $i] :
( ( ( ~ ( in @ SV233 @ SV162 ) )
= $true )
| ( ( subset @ SV233 @ SV122 )
= $true )
| ( ( SV162
= ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1133,plain,
! [SV162: $i,SV122: $i,SV234: $i] :
( ( ( ~ ( subset @ SV234 @ SV122 ) )
= $true )
| ( ( in @ SV234 @ SV162 )
= $true )
| ( ( SV162
= ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1134,plain,
! [SV196: $i,SV167: $i,SV58: $i,SV244: $i] :
( ( ( ! [SY453: $i] :
( ~ ( in @ SV244 @ SV58 )
| ~ ( in @ SY453 @ SV167 )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ SV244 @ SY453 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1135,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) @ SV167 ) )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) ) ) )
= $false )
| ( ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1136,plain,
! [SV197: $i,SV245: $i,SV168: $i,SV58: $i] :
( ( ( ! [SY454: $i,SY455: $i] :
( ~ ( in @ SY454 @ SV58 )
| ~ ( in @ SY455 @ SV168 )
| ( SV245
!= ( ordered_pair @ SY454 @ SY455 ) ) )
| ( in @ SV245 @ SV197 ) )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1137,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( ~ ( in @ SV246 @ SV197 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV168 ) )
| ( SV246
!= ( ordered_pair @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) ) ) ) )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1138,plain,
! [SV235: $i,SV228: $i,SV100: $i,SV59: $i] :
( ( ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV228 @ SV235 ) )
= $false )
| ( ( in @ SV59 @ SV228 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1139,plain,
! [SV230: $i,SV229: $i,SV100: $i,SV59: $i] :
( ( ( in @ ( ordered_pair @ SV59 @ SV100 ) @ ( cartesian_product2 @ SV229 @ SV230 ) )
= $false )
| ( ( in @ SV100 @ SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1140,plain,
! [SV127: $i,SV169: $i] :
( ( ( in @ ( sK23_C @ SV169 @ SV127 ) @ SV169 )
= $false )
| ( ( ( sK23_C @ SV169 @ SV127 )
= SV127 )
= $false )
| ( ( SV169
= ( singleton @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1141,plain,
! [SV170: $i,SV128: $i,SV236: $i] :
( ( ( ( SV236 != SV128 ) )
= $true )
| ( ( in @ SV236 @ SV170 )
= $true )
| ( ( SV170
= ( singleton @ SV128 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1142,plain,
! [SV128: $i,SV170: $i,SV237: $i] :
( ( ( ~ ( in @ SV237 @ SV170 ) )
= $true )
| ( ( SV237 = SV128 )
= $true )
| ( ( SV170
= ( singleton @ SV128 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1143,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV60 ) ) )
= $false )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1144,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV175 ) ) )
= $false )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1107]) ).
thf(1145,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV60 )
= $true )
| ( ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV175 )
= $true )
| ( ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
= $true )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1146,plain,
! [SV176: $i,SV60: $i,SV200: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV200 )
| ( SV247 = SV60 )
| ( SV247 = SV176 ) )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1147,plain,
! [SV176: $i,SV200: $i,SV60: $i] :
( ( ( ~ ! [SY436: $i] :
( ( SY436 != SV60 )
| ( in @ SY436 @ SV200 ) )
| ~ ! [SY437: $i] :
( ( SY437 != SV176 )
| ( in @ SY437 @ SV200 ) ) )
= $false )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1148,plain,
! [SV238: $i,SV141: $i,SV185: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV238 ) )
= $true )
| ( ( ~ ( in @ SV238 @ SV141 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1149,plain,
! [SV141: $i,SV185: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ ( sK11_SY201 @ SV185 @ SV141 ) ) )
= $false )
| ( ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1150,plain,
! [SV141: $i,SV185: $i] :
( ( ( ~ ( in @ ( sK11_SY201 @ SV185 @ SV141 ) @ SV141 ) )
= $false )
| ( ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1151,plain,
! [SV186: $i,SV142: $i,SV239: $i] :
( ( ( ! [SY452: $i] :
( ~ ( in @ SV239 @ SY452 )
| ~ ( in @ SY452 @ SV142 ) ) )
= $true )
| ( ( in @ SV239 @ SV186 )
= $true )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1152,plain,
! [SV142: $i,SV186: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ SV186 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV240 @ ( sK9_D @ SV240 @ SV186 @ SV142 ) )
| ~ ( in @ ( sK9_D @ SV240 @ SV186 @ SV142 ) @ SV142 ) ) )
= $true )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1153,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
= $false )
| ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1154,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1117]) ).
thf(1155,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
| ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1118]) ).
thf(1156,plain,
! [SV191: $i,SV150: $i,SV55: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV55 )
| ( in @ SV241 @ SV150 ) )
= $true )
| ( ( in @ SV241 @ SV191 )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1157,plain,
! [SV150: $i,SV55: $i,SV191: $i] :
( ( ( ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV191 )
| ( in @ SY420 @ SV55 ) ) )
= $false )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1120]) ).
thf(1158,plain,
! [SV55: $i,SV150: $i,SV191: $i] :
( ( ( ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV191 )
| ~ ( in @ SY421 @ SV150 ) ) )
= $false )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1120]) ).
thf(1159,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1160,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
| ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1161,plain,
! [SV152: $i,SV56: $i,SV193: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV193 ) )
= $true )
| ( ( ( in @ SV242 @ SV56 )
| ( in @ SV242 @ SV152 ) )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1162,plain,
! [SV152: $i,SV193: $i,SV56: $i] :
( ( ( ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV56 )
| ( in @ SY423 @ SV193 ) ) )
= $false )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1163,plain,
! [SV56: $i,SV193: $i,SV152: $i] :
( ( ( ~ ! [SY424: $i] :
( ~ ( in @ SY424 @ SV152 )
| ( in @ SY424 @ SV193 ) ) )
= $false )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1164,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
= $false )
| ( ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 ) )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
= $true )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1165,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
= $true )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1127]) ).
thf(1166,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
| ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
= $true )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1167,plain,
! [SV195: $i,SV160: $i,SV57: $i,SV243: $i] :
( ( ( ~ ( in @ SV243 @ SV57 )
| ~ ( in @ SV243 @ SV160 ) )
= $true )
| ( ( in @ SV243 @ SV195 )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1168,plain,
! [SV160: $i,SV57: $i,SV195: $i] :
( ( ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV195 )
| ( in @ SY426 @ SV57 ) ) )
= $false )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1169,plain,
! [SV57: $i,SV160: $i,SV195: $i] :
( ( ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV195 )
| ( in @ SY427 @ SV160 ) ) )
= $false )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1170,plain,
! [SV122: $i,SV162: $i,SV233: $i] :
( ( ( in @ SV233 @ SV162 )
= $false )
| ( ( subset @ SV233 @ SV122 )
= $true )
| ( ( SV162
= ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1171,plain,
! [SV162: $i,SV122: $i,SV234: $i] :
( ( ( subset @ SV234 @ SV122 )
= $false )
| ( ( in @ SV234 @ SV162 )
= $true )
| ( ( SV162
= ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1172,plain,
! [SV196: $i,SV167: $i,SV248: $i,SV58: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV58 )
| ~ ( in @ SV248 @ SV167 )
| ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ SV244 @ SV248 ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1173,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) @ SV167 ) ) )
= $false )
| ( ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1135]) ).
thf(1174,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) ) ) )
= $false )
| ( ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1135]) ).
thf(1175,plain,
! [SV197: $i,SV245: $i,SV168: $i,SV58: $i] :
( ( ( ! [SY454: $i,SY455: $i] :
( ~ ( in @ SY454 @ SV58 )
| ~ ( in @ SY455 @ SV168 )
| ( SV245
!= ( ordered_pair @ SY454 @ SY455 ) ) ) )
= $true )
| ( ( in @ SV245 @ SV197 )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1176,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( ~ ( in @ SV246 @ SV197 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV168 ) )
| ( SV246
!= ( ordered_pair @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) ) ) ) )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1177,plain,
! [SV170: $i,SV128: $i,SV236: $i] :
( ( ( SV236 = SV128 )
= $false )
| ( ( in @ SV236 @ SV170 )
= $true )
| ( ( SV170
= ( singleton @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1178,plain,
! [SV128: $i,SV170: $i,SV237: $i] :
( ( ( in @ SV237 @ SV170 )
= $false )
| ( ( SV237 = SV128 )
= $true )
| ( ( SV170
= ( singleton @ SV128 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1179,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV60 ) )
= $true )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1143]) ).
thf(1180,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
| ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV175 ) )
= $true )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1144]) ).
thf(1181,plain,
! [SV176: $i,SV60: $i,SV200: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV200 ) )
= $true )
| ( ( ( SV247 = SV60 )
| ( SV247 = SV176 ) )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1182,plain,
! [SV176: $i,SV200: $i,SV60: $i] :
( ( ( ~ ! [SY436: $i] :
( ( SY436 != SV60 )
| ( in @ SY436 @ SV200 ) ) )
= $false )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1183,plain,
! [SV60: $i,SV200: $i,SV176: $i] :
( ( ( ~ ! [SY437: $i] :
( ( SY437 != SV176 )
| ( in @ SY437 @ SV200 ) ) )
= $false )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1184,plain,
! [SV238: $i,SV141: $i,SV185: $i] :
( ( ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV238 )
= $false )
| ( ( ~ ( in @ SV238 @ SV141 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1185,plain,
! [SV141: $i,SV185: $i] :
( ( ( in @ ( sK10_C @ SV185 @ SV141 ) @ ( sK11_SY201 @ SV185 @ SV141 ) )
= $true )
| ( ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1149]) ).
thf(1186,plain,
! [SV141: $i,SV185: $i] :
( ( ( in @ ( sK11_SY201 @ SV185 @ SV141 ) @ SV141 )
= $true )
| ( ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1187,plain,
! [SV186: $i,SV142: $i,SV249: $i,SV239: $i] :
( ( ( ~ ( in @ SV239 @ SV249 )
| ~ ( in @ SV249 @ SV142 ) )
= $true )
| ( ( in @ SV239 @ SV186 )
= $true )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1188,plain,
! [SV142: $i,SV186: $i,SV240: $i] :
( ( ( in @ SV240 @ SV186 )
= $false )
| ( ( ~ ( ~ ( in @ SV240 @ ( sK9_D @ SV240 @ SV186 @ SV142 ) )
| ~ ( in @ ( sK9_D @ SV240 @ SV186 @ SV142 ) @ SV142 ) ) )
= $true )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1189,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 )
= $false )
| ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
= $true )
| ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
= $false )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1190,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV55 )
= $true )
| ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 )
= $true )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1191,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 ) )
= $true )
| ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 )
= $true )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1192,plain,
! [SV191: $i,SV150: $i,SV55: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV55 ) )
= $true )
| ( ( in @ SV241 @ SV150 )
= $true )
| ( ( in @ SV241 @ SV191 )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1193,plain,
! [SV150: $i,SV55: $i,SV191: $i] :
( ( ( ! [SY420: $i] :
( ~ ( in @ SY420 @ SV191 )
| ( in @ SY420 @ SV55 ) ) )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1157]) ).
thf(1194,plain,
! [SV55: $i,SV150: $i,SV191: $i] :
( ( ( ! [SY421: $i] :
( ~ ( in @ SY421 @ SV191 )
| ~ ( in @ SY421 @ SV150 ) ) )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1195,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1196,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1197,plain,
! [SV152: $i,SV56: $i,SV193: $i,SV242: $i] :
( ( ( in @ SV242 @ SV193 )
= $false )
| ( ( ( in @ SV242 @ SV56 )
| ( in @ SV242 @ SV152 ) )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1198,plain,
! [SV152: $i,SV193: $i,SV56: $i] :
( ( ( ! [SY423: $i] :
( ~ ( in @ SY423 @ SV56 )
| ( in @ SY423 @ SV193 ) ) )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1162]) ).
thf(1199,plain,
! [SV56: $i,SV193: $i,SV152: $i] :
( ( ( ! [SY424: $i] :
( ~ ( in @ SY424 @ SV152 )
| ( in @ SY424 @ SV193 ) ) )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1163]) ).
thf(1200,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
= $false )
| ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
= $false )
| ( ( ~ ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 ) )
= $true )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1201,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
= $true )
| ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 )
= $true )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1202,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
= $true )
| ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 )
= $true )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1203,plain,
! [SV195: $i,SV160: $i,SV57: $i,SV243: $i] :
( ( ( ~ ( in @ SV243 @ SV57 ) )
= $true )
| ( ( ~ ( in @ SV243 @ SV160 ) )
= $true )
| ( ( in @ SV243 @ SV195 )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1204,plain,
! [SV160: $i,SV57: $i,SV195: $i] :
( ( ( ! [SY426: $i] :
( ~ ( in @ SY426 @ SV195 )
| ( in @ SY426 @ SV57 ) ) )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1168]) ).
thf(1205,plain,
! [SV57: $i,SV160: $i,SV195: $i] :
( ( ( ! [SY427: $i] :
( ~ ( in @ SY427 @ SV195 )
| ( in @ SY427 @ SV160 ) ) )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1169]) ).
thf(1206,plain,
! [SV196: $i,SV167: $i,SV248: $i,SV58: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV58 )
| ~ ( in @ SV248 @ SV167 ) )
= $true )
| ( ( ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ SV244 @ SV248 ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1207,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) @ SV167 ) ) )
= $true )
| ( ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1173]) ).
thf(1208,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( ( sK16_D @ SV196 @ SV167 @ SV58 )
= ( ordered_pair @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) ) )
= $true )
| ( ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1174]) ).
thf(1209,plain,
! [SV197: $i,SV245: $i,SV168: $i,SV58: $i,SV250: $i] :
( ( ( ! [SY456: $i] :
( ~ ( in @ SV250 @ SV58 )
| ~ ( in @ SY456 @ SV168 )
| ( SV245
!= ( ordered_pair @ SV250 @ SY456 ) ) ) )
= $true )
| ( ( in @ SV245 @ SV197 )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1210,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( in @ SV246 @ SV197 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV168 ) )
| ( SV246
!= ( ordered_pair @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) ) ) ) )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1211,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 ) )
= $true )
| ( ( ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV60 ) )
= $true )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1212,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ~ ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 ) )
= $true )
| ( ( ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV175 ) )
= $true )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1213,plain,
! [SV176: $i,SV60: $i,SV200: $i,SV247: $i] :
( ( ( in @ SV247 @ SV200 )
= $false )
| ( ( ( SV247 = SV60 )
| ( SV247 = SV176 ) )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1181]) ).
thf(1214,plain,
! [SV176: $i,SV200: $i,SV60: $i] :
( ( ( ! [SY436: $i] :
( ( SY436 != SV60 )
| ( in @ SY436 @ SV200 ) ) )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1215,plain,
! [SV60: $i,SV200: $i,SV176: $i] :
( ( ( ! [SY437: $i] :
( ( SY437 != SV176 )
| ( in @ SY437 @ SV200 ) ) )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1183]) ).
thf(1216,plain,
! [SV185: $i,SV141: $i,SV238: $i] :
( ( ( in @ SV238 @ SV141 )
= $false )
| ( ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV238 )
= $false )
| ( ( ~ ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 ) )
= $true )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1217,plain,
! [SV186: $i,SV142: $i,SV249: $i,SV239: $i] :
( ( ( ~ ( in @ SV239 @ SV249 ) )
= $true )
| ( ( ~ ( in @ SV249 @ SV142 ) )
= $true )
| ( ( in @ SV239 @ SV186 )
= $true )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1218,plain,
! [SV142: $i,SV186: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ ( sK9_D @ SV240 @ SV186 @ SV142 ) )
| ~ ( in @ ( sK9_D @ SV240 @ SV186 @ SV142 ) @ SV142 ) )
= $false )
| ( ( in @ SV240 @ SV186 )
= $false )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1219,plain,
! [SV55: $i,SV149: $i,SV190: $i] :
( ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV149 )
= $false )
| ( ( in @ ( sK8_D @ SV190 @ SV149 @ SV55 ) @ SV190 )
= $true )
| ( ( SV190
= ( set_difference @ SV55 @ SV149 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1220,plain,
! [SV191: $i,SV150: $i,SV55: $i,SV241: $i] :
( ( ( in @ SV241 @ SV55 )
= $false )
| ( ( in @ SV241 @ SV150 )
= $true )
| ( ( in @ SV241 @ SV191 )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1221,plain,
! [SV150: $i,SV55: $i,SV191: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV191 )
| ( in @ SV251 @ SV55 ) )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1222,plain,
! [SV55: $i,SV150: $i,SV191: $i,SV252: $i] :
( ( ( ~ ( in @ SV252 @ SV191 )
| ~ ( in @ SV252 @ SV150 ) )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1223,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1224,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1225,plain,
! [SV193: $i,SV152: $i,SV56: $i,SV242: $i] :
( ( ( in @ SV242 @ SV56 )
= $true )
| ( ( in @ SV242 @ SV152 )
= $true )
| ( ( in @ SV242 @ SV193 )
= $false )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1226,plain,
! [SV152: $i,SV193: $i,SV56: $i,SV253: $i] :
( ( ( ~ ( in @ SV253 @ SV56 )
| ( in @ SV253 @ SV193 ) )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1227,plain,
! [SV56: $i,SV193: $i,SV152: $i,SV254: $i] :
( ( ( ~ ( in @ SV254 @ SV152 )
| ( in @ SV254 @ SV193 ) )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1228,plain,
! [SV57: $i,SV159: $i,SV194: $i] :
( ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV194 )
= $false )
| ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV57 )
= $false )
| ( ( in @ ( sK12_D @ SV194 @ SV159 @ SV57 ) @ SV159 )
= $false )
| ( ( SV194
= ( set_intersection2 @ SV57 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1229,plain,
! [SV195: $i,SV160: $i,SV57: $i,SV243: $i] :
( ( ( in @ SV243 @ SV57 )
= $false )
| ( ( ~ ( in @ SV243 @ SV160 ) )
= $true )
| ( ( in @ SV243 @ SV195 )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1230,plain,
! [SV160: $i,SV57: $i,SV195: $i,SV255: $i] :
( ( ( ~ ( in @ SV255 @ SV195 )
| ( in @ SV255 @ SV57 ) )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1231,plain,
! [SV57: $i,SV160: $i,SV195: $i,SV256: $i] :
( ( ( ~ ( in @ SV256 @ SV195 )
| ( in @ SV256 @ SV160 ) )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1232,plain,
! [SV196: $i,SV167: $i,SV248: $i,SV58: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV58 ) )
= $true )
| ( ( ~ ( in @ SV248 @ SV167 ) )
= $true )
| ( ( ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ SV244 @ SV248 ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1233,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) @ SV167 ) )
= $false )
| ( ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1234,plain,
! [SV197: $i,SV245: $i,SV168: $i,SV257: $i,SV58: $i,SV250: $i] :
( ( ( ~ ( in @ SV250 @ SV58 )
| ~ ( in @ SV257 @ SV168 )
| ( SV245
!= ( ordered_pair @ SV250 @ SV257 ) ) )
= $true )
| ( ( in @ SV245 @ SV197 )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1235,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV168 ) )
| ( SV246
!= ( ordered_pair @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) ) ) )
= $false )
| ( ( in @ SV246 @ SV197 )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1236,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
= $false )
| ( ( ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV60 ) )
= $true )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1237,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
= $false )
| ( ( ( ( sK20_D @ SV199 @ SV175 @ SV60 )
!= SV175 ) )
= $true )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1238,plain,
! [SV200: $i,SV176: $i,SV60: $i,SV247: $i] :
( ( ( SV247 = SV60 )
= $true )
| ( ( SV247 = SV176 )
= $true )
| ( ( in @ SV247 @ SV200 )
= $false )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1239,plain,
! [SV176: $i,SV200: $i,SV60: $i,SV258: $i] :
( ( ( ( SV258 != SV60 )
| ( in @ SV258 @ SV200 ) )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1240,plain,
! [SV60: $i,SV200: $i,SV176: $i,SV259: $i] :
( ( ( ( SV259 != SV176 )
| ( in @ SV259 @ SV200 ) )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1241,plain,
! [SV238: $i,SV141: $i,SV185: $i] :
( ( ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV185 )
= $false )
| ( ( in @ ( sK10_C @ SV185 @ SV141 ) @ SV238 )
= $false )
| ( ( in @ SV238 @ SV141 )
= $false )
| ( ( SV185
= ( union @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1242,plain,
! [SV186: $i,SV142: $i,SV249: $i,SV239: $i] :
( ( ( in @ SV239 @ SV249 )
= $false )
| ( ( ~ ( in @ SV249 @ SV142 ) )
= $true )
| ( ( in @ SV239 @ SV186 )
= $true )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1243,plain,
! [SV142: $i,SV186: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ ( sK9_D @ SV240 @ SV186 @ SV142 ) ) )
= $false )
| ( ( in @ SV240 @ SV186 )
= $false )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1218]) ).
thf(1244,plain,
! [SV142: $i,SV186: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV240 @ SV186 @ SV142 ) @ SV142 ) )
= $false )
| ( ( in @ SV240 @ SV186 )
= $false )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1218]) ).
thf(1245,plain,
! [SV150: $i,SV55: $i,SV191: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV191 ) )
= $true )
| ( ( in @ SV251 @ SV55 )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1246,plain,
! [SV55: $i,SV150: $i,SV191: $i,SV252: $i] :
( ( ( ~ ( in @ SV252 @ SV191 ) )
= $true )
| ( ( ~ ( in @ SV252 @ SV150 ) )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1247,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV56 )
= $false )
| ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1248,plain,
! [SV56: $i,SV151: $i,SV192: $i] :
( ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV151 )
= $false )
| ( ( in @ ( sK19_D @ SV192 @ SV151 @ SV56 ) @ SV192 )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1224]) ).
thf(1249,plain,
! [SV152: $i,SV193: $i,SV56: $i,SV253: $i] :
( ( ( ~ ( in @ SV253 @ SV56 ) )
= $true )
| ( ( in @ SV253 @ SV193 )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1250,plain,
! [SV56: $i,SV193: $i,SV152: $i,SV254: $i] :
( ( ( ~ ( in @ SV254 @ SV152 ) )
= $true )
| ( ( in @ SV254 @ SV193 )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1251,plain,
! [SV195: $i,SV57: $i,SV160: $i,SV243: $i] :
( ( ( in @ SV243 @ SV160 )
= $false )
| ( ( in @ SV243 @ SV57 )
= $false )
| ( ( in @ SV243 @ SV195 )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1252,plain,
! [SV160: $i,SV57: $i,SV195: $i,SV255: $i] :
( ( ( ~ ( in @ SV255 @ SV195 ) )
= $true )
| ( ( in @ SV255 @ SV57 )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1253,plain,
! [SV57: $i,SV160: $i,SV195: $i,SV256: $i] :
( ( ( ~ ( in @ SV256 @ SV195 ) )
= $true )
| ( ( in @ SV256 @ SV160 )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1231]) ).
thf(1254,plain,
! [SV196: $i,SV167: $i,SV248: $i,SV58: $i,SV244: $i] :
( ( ( in @ SV244 @ SV58 )
= $false )
| ( ( ~ ( in @ SV248 @ SV167 ) )
= $true )
| ( ( ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ SV244 @ SV248 ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1255,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ SV58 ) )
= $false )
| ( ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1233]) ).
thf(1256,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) @ SV167 ) )
= $false )
| ( ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1233]) ).
thf(1257,plain,
! [SV197: $i,SV245: $i,SV168: $i,SV257: $i,SV58: $i,SV250: $i] :
( ( ( ~ ( in @ SV250 @ SV58 )
| ~ ( in @ SV257 @ SV168 ) )
= $true )
| ( ( ( SV245
!= ( ordered_pair @ SV250 @ SV257 ) ) )
= $true )
| ( ( in @ SV245 @ SV197 )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1258,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV168 ) ) )
= $false )
| ( ( in @ SV246 @ SV197 )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1235]) ).
thf(1259,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( ( SV246
!= ( ordered_pair @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) ) ) )
= $false )
| ( ( in @ SV246 @ SV197 )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1235]) ).
thf(1260,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV60 )
= $false )
| ( ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
= $false )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1261,plain,
! [SV60: $i,SV175: $i,SV199: $i] :
( ( ( ( sK20_D @ SV199 @ SV175 @ SV60 )
= SV175 )
= $false )
| ( ( in @ ( sK20_D @ SV199 @ SV175 @ SV60 ) @ SV199 )
= $false )
| ( ( SV199
= ( unordered_pair @ SV60 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1262,plain,
! [SV176: $i,SV200: $i,SV60: $i,SV258: $i] :
( ( ( ( SV258 != SV60 ) )
= $true )
| ( ( in @ SV258 @ SV200 )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1263,plain,
! [SV60: $i,SV200: $i,SV176: $i,SV259: $i] :
( ( ( ( SV259 != SV176 ) )
= $true )
| ( ( in @ SV259 @ SV200 )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1264,plain,
! [SV186: $i,SV239: $i,SV142: $i,SV249: $i] :
( ( ( in @ SV249 @ SV142 )
= $false )
| ( ( in @ SV239 @ SV249 )
= $false )
| ( ( in @ SV239 @ SV186 )
= $true )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1265,plain,
! [SV142: $i,SV186: $i,SV240: $i] :
( ( ( in @ SV240 @ ( sK9_D @ SV240 @ SV186 @ SV142 ) )
= $true )
| ( ( in @ SV240 @ SV186 )
= $false )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1266,plain,
! [SV142: $i,SV186: $i,SV240: $i] :
( ( ( in @ ( sK9_D @ SV240 @ SV186 @ SV142 ) @ SV142 )
= $true )
| ( ( in @ SV240 @ SV186 )
= $false )
| ( ( SV186
= ( union @ SV142 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1244]) ).
thf(1267,plain,
! [SV150: $i,SV55: $i,SV191: $i,SV251: $i] :
( ( ( in @ SV251 @ SV191 )
= $false )
| ( ( in @ SV251 @ SV55 )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1268,plain,
! [SV55: $i,SV150: $i,SV191: $i,SV252: $i] :
( ( ( in @ SV252 @ SV191 )
= $false )
| ( ( ~ ( in @ SV252 @ SV150 ) )
= $true )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1269,plain,
! [SV152: $i,SV193: $i,SV56: $i,SV253: $i] :
( ( ( in @ SV253 @ SV56 )
= $false )
| ( ( in @ SV253 @ SV193 )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1270,plain,
! [SV56: $i,SV193: $i,SV152: $i,SV254: $i] :
( ( ( in @ SV254 @ SV152 )
= $false )
| ( ( in @ SV254 @ SV193 )
= $true )
| ( ( SV193
= ( set_union2 @ SV56 @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1271,plain,
! [SV160: $i,SV57: $i,SV195: $i,SV255: $i] :
( ( ( in @ SV255 @ SV195 )
= $false )
| ( ( in @ SV255 @ SV57 )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1272,plain,
! [SV57: $i,SV160: $i,SV195: $i,SV256: $i] :
( ( ( in @ SV256 @ SV195 )
= $false )
| ( ( in @ SV256 @ SV160 )
= $true )
| ( ( SV195
= ( set_intersection2 @ SV57 @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1273,plain,
! [SV196: $i,SV58: $i,SV244: $i,SV167: $i,SV248: $i] :
( ( ( in @ SV248 @ SV167 )
= $false )
| ( ( in @ SV244 @ SV58 )
= $false )
| ( ( ( ( sK16_D @ SV196 @ SV167 @ SV58 )
!= ( ordered_pair @ SV244 @ SV248 ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1274,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( in @ ( sK17_SY205 @ SV196 @ SV167 @ SV58 ) @ SV58 )
= $true )
| ( ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1255]) ).
thf(1275,plain,
! [SV58: $i,SV167: $i,SV196: $i] :
( ( ( in @ ( sK18_SY207 @ SV196 @ SV167 @ SV58 ) @ SV167 )
= $true )
| ( ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1256]) ).
thf(1276,plain,
! [SV197: $i,SV245: $i,SV168: $i,SV257: $i,SV58: $i,SV250: $i] :
( ( ( ~ ( in @ SV250 @ SV58 ) )
= $true )
| ( ( ~ ( in @ SV257 @ SV168 ) )
= $true )
| ( ( ( SV245
!= ( ordered_pair @ SV250 @ SV257 ) ) )
= $true )
| ( ( in @ SV245 @ SV197 )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1277,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV168 ) ) )
= $true )
| ( ( in @ SV246 @ SV197 )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1258]) ).
thf(1278,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( SV246
= ( ordered_pair @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) ) )
= $true )
| ( ( in @ SV246 @ SV197 )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1259]) ).
thf(1279,plain,
! [SV176: $i,SV200: $i,SV60: $i,SV258: $i] :
( ( ( SV258 = SV60 )
= $false )
| ( ( in @ SV258 @ SV200 )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1280,plain,
! [SV60: $i,SV200: $i,SV176: $i,SV259: $i] :
( ( ( SV259 = SV176 )
= $false )
| ( ( in @ SV259 @ SV200 )
= $true )
| ( ( SV200
= ( unordered_pair @ SV60 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1281,plain,
! [SV55: $i,SV191: $i,SV150: $i,SV252: $i] :
( ( ( in @ SV252 @ SV150 )
= $false )
| ( ( in @ SV252 @ SV191 )
= $false )
| ( ( SV191
= ( set_difference @ SV55 @ SV150 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1282,plain,
! [SV248: $i,SV244: $i,SV58: $i,SV167: $i,SV196: $i] :
( ( ( ( sK16_D @ SV196 @ SV167 @ SV58 )
= ( ordered_pair @ SV244 @ SV248 ) )
= $false )
| ( ( in @ SV244 @ SV58 )
= $false )
| ( ( in @ SV248 @ SV167 )
= $false )
| ( ( ~ ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 ) )
= $true )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1283,plain,
! [SV197: $i,SV245: $i,SV168: $i,SV257: $i,SV58: $i,SV250: $i] :
( ( ( in @ SV250 @ SV58 )
= $false )
| ( ( ~ ( in @ SV257 @ SV168 ) )
= $true )
| ( ( ( SV245
!= ( ordered_pair @ SV250 @ SV257 ) ) )
= $true )
| ( ( in @ SV245 @ SV197 )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1284,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( ~ ( in @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV168 ) )
= $false )
| ( ( in @ SV246 @ SV197 )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1277]) ).
thf(1285,plain,
! [SV244: $i,SV248: $i,SV58: $i,SV167: $i,SV196: $i] :
( ( ( in @ ( sK16_D @ SV196 @ SV167 @ SV58 ) @ SV196 )
= $false )
| ( ( in @ SV248 @ SV167 )
= $false )
| ( ( in @ SV244 @ SV58 )
= $false )
| ( ( ( sK16_D @ SV196 @ SV167 @ SV58 )
= ( ordered_pair @ SV244 @ SV248 ) )
= $false )
| ( ( SV196
= ( cartesian_product2 @ SV58 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1286,plain,
! [SV197: $i,SV245: $i,SV58: $i,SV250: $i,SV168: $i,SV257: $i] :
( ( ( in @ SV257 @ SV168 )
= $false )
| ( ( in @ SV250 @ SV58 )
= $false )
| ( ( ( SV245
!= ( ordered_pair @ SV250 @ SV257 ) ) )
= $true )
| ( ( in @ SV245 @ SV197 )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1287,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( ~ ( in @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV58 ) )
= $false )
| ( ( in @ SV246 @ SV197 )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1284]) ).
thf(1288,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( ~ ( in @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV168 ) )
= $false )
| ( ( in @ SV246 @ SV197 )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1284]) ).
thf(1289,plain,
! [SV197: $i,SV168: $i,SV58: $i,SV257: $i,SV250: $i,SV245: $i] :
( ( ( SV245
= ( ordered_pair @ SV250 @ SV257 ) )
= $false )
| ( ( in @ SV250 @ SV58 )
= $false )
| ( ( in @ SV257 @ SV168 )
= $false )
| ( ( in @ SV245 @ SV197 )
= $true )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1290,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( in @ ( sK14_E @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV58 )
= $true )
| ( ( in @ SV246 @ SV197 )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1287]) ).
thf(1291,plain,
! [SV58: $i,SV168: $i,SV197: $i,SV246: $i] :
( ( ( in @ ( sK15_SY202 @ SV246 @ SV197 @ SV168 @ SV58 ) @ SV168 )
= $true )
| ( ( in @ SV246 @ SV197 )
= $false )
| ( ( SV197
= ( cartesian_product2 @ SV58 @ SV168 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1288]) ).
thf(1292,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[281,1291,1290,1289,1285,1281,1280,1279,1278,1275,1274,1272,1271,1270,1269,1267,1266,1265,1264,1261,1260,1251,1248,1247,1241,1238,1228,1225,1220,1219,1208,1202,1201,1190,1189,1186,1185,1178,1177,1171,1170,1145,1140,1139,1138,1131,1123,1111,1106,1100,1080,1079,1074,1072,1071,1070,1069,1068,1067,1061,1060,1057,1046,1030,1029,1020,1019,1018,1009,1008,1005,987,977,970,962,959,939,927,923,922,910,909,892,891,890,889,883,882,881,880,871,870,869,868,867,866,817,815,807,801,757,740,739,738,737,736,733,732,731,726,669,668,667,663,660,657,656,654,650,648,645,600,589,585,573,563,509,505,504,503,502,495,491,488,486,485,479,471,439,438,437,436,434,433,431,430,419,413,402,348,341,340,339,338,337,336,335,334,333,332,331]) ).
thf(1293,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(1294,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(1295,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(1296,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(1297,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(1298,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(1299,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(1300,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(1301,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(1302,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ D )
| ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) ) )
& ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ A @ C ) )
& ! [C: $i,D: $i] :
( ~ ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( in @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(1303,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(1304,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(1305,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(1306,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(1307,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(1308,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(1309,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(1310,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(1311,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(1312,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(1313,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ! [D: $i] :
( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(1314,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(1315,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(1316,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(1317,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( in @ A @ C )
| ~ ( in @ B @ C )
| ( subset @ ( unordered_pair @ A @ B ) @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ A @ C ) )
& ! [B: $i,C: $i] :
( ~ ( subset @ ( unordered_pair @ A @ B ) @ C )
| ( in @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(1318,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(1319,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(1320,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK25_C @ B @ A ) @ A )
& ( in @ ( sK25_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(1321,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(1322,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(1323,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(1324,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(1325,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(1326,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK24_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(1327,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(1328,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(1329,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(1330,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(1331,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(1332,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(1333,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(1334,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(1335,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(1336,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(1337,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(1338,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(1339,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(1340,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(1341,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(1342,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(1343,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(1344,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(1345,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK23_C @ B @ A )
!= A )
| ~ ( in @ ( sK23_C @ B @ A ) @ B ) )
& ( ( ( sK23_C @ B @ A )
= A )
| ( in @ ( sK23_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(1346,plain,
( ( ! [A: $i] :
( ( in @ ( sK22_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(1347,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK21_C @ B @ A ) @ B )
| ~ ( subset @ ( sK21_C @ B @ A ) @ A ) )
& ( ( in @ ( sK21_C @ B @ A ) @ B )
| ( subset @ ( sK21_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(1348,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK20_D @ C @ B @ A ) @ C )
| ( ( sK20_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK20_D @ C @ B @ A ) @ C )
| ( ( sK20_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK20_D @ C @ B @ A ) @ C )
| ( ( sK20_D @ C @ B @ A )
= A )
| ( ( sK20_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(1349,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK19_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK19_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK19_D @ C @ B @ A ) @ C )
| ( in @ ( sK19_D @ C @ B @ A ) @ A )
| ( in @ ( sK19_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(1350,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY203: $i,SY204: $i] :
( ~ ( in @ SY203 @ A )
| ~ ( in @ SY204 @ B )
| ( ( sK16_D @ C @ B @ A )
!= ( ordered_pair @ SY203 @ SY204 ) ) )
| ~ ( in @ ( sK16_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK17_SY205 @ C @ B @ A ) @ A )
& ( in @ ( sK18_SY207 @ C @ B @ A ) @ B )
& ( ( sK16_D @ C @ B @ A )
= ( ordered_pair @ ( sK17_SY205 @ C @ B @ A ) @ ( sK18_SY207 @ C @ B @ A ) ) ) )
| ( in @ ( sK16_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK14_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK15_SY202 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK14_E @ D @ C @ B @ A ) @ ( sK15_SY202 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(1351,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK13_C @ B @ A ) @ A )
& ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(1352,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK12_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK12_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK12_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK12_D @ C @ B @ A ) @ A )
| ( in @ ( sK12_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK12_D @ C @ B @ A ) @ B )
| ( in @ ( sK12_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(1353,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY200: $i] :
( ~ ( in @ ( sK10_C @ B @ A ) @ SY200 )
| ~ ( in @ SY200 @ A ) )
| ~ ( in @ ( sK10_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK10_C @ B @ A ) @ ( sK11_SY201 @ B @ A ) )
& ( in @ ( sK11_SY201 @ B @ A ) @ A ) )
| ( in @ ( sK10_C @ B @ A ) @ B ) ) )
| ( B
= ( union @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( union @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
( ~ ( in @ C @ D )
| ~ ( in @ D @ A ) )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( ( in @ C @ ( sK9_D @ C @ B @ A ) )
& ( in @ ( sK9_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(1354,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK8_D @ C @ B @ A ) @ A )
| ( in @ ( sK8_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK8_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK8_D @ C @ B @ A ) @ A )
| ( in @ ( sK8_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK8_D @ C @ B @ A ) @ B )
| ( in @ ( sK8_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(1355,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(1356,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(1357,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(1358,plain,
$true = $true,
inference(copy,[status(thm)],[126]) ).
thf(1359,plain,
$true = $true,
inference(copy,[status(thm)],[125]) ).
thf(1360,plain,
$true = $true,
inference(copy,[status(thm)],[124]) ).
thf(1361,plain,
$true = $true,
inference(copy,[status(thm)],[123]) ).
thf(1362,plain,
$true = $true,
inference(copy,[status(thm)],[122]) ).
thf(1363,plain,
$true = $true,
inference(copy,[status(thm)],[121]) ).
thf(1364,plain,
$true = $true,
inference(copy,[status(thm)],[120]) ).
thf(1365,plain,
$true = $true,
inference(copy,[status(thm)],[119]) ).
thf(1366,plain,
$true = $true,
inference(copy,[status(thm)],[118]) ).
thf(1367,plain,
$true = $true,
inference(copy,[status(thm)],[117]) ).
thf(1368,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(1369,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(1370,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(1371,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(1372,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(1373,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(1374,plain,
( ( ! [A: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(1375,plain,
( ( empty @ sK7_A )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(1376,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(1377,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(1378,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(1379,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(1380,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(1381,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_C @ B @ A ) @ A )
| ~ ( in @ ( sK5_C @ B @ A ) @ B ) )
& ( ( in @ ( sK5_C @ B @ A ) @ A )
| ( in @ ( sK5_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(1382,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(1383,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(1384,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(1385,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(1386,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(1387,plain,
( ( ( in @ sK1_A @ sK3_SY197 )
& ( in @ sK2_SY194 @ sK4_SY199 )
& ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(1388,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY201 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK11_SY201 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK9_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1353]) ).
thf(1389,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1329]) ).
thf(1390,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1351]) ).
thf(1391,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK23_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK23_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1345]) ).
thf(1392,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1356]) ).
thf(1393,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1357]) ).
thf(1394,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ( in @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1302]) ).
thf(1395,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1316]) ).
thf(1396,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1352]) ).
thf(1397,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1347]) ).
thf(1398,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK5_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1381]) ).
thf(1399,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1333]) ).
thf(1400,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1313]) ).
thf(1401,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1349]) ).
thf(1402,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1344]) ).
thf(1403,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX2 )
| ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX0 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( subset @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
| ( in @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1317]) ).
thf(1404,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK20_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK20_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK20_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK20_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK20_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK20_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1348]) ).
thf(1405,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK22_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1346]) ).
thf(1406,plain,
( ( ~ ( ~ ~ ( ~ ( in @ sK1_A @ sK3_SY197 )
| ~ ( in @ sK2_SY194 @ sK4_SY199 ) )
| ~ ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1387]) ).
thf(1407,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK8_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1354]) ).
thf(1408,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1298]) ).
thf(1409,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK24_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1326]) ).
thf(1410,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1300]) ).
thf(1411,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1319]) ).
thf(1412,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1297]) ).
thf(1413,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1315]) ).
thf(1414,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1320]) ).
thf(1415,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK16_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK18_SY207 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK16_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK17_SY205 @ SX2 @ SX1 @ SX0 ) @ ( sK18_SY207 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK16_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i,SX5: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK15_SY202 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK14_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK15_SY202 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1350]) ).
thf(1416,plain,
! [SV260: $i] :
( ( ( ( singleton @ SV260 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1417,plain,
! [SV261: $i] :
( ( ! [SY457: $i] :
( ~ ( in @ SV261 @ SY457 )
| ( ( set_union2 @ ( singleton @ SV261 ) @ SY457 )
= SY457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1418,plain,
! [SV262: $i] :
( ( ! [SY458: $i] :
( ~ ( disjoint @ ( singleton @ SV262 ) @ SY458 )
| ~ ( in @ SV262 @ SY458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1419,plain,
! [SV263: $i] :
( ( ! [SY459: $i] :
( ( in @ SV263 @ SY459 )
| ( disjoint @ ( singleton @ SV263 ) @ SY459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1420,plain,
! [SV264: $i] :
( ( ! [SY460: $i] :
( ~ ( subset @ SV264 @ SY460 )
| ! [SY461: $i] :
( ( in @ SY461 @ SV264 )
| ( subset @ SV264 @ ( set_difference @ SY460 @ ( singleton @ SY461 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1421,plain,
! [SV265: $i] :
( ( ! [SY462: $i] :
( ~ ( in @ SV265 @ SY462 )
| ( subset @ SV265 @ ( union @ SY462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1422,plain,
! [SV266: $i] :
( ( ! [SY463: $i,SY464: $i,SY465: $i] :
( ( SV266 = SY465 )
| ( SV266 = SY464 )
| ( ( unordered_pair @ SV266 @ SY463 )
!= ( unordered_pair @ SY464 @ SY465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1423,plain,
! [SV267: $i] :
( ( ! [SY466: $i] :
( ~ ( subset @ SV267 @ SY466 )
| ( ( set_union2 @ SV267 @ SY466 )
= SY466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1424,plain,
! [SV268: $i] :
( ( ! [SY467: $i] : ( subset @ ( set_intersection2 @ SV268 @ SY467 ) @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1425,plain,
! [SV269: $i] :
( ( ! [SY468: $i,SY469: $i] :
( ~ ( subset @ SV269 @ SY468 )
| ~ ( subset @ SV269 @ SY469 )
| ( subset @ SV269 @ ( set_intersection2 @ SY468 @ SY469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1426,plain,
! [SV270: $i] :
( ( ! [SY470: $i,SY471: $i] :
( ~ ( subset @ SV270 @ SY470 )
| ~ ( subset @ SY470 @ SY471 )
| ( subset @ SV270 @ SY471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1427,plain,
! [SV271: $i] :
( ( ! [SY472: $i] :
( ~ ( subset @ SV271 @ SY472 )
| ! [SY473: $i] : ( subset @ ( set_intersection2 @ SV271 @ SY473 ) @ ( set_intersection2 @ SY472 @ SY473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1428,plain,
! [SV272: $i] :
( ( ! [SY474: $i] :
( ~ ( subset @ SV272 @ SY474 )
| ( ( set_intersection2 @ SV272 @ SY474 )
= SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1429,plain,
! [SV273: $i] :
( ( subset @ empty_set @ SV273 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1430,plain,
! [SV274: $i] :
( ( ! [SY475: $i] :
( ~ ( subset @ SV274 @ SY475 )
| ! [SY476: $i] : ( subset @ ( set_difference @ SV274 @ SY476 ) @ ( set_difference @ SY475 @ SY476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1431,plain,
! [SV275: $i] :
( ( ! [SY477: $i] : ( subset @ ( set_difference @ SV275 @ SY477 ) @ SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1432,plain,
! [SV276: $i] :
( ( ! [SY478: $i] :
( ( set_union2 @ SV276 @ ( set_difference @ SY478 @ SV276 ) )
= ( set_union2 @ SV276 @ SY478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1433,plain,
! [SV277: $i] :
( ( ~ ( subset @ SV277 @ empty_set )
| ( SV277 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1434,plain,
! [SV278: $i] :
( ( ! [SY479: $i] :
( ( set_difference @ ( set_union2 @ SV278 @ SY479 ) @ SY479 )
= ( set_difference @ SV278 @ SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1435,plain,
! [SV279: $i] :
( ( ! [SY480: $i] :
( ~ ( subset @ SV279 @ SY480 )
| ( SY480
= ( set_union2 @ SV279 @ ( set_difference @ SY480 @ SV279 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1436,plain,
! [SV280: $i] :
( ( ! [SY481: $i] :
( ~ ( in @ SV280 @ SY481 )
| ( ( set_union2 @ ( singleton @ SV280 ) @ SY481 )
= SY481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1437,plain,
! [SV281: $i] :
( ( ! [SY482: $i] :
( ( set_difference @ SV281 @ ( set_difference @ SV281 @ SY482 ) )
= ( set_intersection2 @ SV281 @ SY482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1438,plain,
! [SV282: $i] :
( ( ! [SY483: $i] :
( ~ ( proper_subset @ SY483 @ SV282 )
| ~ ( subset @ SV282 @ SY483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1439,plain,
! [SV283: $i] :
( ( ! [SY484: $i,SY485: $i] :
( ~ ( disjoint @ SY484 @ SY485 )
| ~ ( subset @ SV283 @ SY484 )
| ( disjoint @ SV283 @ SY485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1440,plain,
! [SV284: $i] :
( ( ( unordered_pair @ SV284 @ SV284 )
= ( singleton @ SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1441,plain,
! [SV285: $i] :
( ( ! [SY486: $i] :
( ~ ( subset @ ( singleton @ SV285 ) @ ( singleton @ SY486 ) )
| ( SV285 = SY486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1442,plain,
! [SV286: $i] :
( ( ! [SY487: $i] : ( subset @ SV286 @ ( set_union2 @ SV286 @ SY487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1443,plain,
! [SV287: $i] :
( ( ! [SY488: $i,SY489: $i] :
( ~ ( subset @ SV287 @ SY488 )
| ~ ( subset @ SY489 @ SY488 )
| ( subset @ ( set_union2 @ SV287 @ SY489 ) @ SY488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1444,plain,
! [SV288: $i] :
( ( ! [SY490: $i] :
( ! [SY491: $i] :
( ( singleton @ SV288 )
!= ( unordered_pair @ SY490 @ SY491 ) )
| ( SV288 = SY490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1445,plain,
! [SV289: $i] :
( ( ! [SY492: $i] :
( ~ ( in @ SV289 @ SY492 )
| ( subset @ SV289 @ ( union @ SY492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1446,plain,
! [SV290: $i] :
( ( ( union @ ( powerset @ SV290 ) )
= SV290 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1447,plain,
! [SV291: $i] :
( ( ! [SY493: $i,SY494: $i] :
( ( ( singleton @ SV291 )
!= ( unordered_pair @ SY493 @ SY494 ) )
| ( SY493 = SY494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1448,plain,
! [SV292: $i] :
( ( ! [SY495: $i] :
( ~ ( in @ SV292 @ SY495 )
| ~ ( in @ SY495 @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1449,plain,
! [SV293: $i] :
( ( ! [SY496: $i] :
( ~ ( proper_subset @ SV293 @ SY496 )
| ~ ( proper_subset @ SY496 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1450,plain,
! [SV294: $i] :
( ( ! [SY497: $i] :
( ( unordered_pair @ SV294 @ SY497 )
= ( unordered_pair @ SY497 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1451,plain,
! [SV295: $i] :
( ( ! [SY498: $i] :
( ( set_union2 @ SV295 @ SY498 )
= ( set_union2 @ SY498 @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1452,plain,
! [SV296: $i] :
( ( ! [SY499: $i] :
( ( set_intersection2 @ SV296 @ SY499 )
= ( set_intersection2 @ SY499 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1453,plain,
! [SV297: $i] :
( ( ! [SY500: $i] :
( ( ordered_pair @ SV297 @ SY500 )
= ( unordered_pair @ ( unordered_pair @ SV297 @ SY500 ) @ ( singleton @ SV297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1454,plain,
! [SV298: $i] :
( ( ! [SY501: $i] :
~ ( empty @ ( ordered_pair @ SV298 @ SY501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1455,plain,
! [SV299: $i] :
( ( ( empty @ SV299 )
| ! [SY502: $i] :
~ ( empty @ ( set_union2 @ SV299 @ SY502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1456,plain,
! [SV300: $i] :
( ( ( empty @ SV300 )
| ! [SY503: $i] :
~ ( empty @ ( set_union2 @ SY503 @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1457,plain,
! [SV301: $i] :
( ( ( set_union2 @ SV301 @ SV301 )
= SV301 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1458,plain,
! [SV302: $i] :
( ( ( set_intersection2 @ SV302 @ SV302 )
= SV302 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1459,plain,
! [SV303: $i] :
( ( ~ ( proper_subset @ SV303 @ SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1460,plain,
( ( empty @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1461,plain,
! [SV304: $i] :
( ( subset @ SV304 @ SV304 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1462,plain,
! [SV305: $i] :
( ( ! [SY504: $i] :
( ~ ( disjoint @ SV305 @ SY504 )
| ( disjoint @ SY504 @ SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1463,plain,
! [SV306: $i] :
( ( ( set_union2 @ SV306 @ empty_set )
= SV306 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1464,plain,
! [SV307: $i] :
( ( ( set_intersection2 @ SV307 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1465,plain,
! [SV308: $i] :
( ( ( set_difference @ SV308 @ empty_set )
= SV308 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1466,plain,
! [SV309: $i] :
( ( ( set_difference @ empty_set @ SV309 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1467,plain,
! [SV310: $i] :
( ( ~ ( empty @ SV310 )
| ( SV310 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1468,plain,
! [SV311: $i] :
( ( ! [SY505: $i] :
( ~ ( empty @ SY505 )
| ~ ( in @ SV311 @ SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1469,plain,
! [SV312: $i] :
( ( ! [SY506: $i] :
( ( SV312 = SY506 )
| ~ ( empty @ SV312 )
| ~ ( empty @ SY506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1470,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY201 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK11_SY201 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK9_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1471,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1472,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1473,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK23_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK23_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1474,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1392]) ).
thf(1475,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1476,plain,
! [SV313: $i] :
( ( ! [SY507: $i] :
~ ( ~ ! [SY508: $i,SY509: $i] :
( ~ ( in @ SV313 @ SY508 )
| ~ ( in @ SY507 @ SY509 )
| ( in @ ( ordered_pair @ SV313 @ SY507 ) @ ( cartesian_product2 @ SY508 @ SY509 ) ) )
| ~ ~ ( ~ ! [SY510: $i] :
( ! [SY511: $i] :
~ ( in @ ( ordered_pair @ SV313 @ SY507 ) @ ( cartesian_product2 @ SY510 @ SY511 ) )
| ( in @ SV313 @ SY510 ) )
| ~ ! [SY512: $i,SY513: $i] :
( ~ ( in @ ( ordered_pair @ SV313 @ SY507 ) @ ( cartesian_product2 @ SY512 @ SY513 ) )
| ( in @ SY507 @ SY513 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1477,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1395]) ).
thf(1478,plain,
! [SV314: $i] :
( ( ~ ( ~ ! [SY514: $i,SY515: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SV314 )
| ~ ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY514 )
| ~ ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY515 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY515 ) )
| ~ ( ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY514 )
| ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY515 ) ) ) )
| ( SY515
= ( set_intersection2 @ SV314 @ SY514 ) ) )
| ~ ! [SY516: $i,SY517: $i] :
( ( SY517
!= ( set_intersection2 @ SV314 @ SY516 ) )
| ~ ( ~ ! [SY518: $i] :
( ~ ( in @ SY518 @ SV314 )
| ~ ( in @ SY518 @ SY516 )
| ( in @ SY518 @ SY517 ) )
| ~ ~ ( ~ ! [SY519: $i] :
( ~ ( in @ SY519 @ SY517 )
| ( in @ SY519 @ SV314 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY517 )
| ( in @ SX3 @ SY516 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1479,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1480,plain,
! [SV315: $i] :
( ( ! [SY521: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_C @ SY521 @ SV315 ) @ SV315 )
| ~ ( in @ ( sK5_C @ SY521 @ SV315 ) @ SY521 ) )
| ~ ( ( in @ ( sK5_C @ SY521 @ SV315 ) @ SV315 )
| ( in @ ( sK5_C @ SY521 @ SV315 ) @ SY521 ) ) )
| ( SV315 = SY521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1481,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1482,plain,
! [SV316: $i] :
( ( ! [SY522: $i] :
~ ( ~ ! [SY523: $i] :
( ! [SY524: $i] :
( ( ordered_pair @ SV316 @ SY522 )
!= ( ordered_pair @ SY523 @ SY524 ) )
| ( SV316 = SY523 ) )
| ~ ! [SY525: $i,SY526: $i] :
( ( ( ordered_pair @ SV316 @ SY522 )
!= ( ordered_pair @ SY525 @ SY526 ) )
| ( SY522 = SY526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1483,plain,
! [SV317: $i] :
( ( ~ ( ~ ! [SY527: $i,SY528: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY528 )
| ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SV317 ) )
| ~ ( ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY528 )
| ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY527 ) ) )
| ~ ( ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY528 )
| ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SV317 )
| ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY527 ) ) )
| ( SY528
= ( set_union2 @ SV317 @ SY527 ) ) )
| ~ ! [SY529: $i,SY530: $i] :
( ( SY530
!= ( set_union2 @ SV317 @ SY529 ) )
| ~ ( ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SY530 )
| ( in @ SY531 @ SV317 )
| ( in @ SY531 @ SY529 ) )
| ~ ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV317 )
| ( in @ SY532 @ SY530 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY529 )
| ( in @ SX3 @ SY530 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1484,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1485,plain,
! [SV318: $i] :
( ( ~ ( ~ ! [SY534: $i,SY535: $i] :
( ~ ( in @ SV318 @ SY535 )
| ~ ( in @ SY534 @ SY535 )
| ( subset @ ( unordered_pair @ SV318 @ SY534 ) @ SY535 ) )
| ~ ~ ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY536 ) @ SY537 )
| ( in @ SV318 @ SY537 ) )
| ~ ! [SY538: $i,SY539: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY538 ) @ SY539 )
| ( in @ SY538 @ SY539 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1486,plain,
! [SV319: $i] :
( ( ~ ( ~ ! [SY540: $i,SY541: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SY541 @ SY540 @ SV319 ) @ SY541 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
!= SV319 ) )
| ~ ( ~ ( in @ ( sK20_D @ SY541 @ SY540 @ SV319 ) @ SY541 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
!= SY540 ) ) )
| ~ ( ( in @ ( sK20_D @ SY541 @ SY540 @ SV319 ) @ SY541 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
= SV319 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
= SY540 ) ) )
| ( SY541
= ( unordered_pair @ SV319 @ SY540 ) ) )
| ~ ! [SY542: $i,SY543: $i] :
( ( SY543
!= ( unordered_pair @ SV319 @ SY542 ) )
| ~ ( ~ ! [SY544: $i] :
( ~ ( in @ SY544 @ SY543 )
| ( SY544 = SV319 )
| ( SY544 = SY542 ) )
| ~ ~ ( ~ ! [SY545: $i] :
( ( SY545 != SV319 )
| ( in @ SY545 @ SY543 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY542 )
| ( in @ SX3 @ SY543 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1487,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK22_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1488,plain,
( ( ~ ~ ( ~ ( in @ sK1_A @ sK3_SY197 )
| ~ ( in @ sK2_SY194 @ sK4_SY199 ) )
| ~ ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1489,plain,
! [SV320: $i] :
( ( ~ ( ~ ! [SY547: $i,SY548: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY547 )
| ~ ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY548 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY548 ) )
| ~ ( ~ ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY547 )
| ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY548 ) ) ) )
| ( SY548
= ( set_difference @ SV320 @ SY547 ) ) )
| ~ ! [SY549: $i,SY550: $i] :
( ( SY550
!= ( set_difference @ SV320 @ SY549 ) )
| ~ ( ~ ! [SY551: $i] :
( ~ ( in @ SY551 @ SV320 )
| ( in @ SY551 @ SY549 )
| ( in @ SY551 @ SY550 ) )
| ~ ~ ( ~ ! [SY552: $i] :
( ~ ( in @ SY552 @ SY550 )
| ( in @ SY552 @ SV320 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY550 )
| ~ ( in @ SX3 @ SY549 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1490,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1491,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK24_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1492,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1493,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1494,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1495,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1496,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1497,plain,
! [SV321: $i] :
( ( ~ ( ~ ! [SY554: $i,SY555: $i] :
( ~ ( ~ ( ! [SY556: $i,SY557: $i] :
( ~ ( in @ SY556 @ SV321 )
| ~ ( in @ SY557 @ SY554 )
| ( ( sK16_D @ SY555 @ SY554 @ SV321 )
!= ( ordered_pair @ SY556 @ SY557 ) ) )
| ~ ( in @ ( sK16_D @ SY555 @ SY554 @ SV321 ) @ SY555 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SY555 @ SY554 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SY555 @ SY554 @ SV321 ) @ SY554 ) )
| ( ( sK16_D @ SY555 @ SY554 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SY555 @ SY554 @ SV321 ) @ ( sK18_SY207 @ SY555 @ SY554 @ SV321 ) ) ) )
| ( in @ ( sK16_D @ SY555 @ SY554 @ SV321 ) @ SY555 ) ) )
| ( SY555
= ( cartesian_product2 @ SV321 @ SY554 ) ) )
| ~ ! [SY558: $i,SY559: $i] :
( ( SY559
!= ( cartesian_product2 @ SV321 @ SY558 ) )
| ~ ( ~ ! [SY560: $i] :
( ! [SY561: $i,SY562: $i] :
( ~ ( in @ SY561 @ SV321 )
| ~ ( in @ SY562 @ SY558 )
| ( SY560
!= ( ordered_pair @ SY561 @ SY562 ) ) )
| ( in @ SY560 @ SY559 ) )
| ~ ! [SY563: $i] :
( ~ ( in @ SY563 @ SY559 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY563 @ SY559 @ SY558 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SY563 @ SY559 @ SY558 @ SV321 ) @ SY558 ) )
| ( SY563
!= ( ordered_pair @ ( sK14_E @ SY563 @ SY559 @ SY558 @ SV321 ) @ ( sK15_SY202 @ SY563 @ SY559 @ SY558 @ SV321 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1498,plain,
! [SV260: $i] :
( ( ( singleton @ SV260 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1499,plain,
! [SV322: $i,SV261: $i] :
( ( ~ ( in @ SV261 @ SV322 )
| ( ( set_union2 @ ( singleton @ SV261 ) @ SV322 )
= SV322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1500,plain,
! [SV323: $i,SV262: $i] :
( ( ~ ( disjoint @ ( singleton @ SV262 ) @ SV323 )
| ~ ( in @ SV262 @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1501,plain,
! [SV324: $i,SV263: $i] :
( ( ( in @ SV263 @ SV324 )
| ( disjoint @ ( singleton @ SV263 ) @ SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1502,plain,
! [SV325: $i,SV264: $i] :
( ( ~ ( subset @ SV264 @ SV325 )
| ! [SY564: $i] :
( ( in @ SY564 @ SV264 )
| ( subset @ SV264 @ ( set_difference @ SV325 @ ( singleton @ SY564 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1503,plain,
! [SV326: $i,SV265: $i] :
( ( ~ ( in @ SV265 @ SV326 )
| ( subset @ SV265 @ ( union @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1504,plain,
! [SV327: $i,SV266: $i] :
( ( ! [SY565: $i,SY566: $i] :
( ( SV266 = SY566 )
| ( SV266 = SY565 )
| ( ( unordered_pair @ SV266 @ SV327 )
!= ( unordered_pair @ SY565 @ SY566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1505,plain,
! [SV328: $i,SV267: $i] :
( ( ~ ( subset @ SV267 @ SV328 )
| ( ( set_union2 @ SV267 @ SV328 )
= SV328 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1506,plain,
! [SV329: $i,SV268: $i] :
( ( subset @ ( set_intersection2 @ SV268 @ SV329 ) @ SV268 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1507,plain,
! [SV330: $i,SV269: $i] :
( ( ! [SY567: $i] :
( ~ ( subset @ SV269 @ SV330 )
| ~ ( subset @ SV269 @ SY567 )
| ( subset @ SV269 @ ( set_intersection2 @ SV330 @ SY567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1508,plain,
! [SV331: $i,SV270: $i] :
( ( ! [SY568: $i] :
( ~ ( subset @ SV270 @ SV331 )
| ~ ( subset @ SV331 @ SY568 )
| ( subset @ SV270 @ SY568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1509,plain,
! [SV332: $i,SV271: $i] :
( ( ~ ( subset @ SV271 @ SV332 )
| ! [SY569: $i] : ( subset @ ( set_intersection2 @ SV271 @ SY569 ) @ ( set_intersection2 @ SV332 @ SY569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1510,plain,
! [SV333: $i,SV272: $i] :
( ( ~ ( subset @ SV272 @ SV333 )
| ( ( set_intersection2 @ SV272 @ SV333 )
= SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1511,plain,
! [SV334: $i,SV274: $i] :
( ( ~ ( subset @ SV274 @ SV334 )
| ! [SY570: $i] : ( subset @ ( set_difference @ SV274 @ SY570 ) @ ( set_difference @ SV334 @ SY570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1512,plain,
! [SV335: $i,SV275: $i] :
( ( subset @ ( set_difference @ SV275 @ SV335 ) @ SV275 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1513,plain,
! [SV336: $i,SV276: $i] :
( ( ( set_union2 @ SV276 @ ( set_difference @ SV336 @ SV276 ) )
= ( set_union2 @ SV276 @ SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1514,plain,
! [SV277: $i] :
( ( ( ~ ( subset @ SV277 @ empty_set ) )
= $true )
| ( ( SV277 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1515,plain,
! [SV337: $i,SV278: $i] :
( ( ( set_difference @ ( set_union2 @ SV278 @ SV337 ) @ SV337 )
= ( set_difference @ SV278 @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1516,plain,
! [SV338: $i,SV279: $i] :
( ( ~ ( subset @ SV279 @ SV338 )
| ( SV338
= ( set_union2 @ SV279 @ ( set_difference @ SV338 @ SV279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1517,plain,
! [SV339: $i,SV280: $i] :
( ( ~ ( in @ SV280 @ SV339 )
| ( ( set_union2 @ ( singleton @ SV280 ) @ SV339 )
= SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1518,plain,
! [SV340: $i,SV281: $i] :
( ( ( set_difference @ SV281 @ ( set_difference @ SV281 @ SV340 ) )
= ( set_intersection2 @ SV281 @ SV340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1519,plain,
! [SV282: $i,SV341: $i] :
( ( ~ ( proper_subset @ SV341 @ SV282 )
| ~ ( subset @ SV282 @ SV341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1520,plain,
! [SV283: $i,SV342: $i] :
( ( ! [SY571: $i] :
( ~ ( disjoint @ SV342 @ SY571 )
| ~ ( subset @ SV283 @ SV342 )
| ( disjoint @ SV283 @ SY571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1521,plain,
! [SV343: $i,SV285: $i] :
( ( ~ ( subset @ ( singleton @ SV285 ) @ ( singleton @ SV343 ) )
| ( SV285 = SV343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1522,plain,
! [SV344: $i,SV286: $i] :
( ( subset @ SV286 @ ( set_union2 @ SV286 @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1523,plain,
! [SV345: $i,SV287: $i] :
( ( ! [SY572: $i] :
( ~ ( subset @ SV287 @ SV345 )
| ~ ( subset @ SY572 @ SV345 )
| ( subset @ ( set_union2 @ SV287 @ SY572 ) @ SV345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1524,plain,
! [SV346: $i,SV288: $i] :
( ( ! [SY573: $i] :
( ( singleton @ SV288 )
!= ( unordered_pair @ SV346 @ SY573 ) )
| ( SV288 = SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1525,plain,
! [SV347: $i,SV289: $i] :
( ( ~ ( in @ SV289 @ SV347 )
| ( subset @ SV289 @ ( union @ SV347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1526,plain,
! [SV348: $i,SV291: $i] :
( ( ! [SY574: $i] :
( ( ( singleton @ SV291 )
!= ( unordered_pair @ SV348 @ SY574 ) )
| ( SV348 = SY574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1527,plain,
! [SV349: $i,SV292: $i] :
( ( ~ ( in @ SV292 @ SV349 )
| ~ ( in @ SV349 @ SV292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1528,plain,
! [SV350: $i,SV293: $i] :
( ( ~ ( proper_subset @ SV293 @ SV350 )
| ~ ( proper_subset @ SV350 @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1529,plain,
! [SV351: $i,SV294: $i] :
( ( ( unordered_pair @ SV294 @ SV351 )
= ( unordered_pair @ SV351 @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1530,plain,
! [SV352: $i,SV295: $i] :
( ( ( set_union2 @ SV295 @ SV352 )
= ( set_union2 @ SV352 @ SV295 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1531,plain,
! [SV353: $i,SV296: $i] :
( ( ( set_intersection2 @ SV296 @ SV353 )
= ( set_intersection2 @ SV353 @ SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1532,plain,
! [SV354: $i,SV297: $i] :
( ( ( ordered_pair @ SV297 @ SV354 )
= ( unordered_pair @ ( unordered_pair @ SV297 @ SV354 ) @ ( singleton @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1533,plain,
! [SV355: $i,SV298: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV298 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1534,plain,
! [SV299: $i] :
( ( ( empty @ SV299 )
= $true )
| ( ( ! [SY502: $i] :
~ ( empty @ ( set_union2 @ SV299 @ SY502 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1535,plain,
! [SV300: $i] :
( ( ( empty @ SV300 )
= $true )
| ( ( ! [SY503: $i] :
~ ( empty @ ( set_union2 @ SY503 @ SV300 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1456]) ).
thf(1536,plain,
! [SV303: $i] :
( ( proper_subset @ SV303 @ SV303 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1459]) ).
thf(1537,plain,
! [SV356: $i,SV305: $i] :
( ( ~ ( disjoint @ SV305 @ SV356 )
| ( disjoint @ SV356 @ SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1538,plain,
! [SV310: $i] :
( ( ( ~ ( empty @ SV310 ) )
= $true )
| ( ( SV310 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1539,plain,
! [SV311: $i,SV357: $i] :
( ( ~ ( empty @ SV357 )
| ~ ( in @ SV311 @ SV357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1540,plain,
! [SV358: $i,SV312: $i] :
( ( ( SV312 = SV358 )
| ~ ( empty @ SV312 )
| ~ ( empty @ SV358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1541,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY201 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK11_SY201 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1470]) ).
thf(1542,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK9_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1470]) ).
thf(1543,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1544,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1471]) ).
thf(1545,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1546,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1472]) ).
thf(1547,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK23_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK23_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1473]) ).
thf(1548,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1473]) ).
thf(1549,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1474]) ).
thf(1550,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1474]) ).
thf(1551,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1475]) ).
thf(1552,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1475]) ).
thf(1553,plain,
! [SV359: $i,SV313: $i] :
( ( ~ ( ~ ! [SY575: $i,SY576: $i] :
( ~ ( in @ SV313 @ SY575 )
| ~ ( in @ SV359 @ SY576 )
| ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY575 @ SY576 ) ) )
| ~ ~ ( ~ ! [SY577: $i] :
( ! [SY578: $i] :
~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY577 @ SY578 ) )
| ( in @ SV313 @ SY577 ) )
| ~ ! [SY579: $i,SY580: $i] :
( ~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY579 @ SY580 ) )
| ( in @ SV359 @ SY580 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1554,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1555,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1556,plain,
! [SV314: $i] :
( ( ~ ! [SY514: $i,SY515: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SV314 )
| ~ ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY514 )
| ~ ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY515 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY515 ) )
| ~ ( ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY514 )
| ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY515 ) ) ) )
| ( SY515
= ( set_intersection2 @ SV314 @ SY514 ) ) )
| ~ ! [SY516: $i,SY517: $i] :
( ( SY517
!= ( set_intersection2 @ SV314 @ SY516 ) )
| ~ ( ~ ! [SY518: $i] :
( ~ ( in @ SY518 @ SV314 )
| ~ ( in @ SY518 @ SY516 )
| ( in @ SY518 @ SY517 ) )
| ~ ~ ( ~ ! [SY519: $i] :
( ~ ( in @ SY519 @ SY517 )
| ( in @ SY519 @ SV314 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY517 )
| ( in @ SX3 @ SY516 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1478]) ).
thf(1557,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1479]) ).
thf(1558,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1479]) ).
thf(1559,plain,
! [SV315: $i,SV360: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
| ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 ) )
| ~ ( ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
| ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 ) ) )
| ( SV315 = SV360 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1560,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1561,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1562,plain,
! [SV361: $i,SV316: $i] :
( ( ~ ( ~ ! [SY581: $i] :
( ! [SY582: $i] :
( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SY581 @ SY582 ) )
| ( SV316 = SY581 ) )
| ~ ! [SY583: $i,SY584: $i] :
( ( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SY583 @ SY584 ) )
| ( SV361 = SY584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1563,plain,
! [SV317: $i] :
( ( ~ ! [SY527: $i,SY528: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY528 )
| ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SV317 ) )
| ~ ( ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY528 )
| ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY527 ) ) )
| ~ ( ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY528 )
| ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SV317 )
| ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY527 ) ) )
| ( SY528
= ( set_union2 @ SV317 @ SY527 ) ) )
| ~ ! [SY529: $i,SY530: $i] :
( ( SY530
!= ( set_union2 @ SV317 @ SY529 ) )
| ~ ( ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SY530 )
| ( in @ SY531 @ SV317 )
| ( in @ SY531 @ SY529 ) )
| ~ ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV317 )
| ( in @ SY532 @ SY530 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY529 )
| ( in @ SX3 @ SY530 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1483]) ).
thf(1564,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1565,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1484]) ).
thf(1566,plain,
! [SV318: $i] :
( ( ~ ! [SY534: $i,SY535: $i] :
( ~ ( in @ SV318 @ SY535 )
| ~ ( in @ SY534 @ SY535 )
| ( subset @ ( unordered_pair @ SV318 @ SY534 ) @ SY535 ) )
| ~ ~ ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY536 ) @ SY537 )
| ( in @ SV318 @ SY537 ) )
| ~ ! [SY538: $i,SY539: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY538 ) @ SY539 )
| ( in @ SY538 @ SY539 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1567,plain,
! [SV319: $i] :
( ( ~ ! [SY540: $i,SY541: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SY541 @ SY540 @ SV319 ) @ SY541 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
!= SV319 ) )
| ~ ( ~ ( in @ ( sK20_D @ SY541 @ SY540 @ SV319 ) @ SY541 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
!= SY540 ) ) )
| ~ ( ( in @ ( sK20_D @ SY541 @ SY540 @ SV319 ) @ SY541 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
= SV319 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
= SY540 ) ) )
| ( SY541
= ( unordered_pair @ SV319 @ SY540 ) ) )
| ~ ! [SY542: $i,SY543: $i] :
( ( SY543
!= ( unordered_pair @ SV319 @ SY542 ) )
| ~ ( ~ ! [SY544: $i] :
( ~ ( in @ SY544 @ SY543 )
| ( SY544 = SV319 )
| ( SY544 = SY542 ) )
| ~ ~ ( ~ ! [SY545: $i] :
( ( SY545 != SV319 )
| ( in @ SY545 @ SY543 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY542 )
| ( in @ SX3 @ SY543 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1568,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK22_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1487]) ).
thf(1569,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1487]) ).
thf(1570,plain,
( ( ~ ~ ( ~ ( in @ sK1_A @ sK3_SY197 )
| ~ ( in @ sK2_SY194 @ sK4_SY199 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1488]) ).
thf(1571,plain,
( ( ~ ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1488]) ).
thf(1572,plain,
! [SV320: $i] :
( ( ~ ! [SY547: $i,SY548: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY547 )
| ~ ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY548 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY548 ) )
| ~ ( ~ ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY547 )
| ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY548 ) ) ) )
| ( SY548
= ( set_difference @ SV320 @ SY547 ) ) )
| ~ ! [SY549: $i,SY550: $i] :
( ( SY550
!= ( set_difference @ SV320 @ SY549 ) )
| ~ ( ~ ! [SY551: $i] :
( ~ ( in @ SY551 @ SV320 )
| ( in @ SY551 @ SY549 )
| ( in @ SY551 @ SY550 ) )
| ~ ~ ( ~ ! [SY552: $i] :
( ~ ( in @ SY552 @ SY550 )
| ( in @ SY552 @ SV320 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY550 )
| ~ ( in @ SX3 @ SY549 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1573,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1490]) ).
thf(1574,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1490]) ).
thf(1575,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK24_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1576,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1491]) ).
thf(1577,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1578,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1579,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1493]) ).
thf(1580,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1493]) ).
thf(1581,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1582,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1494]) ).
thf(1583,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1584,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1585,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1586,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1496]) ).
thf(1587,plain,
! [SV321: $i] :
( ( ~ ! [SY554: $i,SY555: $i] :
( ~ ( ~ ( ! [SY556: $i,SY557: $i] :
( ~ ( in @ SY556 @ SV321 )
| ~ ( in @ SY557 @ SY554 )
| ( ( sK16_D @ SY555 @ SY554 @ SV321 )
!= ( ordered_pair @ SY556 @ SY557 ) ) )
| ~ ( in @ ( sK16_D @ SY555 @ SY554 @ SV321 ) @ SY555 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SY555 @ SY554 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SY555 @ SY554 @ SV321 ) @ SY554 ) )
| ( ( sK16_D @ SY555 @ SY554 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SY555 @ SY554 @ SV321 ) @ ( sK18_SY207 @ SY555 @ SY554 @ SV321 ) ) ) )
| ( in @ ( sK16_D @ SY555 @ SY554 @ SV321 ) @ SY555 ) ) )
| ( SY555
= ( cartesian_product2 @ SV321 @ SY554 ) ) )
| ~ ! [SY558: $i,SY559: $i] :
( ( SY559
!= ( cartesian_product2 @ SV321 @ SY558 ) )
| ~ ( ~ ! [SY560: $i] :
( ! [SY561: $i,SY562: $i] :
( ~ ( in @ SY561 @ SV321 )
| ~ ( in @ SY562 @ SY558 )
| ( SY560
!= ( ordered_pair @ SY561 @ SY562 ) ) )
| ( in @ SY560 @ SY559 ) )
| ~ ! [SY563: $i] :
( ~ ( in @ SY563 @ SY559 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY563 @ SY559 @ SY558 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SY563 @ SY559 @ SY558 @ SV321 ) @ SY558 ) )
| ( SY563
!= ( ordered_pair @ ( sK14_E @ SY563 @ SY559 @ SY558 @ SV321 ) @ ( sK15_SY202 @ SY563 @ SY559 @ SY558 @ SV321 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1588,plain,
! [SV322: $i,SV261: $i] :
( ( ( ~ ( in @ SV261 @ SV322 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV261 ) @ SV322 )
= SV322 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1499]) ).
thf(1589,plain,
! [SV323: $i,SV262: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV262 ) @ SV323 ) )
= $true )
| ( ( ~ ( in @ SV262 @ SV323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1590,plain,
! [SV324: $i,SV263: $i] :
( ( ( in @ SV263 @ SV324 )
= $true )
| ( ( disjoint @ ( singleton @ SV263 ) @ SV324 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1591,plain,
! [SV325: $i,SV264: $i] :
( ( ( ~ ( subset @ SV264 @ SV325 ) )
= $true )
| ( ( ! [SY564: $i] :
( ( in @ SY564 @ SV264 )
| ( subset @ SV264 @ ( set_difference @ SV325 @ ( singleton @ SY564 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1592,plain,
! [SV326: $i,SV265: $i] :
( ( ( ~ ( in @ SV265 @ SV326 ) )
= $true )
| ( ( subset @ SV265 @ ( union @ SV326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1503]) ).
thf(1593,plain,
! [SV327: $i,SV362: $i,SV266: $i] :
( ( ! [SY585: $i] :
( ( SV266 = SY585 )
| ( SV266 = SV362 )
| ( ( unordered_pair @ SV266 @ SV327 )
!= ( unordered_pair @ SV362 @ SY585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1594,plain,
! [SV328: $i,SV267: $i] :
( ( ( ~ ( subset @ SV267 @ SV328 ) )
= $true )
| ( ( ( set_union2 @ SV267 @ SV328 )
= SV328 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1595,plain,
! [SV363: $i,SV330: $i,SV269: $i] :
( ( ~ ( subset @ SV269 @ SV330 )
| ~ ( subset @ SV269 @ SV363 )
| ( subset @ SV269 @ ( set_intersection2 @ SV330 @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1596,plain,
! [SV364: $i,SV331: $i,SV270: $i] :
( ( ~ ( subset @ SV270 @ SV331 )
| ~ ( subset @ SV331 @ SV364 )
| ( subset @ SV270 @ SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1597,plain,
! [SV332: $i,SV271: $i] :
( ( ( ~ ( subset @ SV271 @ SV332 ) )
= $true )
| ( ( ! [SY569: $i] : ( subset @ ( set_intersection2 @ SV271 @ SY569 ) @ ( set_intersection2 @ SV332 @ SY569 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1598,plain,
! [SV333: $i,SV272: $i] :
( ( ( ~ ( subset @ SV272 @ SV333 ) )
= $true )
| ( ( ( set_intersection2 @ SV272 @ SV333 )
= SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1510]) ).
thf(1599,plain,
! [SV334: $i,SV274: $i] :
( ( ( ~ ( subset @ SV274 @ SV334 ) )
= $true )
| ( ( ! [SY570: $i] : ( subset @ ( set_difference @ SV274 @ SY570 ) @ ( set_difference @ SV334 @ SY570 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1600,plain,
! [SV277: $i] :
( ( ( subset @ SV277 @ empty_set )
= $false )
| ( ( SV277 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1601,plain,
! [SV338: $i,SV279: $i] :
( ( ( ~ ( subset @ SV279 @ SV338 ) )
= $true )
| ( ( SV338
= ( set_union2 @ SV279 @ ( set_difference @ SV338 @ SV279 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1602,plain,
! [SV339: $i,SV280: $i] :
( ( ( ~ ( in @ SV280 @ SV339 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV280 ) @ SV339 )
= SV339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1517]) ).
thf(1603,plain,
! [SV282: $i,SV341: $i] :
( ( ( ~ ( proper_subset @ SV341 @ SV282 ) )
= $true )
| ( ( ~ ( subset @ SV282 @ SV341 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1519]) ).
thf(1604,plain,
! [SV283: $i,SV365: $i,SV342: $i] :
( ( ~ ( disjoint @ SV342 @ SV365 )
| ~ ( subset @ SV283 @ SV342 )
| ( disjoint @ SV283 @ SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1605,plain,
! [SV343: $i,SV285: $i] :
( ( ( ~ ( subset @ ( singleton @ SV285 ) @ ( singleton @ SV343 ) ) )
= $true )
| ( ( SV285 = SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1606,plain,
! [SV366: $i,SV345: $i,SV287: $i] :
( ( ~ ( subset @ SV287 @ SV345 )
| ~ ( subset @ SV366 @ SV345 )
| ( subset @ ( set_union2 @ SV287 @ SV366 ) @ SV345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1607,plain,
! [SV346: $i,SV288: $i] :
( ( ( ! [SY573: $i] :
( ( singleton @ SV288 )
!= ( unordered_pair @ SV346 @ SY573 ) ) )
= $true )
| ( ( SV288 = SV346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1524]) ).
thf(1608,plain,
! [SV347: $i,SV289: $i] :
( ( ( ~ ( in @ SV289 @ SV347 ) )
= $true )
| ( ( subset @ SV289 @ ( union @ SV347 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1609,plain,
! [SV367: $i,SV348: $i,SV291: $i] :
( ( ( ( singleton @ SV291 )
!= ( unordered_pair @ SV348 @ SV367 ) )
| ( SV348 = SV367 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1610,plain,
! [SV349: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV349 ) )
= $true )
| ( ( ~ ( in @ SV349 @ SV292 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1611,plain,
! [SV350: $i,SV293: $i] :
( ( ( ~ ( proper_subset @ SV293 @ SV350 ) )
= $true )
| ( ( ~ ( proper_subset @ SV350 @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1528]) ).
thf(1612,plain,
! [SV355: $i,SV298: $i] :
( ( empty @ ( ordered_pair @ SV298 @ SV355 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1613,plain,
! [SV368: $i,SV299: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV299 @ SV368 ) ) )
= $true )
| ( ( empty @ SV299 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1614,plain,
! [SV300: $i,SV369: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV369 @ SV300 ) ) )
= $true )
| ( ( empty @ SV300 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1615,plain,
! [SV356: $i,SV305: $i] :
( ( ( ~ ( disjoint @ SV305 @ SV356 ) )
= $true )
| ( ( disjoint @ SV356 @ SV305 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1537]) ).
thf(1616,plain,
! [SV310: $i] :
( ( ( empty @ SV310 )
= $false )
| ( ( SV310 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1538]) ).
thf(1617,plain,
! [SV311: $i,SV357: $i] :
( ( ( ~ ( empty @ SV357 ) )
= $true )
| ( ( ~ ( in @ SV311 @ SV357 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1539]) ).
thf(1618,plain,
! [SV358: $i,SV312: $i] :
( ( ( ( SV312 = SV358 )
| ~ ( empty @ SV312 ) )
= $true )
| ( ( ~ ( empty @ SV358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1619,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SX1 @ SX0 ) @ ( sK11_SY201 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK11_SY201 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK10_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1541]) ).
thf(1620,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( union @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( ~ ( in @ SX2 @ ( sK9_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1542]) ).
thf(1621,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1543]) ).
thf(1622,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1544]) ).
thf(1623,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1545]) ).
thf(1624,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1546]) ).
thf(1625,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK23_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK23_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1626,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1548]) ).
thf(1627,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1549]) ).
thf(1628,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1550]) ).
thf(1629,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1551]) ).
thf(1630,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1552]) ).
thf(1631,plain,
! [SV359: $i,SV313: $i] :
( ( ~ ! [SY575: $i,SY576: $i] :
( ~ ( in @ SV313 @ SY575 )
| ~ ( in @ SV359 @ SY576 )
| ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY575 @ SY576 ) ) )
| ~ ~ ( ~ ! [SY577: $i] :
( ! [SY578: $i] :
~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY577 @ SY578 ) )
| ( in @ SV313 @ SY577 ) )
| ~ ! [SY579: $i,SY580: $i] :
( ~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY579 @ SY580 ) )
| ( in @ SV359 @ SY580 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1632,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1554]) ).
thf(1633,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1555]) ).
thf(1634,plain,
! [SV314: $i] :
( ( ~ ! [SY514: $i,SY515: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SV314 )
| ~ ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY514 )
| ~ ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY515 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY515 ) )
| ~ ( ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY514 )
| ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY515 ) ) ) )
| ( SY515
= ( set_intersection2 @ SV314 @ SY514 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1635,plain,
! [SV314: $i] :
( ( ~ ! [SY516: $i,SY517: $i] :
( ( SY517
!= ( set_intersection2 @ SV314 @ SY516 ) )
| ~ ( ~ ! [SY518: $i] :
( ~ ( in @ SY518 @ SV314 )
| ~ ( in @ SY518 @ SY516 )
| ( in @ SY518 @ SY517 ) )
| ~ ~ ( ~ ! [SY519: $i] :
( ~ ( in @ SY519 @ SY517 )
| ( in @ SY519 @ SV314 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY517 )
| ( in @ SX3 @ SY516 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1636,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK21_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1557]) ).
thf(1637,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1558]) ).
thf(1638,plain,
! [SV315: $i,SV360: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
| ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 ) )
| ~ ( ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
| ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 ) ) ) )
= $true )
| ( ( SV315 = SV360 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1559]) ).
thf(1639,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1560]) ).
thf(1640,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1641,plain,
! [SV361: $i,SV316: $i] :
( ( ~ ! [SY581: $i] :
( ! [SY582: $i] :
( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SY581 @ SY582 ) )
| ( SV316 = SY581 ) )
| ~ ! [SY583: $i,SY584: $i] :
( ( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SY583 @ SY584 ) )
| ( SV361 = SY584 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1642,plain,
! [SV317: $i] :
( ( ~ ! [SY527: $i,SY528: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY528 )
| ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SV317 ) )
| ~ ( ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY528 )
| ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY527 ) ) )
| ~ ( ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY528 )
| ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SV317 )
| ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY527 ) ) )
| ( SY528
= ( set_union2 @ SV317 @ SY527 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1643,plain,
! [SV317: $i] :
( ( ~ ! [SY529: $i,SY530: $i] :
( ( SY530
!= ( set_union2 @ SV317 @ SY529 ) )
| ~ ( ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SY530 )
| ( in @ SY531 @ SV317 )
| ( in @ SY531 @ SY529 ) )
| ~ ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV317 )
| ( in @ SY532 @ SY530 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY529 )
| ( in @ SX3 @ SY530 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1563]) ).
thf(1644,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1564]) ).
thf(1645,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1565]) ).
thf(1646,plain,
! [SV318: $i] :
( ( ~ ! [SY534: $i,SY535: $i] :
( ~ ( in @ SV318 @ SY535 )
| ~ ( in @ SY534 @ SY535 )
| ( subset @ ( unordered_pair @ SV318 @ SY534 ) @ SY535 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1647,plain,
! [SV318: $i] :
( ( ~ ~ ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY536 ) @ SY537 )
| ( in @ SV318 @ SY537 ) )
| ~ ! [SY538: $i,SY539: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY538 ) @ SY539 )
| ( in @ SY538 @ SY539 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1566]) ).
thf(1648,plain,
! [SV319: $i] :
( ( ~ ! [SY540: $i,SY541: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SY541 @ SY540 @ SV319 ) @ SY541 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
!= SV319 ) )
| ~ ( ~ ( in @ ( sK20_D @ SY541 @ SY540 @ SV319 ) @ SY541 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
!= SY540 ) ) )
| ~ ( ( in @ ( sK20_D @ SY541 @ SY540 @ SV319 ) @ SY541 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
= SV319 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
= SY540 ) ) )
| ( SY541
= ( unordered_pair @ SV319 @ SY540 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1649,plain,
! [SV319: $i] :
( ( ~ ! [SY542: $i,SY543: $i] :
( ( SY543
!= ( unordered_pair @ SV319 @ SY542 ) )
| ~ ( ~ ! [SY544: $i] :
( ~ ( in @ SY544 @ SY543 )
| ( SY544 = SV319 )
| ( SY544 = SY542 ) )
| ~ ~ ( ~ ! [SY545: $i] :
( ( SY545 != SV319 )
| ( in @ SY545 @ SY543 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY542 )
| ( in @ SX3 @ SY543 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1650,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK22_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1568]) ).
thf(1651,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1569]) ).
thf(1652,plain,
( ( ~ ( ~ ( in @ sK1_A @ sK3_SY197 )
| ~ ( in @ sK2_SY194 @ sK4_SY199 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1570]) ).
thf(1653,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1571]) ).
thf(1654,plain,
! [SV320: $i] :
( ( ~ ! [SY547: $i,SY548: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY547 )
| ~ ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY548 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY548 ) )
| ~ ( ~ ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY547 )
| ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY548 ) ) ) )
| ( SY548
= ( set_difference @ SV320 @ SY547 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1655,plain,
! [SV320: $i] :
( ( ~ ! [SY549: $i,SY550: $i] :
( ( SY550
!= ( set_difference @ SV320 @ SY549 ) )
| ~ ( ~ ! [SY551: $i] :
( ~ ( in @ SY551 @ SV320 )
| ( in @ SY551 @ SY549 )
| ( in @ SY551 @ SY550 ) )
| ~ ~ ( ~ ! [SY552: $i] :
( ~ ( in @ SY552 @ SY550 )
| ( in @ SY552 @ SV320 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY550 )
| ~ ( in @ SX3 @ SY549 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1572]) ).
thf(1656,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1657,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1658,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK24_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1575]) ).
thf(1659,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1576]) ).
thf(1660,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1577]) ).
thf(1661,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1578]) ).
thf(1662,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1579]) ).
thf(1663,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1580]) ).
thf(1664,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1581]) ).
thf(1665,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1582]) ).
thf(1666,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1583]) ).
thf(1667,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1584]) ).
thf(1668,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK25_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1585]) ).
thf(1669,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1586]) ).
thf(1670,plain,
! [SV321: $i] :
( ( ~ ! [SY554: $i,SY555: $i] :
( ~ ( ~ ( ! [SY556: $i,SY557: $i] :
( ~ ( in @ SY556 @ SV321 )
| ~ ( in @ SY557 @ SY554 )
| ( ( sK16_D @ SY555 @ SY554 @ SV321 )
!= ( ordered_pair @ SY556 @ SY557 ) ) )
| ~ ( in @ ( sK16_D @ SY555 @ SY554 @ SV321 ) @ SY555 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SY555 @ SY554 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SY555 @ SY554 @ SV321 ) @ SY554 ) )
| ( ( sK16_D @ SY555 @ SY554 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SY555 @ SY554 @ SV321 ) @ ( sK18_SY207 @ SY555 @ SY554 @ SV321 ) ) ) )
| ( in @ ( sK16_D @ SY555 @ SY554 @ SV321 ) @ SY555 ) ) )
| ( SY555
= ( cartesian_product2 @ SV321 @ SY554 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1587]) ).
thf(1671,plain,
! [SV321: $i] :
( ( ~ ! [SY558: $i,SY559: $i] :
( ( SY559
!= ( cartesian_product2 @ SV321 @ SY558 ) )
| ~ ( ~ ! [SY560: $i] :
( ! [SY561: $i,SY562: $i] :
( ~ ( in @ SY561 @ SV321 )
| ~ ( in @ SY562 @ SY558 )
| ( SY560
!= ( ordered_pair @ SY561 @ SY562 ) ) )
| ( in @ SY560 @ SY559 ) )
| ~ ! [SY563: $i] :
( ~ ( in @ SY563 @ SY559 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY563 @ SY559 @ SY558 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SY563 @ SY559 @ SY558 @ SV321 ) @ SY558 ) )
| ( SY563
!= ( ordered_pair @ ( sK14_E @ SY563 @ SY559 @ SY558 @ SV321 ) @ ( sK15_SY202 @ SY563 @ SY559 @ SY558 @ SV321 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1587]) ).
thf(1672,plain,
! [SV322: $i,SV261: $i] :
( ( ( in @ SV261 @ SV322 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV261 ) @ SV322 )
= SV322 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1588]) ).
thf(1673,plain,
! [SV323: $i,SV262: $i] :
( ( ( disjoint @ ( singleton @ SV262 ) @ SV323 )
= $false )
| ( ( ~ ( in @ SV262 @ SV323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1674,plain,
! [SV325: $i,SV264: $i] :
( ( ( subset @ SV264 @ SV325 )
= $false )
| ( ( ! [SY564: $i] :
( ( in @ SY564 @ SV264 )
| ( subset @ SV264 @ ( set_difference @ SV325 @ ( singleton @ SY564 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1675,plain,
! [SV326: $i,SV265: $i] :
( ( ( in @ SV265 @ SV326 )
= $false )
| ( ( subset @ SV265 @ ( union @ SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1676,plain,
! [SV327: $i,SV362: $i,SV370: $i,SV266: $i] :
( ( ( SV266 = SV370 )
| ( SV266 = SV362 )
| ( ( unordered_pair @ SV266 @ SV327 )
!= ( unordered_pair @ SV362 @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(1677,plain,
! [SV328: $i,SV267: $i] :
( ( ( subset @ SV267 @ SV328 )
= $false )
| ( ( ( set_union2 @ SV267 @ SV328 )
= SV328 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1678,plain,
! [SV363: $i,SV330: $i,SV269: $i] :
( ( ( ~ ( subset @ SV269 @ SV330 )
| ~ ( subset @ SV269 @ SV363 ) )
= $true )
| ( ( subset @ SV269 @ ( set_intersection2 @ SV330 @ SV363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1679,plain,
! [SV364: $i,SV331: $i,SV270: $i] :
( ( ( ~ ( subset @ SV270 @ SV331 )
| ~ ( subset @ SV331 @ SV364 ) )
= $true )
| ( ( subset @ SV270 @ SV364 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1680,plain,
! [SV332: $i,SV271: $i] :
( ( ( subset @ SV271 @ SV332 )
= $false )
| ( ( ! [SY569: $i] : ( subset @ ( set_intersection2 @ SV271 @ SY569 ) @ ( set_intersection2 @ SV332 @ SY569 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1681,plain,
! [SV333: $i,SV272: $i] :
( ( ( subset @ SV272 @ SV333 )
= $false )
| ( ( ( set_intersection2 @ SV272 @ SV333 )
= SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1682,plain,
! [SV334: $i,SV274: $i] :
( ( ( subset @ SV274 @ SV334 )
= $false )
| ( ( ! [SY570: $i] : ( subset @ ( set_difference @ SV274 @ SY570 ) @ ( set_difference @ SV334 @ SY570 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1683,plain,
! [SV338: $i,SV279: $i] :
( ( ( subset @ SV279 @ SV338 )
= $false )
| ( ( SV338
= ( set_union2 @ SV279 @ ( set_difference @ SV338 @ SV279 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1684,plain,
! [SV339: $i,SV280: $i] :
( ( ( in @ SV280 @ SV339 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV280 ) @ SV339 )
= SV339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1685,plain,
! [SV282: $i,SV341: $i] :
( ( ( proper_subset @ SV341 @ SV282 )
= $false )
| ( ( ~ ( subset @ SV282 @ SV341 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1686,plain,
! [SV283: $i,SV365: $i,SV342: $i] :
( ( ( ~ ( disjoint @ SV342 @ SV365 )
| ~ ( subset @ SV283 @ SV342 ) )
= $true )
| ( ( disjoint @ SV283 @ SV365 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1604]) ).
thf(1687,plain,
! [SV343: $i,SV285: $i] :
( ( ( subset @ ( singleton @ SV285 ) @ ( singleton @ SV343 ) )
= $false )
| ( ( SV285 = SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1688,plain,
! [SV366: $i,SV345: $i,SV287: $i] :
( ( ( ~ ( subset @ SV287 @ SV345 )
| ~ ( subset @ SV366 @ SV345 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV287 @ SV366 ) @ SV345 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1689,plain,
! [SV371: $i,SV346: $i,SV288: $i] :
( ( ( ( ( singleton @ SV288 )
!= ( unordered_pair @ SV346 @ SV371 ) ) )
= $true )
| ( ( SV288 = SV346 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(1690,plain,
! [SV347: $i,SV289: $i] :
( ( ( in @ SV289 @ SV347 )
= $false )
| ( ( subset @ SV289 @ ( union @ SV347 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1691,plain,
! [SV367: $i,SV348: $i,SV291: $i] :
( ( ( ( ( singleton @ SV291 )
!= ( unordered_pair @ SV348 @ SV367 ) ) )
= $true )
| ( ( SV348 = SV367 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1609]) ).
thf(1692,plain,
! [SV349: $i,SV292: $i] :
( ( ( in @ SV292 @ SV349 )
= $false )
| ( ( ~ ( in @ SV349 @ SV292 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1693,plain,
! [SV350: $i,SV293: $i] :
( ( ( proper_subset @ SV293 @ SV350 )
= $false )
| ( ( ~ ( proper_subset @ SV350 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1611]) ).
thf(1694,plain,
! [SV368: $i,SV299: $i] :
( ( ( empty @ ( set_union2 @ SV299 @ SV368 ) )
= $false )
| ( ( empty @ SV299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1613]) ).
thf(1695,plain,
! [SV300: $i,SV369: $i] :
( ( ( empty @ ( set_union2 @ SV369 @ SV300 ) )
= $false )
| ( ( empty @ SV300 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1696,plain,
! [SV356: $i,SV305: $i] :
( ( ( disjoint @ SV305 @ SV356 )
= $false )
| ( ( disjoint @ SV356 @ SV305 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1697,plain,
! [SV311: $i,SV357: $i] :
( ( ( empty @ SV357 )
= $false )
| ( ( ~ ( in @ SV311 @ SV357 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1698,plain,
! [SV358: $i,SV312: $i] :
( ( ( SV312 = SV358 )
= $true )
| ( ( ~ ( empty @ SV312 ) )
= $true )
| ( ( ~ ( empty @ SV358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1618]) ).
thf(1699,plain,
! [SV372: $i] :
( ( ! [SY586: $i] :
( ~ ( ~ ( ! [SY587: $i] :
( ~ ( in @ ( sK10_C @ SY586 @ SV372 ) @ SY587 )
| ~ ( in @ SY587 @ SV372 ) )
| ~ ( in @ ( sK10_C @ SY586 @ SV372 ) @ SY586 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SY586 @ SV372 ) @ ( sK11_SY201 @ SY586 @ SV372 ) )
| ~ ( in @ ( sK11_SY201 @ SY586 @ SV372 ) @ SV372 ) )
| ( in @ ( sK10_C @ SY586 @ SV372 ) @ SY586 ) ) )
| ( SY586
= ( union @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1700,plain,
! [SV373: $i] :
( ( ! [SY588: $i] :
( ( SY588
!= ( union @ SV373 ) )
| ~ ( ~ ! [SY589: $i] :
( ! [SY590: $i] :
( ~ ( in @ SY589 @ SY590 )
| ~ ( in @ SY590 @ SV373 ) )
| ( in @ SY589 @ SY588 ) )
| ~ ! [SY591: $i] :
( ~ ( in @ SY591 @ SY588 )
| ~ ( ~ ( in @ SY591 @ ( sK9_D @ SY591 @ SY588 @ SV373 ) )
| ~ ( in @ ( sK9_D @ SY591 @ SY588 @ SV373 ) @ SV373 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1701,plain,
! [SV374: $i] :
( ( ! [SY592: $i] :
( ( ( set_difference @ SV374 @ ( singleton @ SY592 ) )
!= SV374 )
| ~ ( in @ SY592 @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1702,plain,
! [SV375: $i] :
( ( ! [SY593: $i] :
( ( in @ SY593 @ SV375 )
| ( ( set_difference @ SV375 @ ( singleton @ SY593 ) )
= SV375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1703,plain,
! [SV376: $i] :
( ( ! [SY594: $i] :
( ~ ( ~ ( in @ ( sK13_C @ SY594 @ SV376 ) @ SV376 )
| ~ ~ ( in @ ( sK13_C @ SY594 @ SV376 ) @ SY594 ) )
| ( subset @ SV376 @ SY594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1704,plain,
! [SV377: $i] :
( ( ! [SY595: $i] :
( ~ ( subset @ SV377 @ SY595 )
| ! [SY596: $i] :
( ~ ( in @ SY596 @ SV377 )
| ( in @ SY596 @ SY595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1705,plain,
! [SV378: $i] :
( ( ! [SY597: $i] :
( ~ ( ~ ( ( ( sK23_C @ SY597 @ SV378 )
!= SV378 )
| ~ ( in @ ( sK23_C @ SY597 @ SV378 ) @ SY597 ) )
| ~ ( ( ( sK23_C @ SY597 @ SV378 )
= SV378 )
| ( in @ ( sK23_C @ SY597 @ SV378 ) @ SY597 ) ) )
| ( SY597
= ( singleton @ SV378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1706,plain,
! [SV379: $i] :
( ( ! [SY598: $i] :
( ( SY598
!= ( singleton @ SV379 ) )
| ~ ( ~ ! [SY599: $i] :
( ( SY599 != SV379 )
| ( in @ SY599 @ SY598 ) )
| ~ ! [SY600: $i] :
( ~ ( in @ SY600 @ SY598 )
| ( SY600 = SV379 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1707,plain,
! [SV380: $i] :
( ( ! [SY601: $i] :
( ( ( set_intersection2 @ SV380 @ SY601 )
!= empty_set )
| ( disjoint @ SV380 @ SY601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(1708,plain,
! [SV381: $i] :
( ( ! [SY602: $i] :
( ~ ( disjoint @ SV381 @ SY602 )
| ( ( set_intersection2 @ SV381 @ SY602 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1709,plain,
! [SV382: $i] :
( ( ! [SY603: $i] :
( ( SV382 = SY603 )
| ~ ( subset @ SV382 @ SY603 )
| ( proper_subset @ SV382 @ SY603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(1710,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1711,plain,
! [SV359: $i,SV313: $i] :
( ( ~ ! [SY575: $i,SY576: $i] :
( ~ ( in @ SV313 @ SY575 )
| ~ ( in @ SV359 @ SY576 )
| ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY575 @ SY576 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1631]) ).
thf(1712,plain,
! [SV359: $i,SV313: $i] :
( ( ~ ~ ( ~ ! [SY577: $i] :
( ! [SY578: $i] :
~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY577 @ SY578 ) )
| ( in @ SV313 @ SY577 ) )
| ~ ! [SY579: $i,SY580: $i] :
( ~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY579 @ SY580 ) )
| ( in @ SV359 @ SY580 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1631]) ).
thf(1713,plain,
! [SV383: $i] :
( ( ! [SY604: $i] :
( ~ ( in @ SV383 @ SY604 )
| ( subset @ ( singleton @ SV383 ) @ SY604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1714,plain,
! [SV384: $i] :
( ( ! [SY605: $i] :
( ~ ( subset @ ( singleton @ SV384 ) @ SY605 )
| ( in @ SV384 @ SY605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1715,plain,
! [SV314: $i] :
( ( ! [SY514: $i,SY515: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SV314 )
| ~ ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY514 )
| ~ ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY515 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY515 ) )
| ~ ( ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY514 )
| ( in @ ( sK12_D @ SY515 @ SY514 @ SV314 ) @ SY515 ) ) ) )
| ( SY515
= ( set_intersection2 @ SV314 @ SY514 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1634]) ).
thf(1716,plain,
! [SV314: $i] :
( ( ! [SY516: $i,SY517: $i] :
( ( SY517
!= ( set_intersection2 @ SV314 @ SY516 ) )
| ~ ( ~ ! [SY518: $i] :
( ~ ( in @ SY518 @ SV314 )
| ~ ( in @ SY518 @ SY516 )
| ( in @ SY518 @ SY517 ) )
| ~ ~ ( ~ ! [SY519: $i] :
( ~ ( in @ SY519 @ SY517 )
| ( in @ SY519 @ SV314 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY517 )
| ( in @ SX3 @ SY516 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1635]) ).
thf(1717,plain,
! [SV385: $i] :
( ( ! [SY606: $i] :
( ~ ( ~ ( ~ ( in @ ( sK21_C @ SY606 @ SV385 ) @ SY606 )
| ~ ( subset @ ( sK21_C @ SY606 @ SV385 ) @ SV385 ) )
| ~ ( ( in @ ( sK21_C @ SY606 @ SV385 ) @ SY606 )
| ( subset @ ( sK21_C @ SY606 @ SV385 ) @ SV385 ) ) )
| ( SY606
= ( powerset @ SV385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1718,plain,
! [SV386: $i] :
( ( ! [SY607: $i] :
( ( SY607
!= ( powerset @ SV386 ) )
| ~ ( ~ ! [SY608: $i] :
( ~ ( in @ SY608 @ SY607 )
| ( subset @ SY608 @ SV386 ) )
| ~ ! [SY609: $i] :
( ~ ( subset @ SY609 @ SV386 )
| ( in @ SY609 @ SY607 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1719,plain,
! [SV315: $i,SV360: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
| ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 ) )
| ~ ( ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
| ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 ) ) )
= $false )
| ( ( SV315 = SV360 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1720,plain,
! [SV387: $i] :
( ( ! [SY610: $i] :
( ( ( set_difference @ SV387 @ SY610 )
!= SV387 )
| ( disjoint @ SV387 @ SY610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1721,plain,
! [SV388: $i] :
( ( ! [SY611: $i] :
( ~ ( disjoint @ SV388 @ SY611 )
| ( ( set_difference @ SV388 @ SY611 )
= SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1722,plain,
! [SV361: $i,SV316: $i] :
( ( ~ ! [SY581: $i] :
( ! [SY582: $i] :
( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SY581 @ SY582 ) )
| ( SV316 = SY581 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1723,plain,
! [SV361: $i,SV316: $i] :
( ( ~ ! [SY583: $i,SY584: $i] :
( ( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SY583 @ SY584 ) )
| ( SV361 = SY584 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1641]) ).
thf(1724,plain,
! [SV317: $i] :
( ( ! [SY527: $i,SY528: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY528 )
| ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SV317 ) )
| ~ ( ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY528 )
| ~ ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY527 ) ) )
| ~ ( ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY528 )
| ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SV317 )
| ( in @ ( sK19_D @ SY528 @ SY527 @ SV317 ) @ SY527 ) ) )
| ( SY528
= ( set_union2 @ SV317 @ SY527 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1642]) ).
thf(1725,plain,
! [SV317: $i] :
( ( ! [SY529: $i,SY530: $i] :
( ( SY530
!= ( set_union2 @ SV317 @ SY529 ) )
| ~ ( ~ ! [SY531: $i] :
( ~ ( in @ SY531 @ SY530 )
| ( in @ SY531 @ SV317 )
| ( in @ SY531 @ SY529 ) )
| ~ ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV317 )
| ( in @ SY532 @ SY530 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY529 )
| ( in @ SX3 @ SY530 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1643]) ).
thf(1726,plain,
! [SV389: $i] :
( ( ! [SY612: $i] :
( ~ ( subset @ SV389 @ SY612 )
| ~ ( subset @ SY612 @ SV389 )
| ( SV389 = SY612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1727,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1728,plain,
! [SV318: $i] :
( ( ! [SY534: $i,SY535: $i] :
( ~ ( in @ SV318 @ SY535 )
| ~ ( in @ SY534 @ SY535 )
| ( subset @ ( unordered_pair @ SV318 @ SY534 ) @ SY535 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1646]) ).
thf(1729,plain,
! [SV318: $i] :
( ( ~ ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY536 ) @ SY537 )
| ( in @ SV318 @ SY537 ) )
| ~ ! [SY538: $i,SY539: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY538 ) @ SY539 )
| ( in @ SY538 @ SY539 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1730,plain,
! [SV319: $i] :
( ( ! [SY540: $i,SY541: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SY541 @ SY540 @ SV319 ) @ SY541 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
!= SV319 ) )
| ~ ( ~ ( in @ ( sK20_D @ SY541 @ SY540 @ SV319 ) @ SY541 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
!= SY540 ) ) )
| ~ ( ( in @ ( sK20_D @ SY541 @ SY540 @ SV319 ) @ SY541 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
= SV319 )
| ( ( sK20_D @ SY541 @ SY540 @ SV319 )
= SY540 ) ) )
| ( SY541
= ( unordered_pair @ SV319 @ SY540 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1648]) ).
thf(1731,plain,
! [SV319: $i] :
( ( ! [SY542: $i,SY543: $i] :
( ( SY543
!= ( unordered_pair @ SV319 @ SY542 ) )
| ~ ( ~ ! [SY544: $i] :
( ~ ( in @ SY544 @ SY543 )
| ( SY544 = SV319 )
| ( SY544 = SY542 ) )
| ~ ~ ( ~ ! [SY545: $i] :
( ( SY545 != SV319 )
| ( in @ SY545 @ SY543 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY542 )
| ( in @ SX3 @ SY543 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1649]) ).
thf(1732,plain,
! [SV390: $i] :
( ( ( in @ ( sK22_B @ SV390 ) @ SV390 )
| ( SV390 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(1733,plain,
! [SV391: $i] :
( ( ( SV391 != empty_set )
| ! [SY613: $i] :
~ ( in @ SY613 @ SV391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(1734,plain,
( ( ~ ( in @ sK1_A @ sK3_SY197 )
| ~ ( in @ sK2_SY194 @ sK4_SY199 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1735,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY194 ) @ ( cartesian_product2 @ sK3_SY197 @ sK4_SY199 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1736,plain,
! [SV320: $i] :
( ( ! [SY547: $i,SY548: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY547 )
| ~ ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY548 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY548 ) )
| ~ ( ~ ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY547 )
| ( in @ ( sK8_D @ SY548 @ SY547 @ SV320 ) @ SY548 ) ) ) )
| ( SY548
= ( set_difference @ SV320 @ SY547 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1654]) ).
thf(1737,plain,
! [SV320: $i] :
( ( ! [SY549: $i,SY550: $i] :
( ( SY550
!= ( set_difference @ SV320 @ SY549 ) )
| ~ ( ~ ! [SY551: $i] :
( ~ ( in @ SY551 @ SV320 )
| ( in @ SY551 @ SY549 )
| ( in @ SY551 @ SY550 ) )
| ~ ~ ( ~ ! [SY552: $i] :
( ~ ( in @ SY552 @ SY550 )
| ( in @ SY552 @ SV320 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY550 )
| ~ ( in @ SX3 @ SY549 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1655]) ).
thf(1738,plain,
! [SV392: $i] :
( ( ! [SY614: $i] :
( ( ( set_difference @ SV392 @ SY614 )
!= empty_set )
| ( subset @ SV392 @ SY614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1739,plain,
! [SV393: $i] :
( ( ! [SY615: $i] :
( ~ ( subset @ SV393 @ SY615 )
| ( ( set_difference @ SV393 @ SY615 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(1740,plain,
! [SV394: $i] :
( ( ! [SY616: $i] :
( ( disjoint @ SV394 @ SY616 )
| ( in @ ( sK24_C @ SY616 @ SV394 ) @ ( set_intersection2 @ SV394 @ SY616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(1741,plain,
! [SV395: $i] :
( ( ! [SY617: $i] :
( ! [SY618: $i] :
~ ( in @ SY618 @ ( set_intersection2 @ SV395 @ SY617 ) )
| ~ ( disjoint @ SV395 @ SY617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(1742,plain,
! [SV396: $i] :
( ( ! [SY619: $i] :
( ~ ( subset @ SV396 @ ( singleton @ SY619 ) )
| ( SV396 = empty_set )
| ( SV396
= ( singleton @ SY619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1743,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1661]) ).
thf(1744,plain,
! [SV397: $i] :
( ( ! [SY620: $i] :
( ~ ( subset @ SV397 @ ( singleton @ SY620 ) )
| ( SV397 = empty_set )
| ( SV397
= ( singleton @ SY620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(1745,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1746,plain,
! [SV398: $i] :
( ( ! [SY621: $i] :
( ~ ( in @ SV398 @ SY621 )
| ( subset @ ( singleton @ SV398 ) @ SY621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(1747,plain,
! [SV399: $i] :
( ( ! [SY622: $i] :
( ~ ( subset @ ( singleton @ SV399 ) @ SY622 )
| ( in @ SV399 @ SY622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(1748,plain,
! [SV400: $i] :
( ( ! [SY623: $i] :
( ( ( set_difference @ SV400 @ SY623 )
!= empty_set )
| ( subset @ SV400 @ SY623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1749,plain,
! [SV401: $i] :
( ( ! [SY624: $i] :
( ~ ( subset @ SV401 @ SY624 )
| ( ( set_difference @ SV401 @ SY624 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1750,plain,
! [SV402: $i] :
( ( ! [SY625: $i] :
( ( disjoint @ SV402 @ SY625 )
| ~ ( ~ ( in @ ( sK25_C @ SY625 @ SV402 ) @ SV402 )
| ~ ( in @ ( sK25_C @ SY625 @ SV402 ) @ SY625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1751,plain,
! [SV403: $i] :
( ( ! [SY626: $i] :
( ! [SY627: $i] :
( ~ ( in @ SY627 @ SV403 )
| ~ ( in @ SY627 @ SY626 ) )
| ~ ( disjoint @ SV403 @ SY626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1752,plain,
! [SV321: $i] :
( ( ! [SY554: $i,SY555: $i] :
( ~ ( ~ ( ! [SY556: $i,SY557: $i] :
( ~ ( in @ SY556 @ SV321 )
| ~ ( in @ SY557 @ SY554 )
| ( ( sK16_D @ SY555 @ SY554 @ SV321 )
!= ( ordered_pair @ SY556 @ SY557 ) ) )
| ~ ( in @ ( sK16_D @ SY555 @ SY554 @ SV321 ) @ SY555 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SY555 @ SY554 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SY555 @ SY554 @ SV321 ) @ SY554 ) )
| ( ( sK16_D @ SY555 @ SY554 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SY555 @ SY554 @ SV321 ) @ ( sK18_SY207 @ SY555 @ SY554 @ SV321 ) ) ) )
| ( in @ ( sK16_D @ SY555 @ SY554 @ SV321 ) @ SY555 ) ) )
| ( SY555
= ( cartesian_product2 @ SV321 @ SY554 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1753,plain,
! [SV321: $i] :
( ( ! [SY558: $i,SY559: $i] :
( ( SY559
!= ( cartesian_product2 @ SV321 @ SY558 ) )
| ~ ( ~ ! [SY560: $i] :
( ! [SY561: $i,SY562: $i] :
( ~ ( in @ SY561 @ SV321 )
| ~ ( in @ SY562 @ SY558 )
| ( SY560
!= ( ordered_pair @ SY561 @ SY562 ) ) )
| ( in @ SY560 @ SY559 ) )
| ~ ! [SY563: $i] :
( ~ ( in @ SY563 @ SY559 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY563 @ SY559 @ SY558 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SY563 @ SY559 @ SY558 @ SV321 ) @ SY558 ) )
| ( SY563
!= ( ordered_pair @ ( sK14_E @ SY563 @ SY559 @ SY558 @ SV321 ) @ ( sK15_SY202 @ SY563 @ SY559 @ SY558 @ SV321 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1754,plain,
! [SV323: $i,SV262: $i] :
( ( ( in @ SV262 @ SV323 )
= $false )
| ( ( disjoint @ ( singleton @ SV262 ) @ SV323 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1755,plain,
! [SV325: $i,SV264: $i,SV404: $i] :
( ( ( ( in @ SV404 @ SV264 )
| ( subset @ SV264 @ ( set_difference @ SV325 @ ( singleton @ SV404 ) ) ) )
= $true )
| ( ( subset @ SV264 @ SV325 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(1756,plain,
! [SV327: $i,SV362: $i,SV370: $i,SV266: $i] :
( ( ( SV266 = SV370 )
= $true )
| ( ( ( SV266 = SV362 )
| ( ( unordered_pair @ SV266 @ SV327 )
!= ( unordered_pair @ SV362 @ SV370 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1676]) ).
thf(1757,plain,
! [SV363: $i,SV330: $i,SV269: $i] :
( ( ( ~ ( subset @ SV269 @ SV330 ) )
= $true )
| ( ( ~ ( subset @ SV269 @ SV363 ) )
= $true )
| ( ( subset @ SV269 @ ( set_intersection2 @ SV330 @ SV363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1758,plain,
! [SV364: $i,SV331: $i,SV270: $i] :
( ( ( ~ ( subset @ SV270 @ SV331 ) )
= $true )
| ( ( ~ ( subset @ SV331 @ SV364 ) )
= $true )
| ( ( subset @ SV270 @ SV364 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1759,plain,
! [SV332: $i,SV405: $i,SV271: $i] :
( ( ( subset @ ( set_intersection2 @ SV271 @ SV405 ) @ ( set_intersection2 @ SV332 @ SV405 ) )
= $true )
| ( ( subset @ SV271 @ SV332 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(1760,plain,
! [SV334: $i,SV406: $i,SV274: $i] :
( ( ( subset @ ( set_difference @ SV274 @ SV406 ) @ ( set_difference @ SV334 @ SV406 ) )
= $true )
| ( ( subset @ SV274 @ SV334 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1761,plain,
! [SV341: $i,SV282: $i] :
( ( ( subset @ SV282 @ SV341 )
= $false )
| ( ( proper_subset @ SV341 @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1762,plain,
! [SV283: $i,SV365: $i,SV342: $i] :
( ( ( ~ ( disjoint @ SV342 @ SV365 ) )
= $true )
| ( ( ~ ( subset @ SV283 @ SV342 ) )
= $true )
| ( ( disjoint @ SV283 @ SV365 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1686]) ).
thf(1763,plain,
! [SV366: $i,SV345: $i,SV287: $i] :
( ( ( ~ ( subset @ SV287 @ SV345 ) )
= $true )
| ( ( ~ ( subset @ SV366 @ SV345 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV287 @ SV366 ) @ SV345 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1764,plain,
! [SV371: $i,SV346: $i,SV288: $i] :
( ( ( ( singleton @ SV288 )
= ( unordered_pair @ SV346 @ SV371 ) )
= $false )
| ( ( SV288 = SV346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1765,plain,
! [SV367: $i,SV348: $i,SV291: $i] :
( ( ( ( singleton @ SV291 )
= ( unordered_pair @ SV348 @ SV367 ) )
= $false )
| ( ( SV348 = SV367 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1766,plain,
! [SV292: $i,SV349: $i] :
( ( ( in @ SV349 @ SV292 )
= $false )
| ( ( in @ SV292 @ SV349 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(1767,plain,
! [SV293: $i,SV350: $i] :
( ( ( proper_subset @ SV350 @ SV293 )
= $false )
| ( ( proper_subset @ SV293 @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1768,plain,
! [SV357: $i,SV311: $i] :
( ( ( in @ SV311 @ SV357 )
= $false )
| ( ( empty @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1769,plain,
! [SV358: $i,SV312: $i] :
( ( ( empty @ SV312 )
= $false )
| ( ( SV312 = SV358 )
= $true )
| ( ( ~ ( empty @ SV358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1770,plain,
! [SV372: $i,SV407: $i] :
( ( ~ ( ~ ( ! [SY628: $i] :
( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SY628 )
| ~ ( in @ SY628 @ SV372 ) )
| ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ ( sK11_SY201 @ SV407 @ SV372 ) )
| ~ ( in @ ( sK11_SY201 @ SV407 @ SV372 ) @ SV372 ) )
| ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) ) )
| ( SV407
= ( union @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(1771,plain,
! [SV373: $i,SV408: $i] :
( ( ( SV408
!= ( union @ SV373 ) )
| ~ ( ~ ! [SY629: $i] :
( ! [SY590: $i] :
( ~ ( in @ SY629 @ SY590 )
| ~ ( in @ SY590 @ SV373 ) )
| ( in @ SY629 @ SV408 ) )
| ~ ! [SY631: $i] :
( ~ ( in @ SY631 @ SV408 )
| ~ ( ~ ( in @ SY631 @ ( sK9_D @ SY631 @ SV408 @ SV373 ) )
| ~ ( in @ ( sK9_D @ SY631 @ SV408 @ SV373 ) @ SV373 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(1772,plain,
! [SV409: $i,SV374: $i] :
( ( ( ( set_difference @ SV374 @ ( singleton @ SV409 ) )
!= SV374 )
| ~ ( in @ SV409 @ SV374 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(1773,plain,
! [SV375: $i,SV410: $i] :
( ( ( in @ SV410 @ SV375 )
| ( ( set_difference @ SV375 @ ( singleton @ SV410 ) )
= SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(1774,plain,
! [SV376: $i,SV411: $i] :
( ( ~ ( ~ ( in @ ( sK13_C @ SV411 @ SV376 ) @ SV376 )
| ~ ~ ( in @ ( sK13_C @ SV411 @ SV376 ) @ SV411 ) )
| ( subset @ SV376 @ SV411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(1775,plain,
! [SV412: $i,SV377: $i] :
( ( ~ ( subset @ SV377 @ SV412 )
| ! [SY632: $i] :
( ~ ( in @ SY632 @ SV377 )
| ( in @ SY632 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(1776,plain,
! [SV378: $i,SV413: $i] :
( ( ~ ( ~ ( ( ( sK23_C @ SV413 @ SV378 )
!= SV378 )
| ~ ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 ) )
| ~ ( ( ( sK23_C @ SV413 @ SV378 )
= SV378 )
| ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 ) ) )
| ( SV413
= ( singleton @ SV378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(1777,plain,
! [SV379: $i,SV414: $i] :
( ( ( SV414
!= ( singleton @ SV379 ) )
| ~ ( ~ ! [SY633: $i] :
( ( SY633 != SV379 )
| ( in @ SY633 @ SV414 ) )
| ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV414 )
| ( SY634 = SV379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(1778,plain,
! [SV415: $i,SV380: $i] :
( ( ( ( set_intersection2 @ SV380 @ SV415 )
!= empty_set )
| ( disjoint @ SV380 @ SV415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(1779,plain,
! [SV416: $i,SV381: $i] :
( ( ~ ( disjoint @ SV381 @ SV416 )
| ( ( set_intersection2 @ SV381 @ SV416 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(1780,plain,
! [SV417: $i,SV382: $i] :
( ( ( SV382 = SV417 )
| ~ ( subset @ SV382 @ SV417 )
| ( proper_subset @ SV382 @ SV417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(1781,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1710]) ).
thf(1782,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1710]) ).
thf(1783,plain,
! [SV359: $i,SV313: $i] :
( ( ! [SY575: $i,SY576: $i] :
( ~ ( in @ SV313 @ SY575 )
| ~ ( in @ SV359 @ SY576 )
| ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY575 @ SY576 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1711]) ).
thf(1784,plain,
! [SV359: $i,SV313: $i] :
( ( ~ ( ~ ! [SY577: $i] :
( ! [SY578: $i] :
~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY577 @ SY578 ) )
| ( in @ SV313 @ SY577 ) )
| ~ ! [SY579: $i,SY580: $i] :
( ~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY579 @ SY580 ) )
| ( in @ SV359 @ SY580 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1712]) ).
thf(1785,plain,
! [SV418: $i,SV383: $i] :
( ( ~ ( in @ SV383 @ SV418 )
| ( subset @ ( singleton @ SV383 ) @ SV418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(1786,plain,
! [SV419: $i,SV384: $i] :
( ( ~ ( subset @ ( singleton @ SV384 ) @ SV419 )
| ( in @ SV384 @ SV419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(1787,plain,
! [SV314: $i,SV420: $i] :
( ( ! [SY635: $i] :
( ~ ( ~ ( ~ ( in @ ( sK12_D @ SY635 @ SV420 @ SV314 ) @ SV314 )
| ~ ( in @ ( sK12_D @ SY635 @ SV420 @ SV314 ) @ SV420 )
| ~ ( in @ ( sK12_D @ SY635 @ SV420 @ SV314 ) @ SY635 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SY635 @ SV420 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SY635 @ SV420 @ SV314 ) @ SY635 ) )
| ~ ( ( in @ ( sK12_D @ SY635 @ SV420 @ SV314 ) @ SV420 )
| ( in @ ( sK12_D @ SY635 @ SV420 @ SV314 ) @ SY635 ) ) ) )
| ( SY635
= ( set_intersection2 @ SV314 @ SV420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(1788,plain,
! [SV421: $i,SV314: $i] :
( ( ! [SY636: $i] :
( ( SY636
!= ( set_intersection2 @ SV314 @ SV421 ) )
| ~ ( ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ SV314 )
| ~ ( in @ SY637 @ SV421 )
| ( in @ SY637 @ SY636 ) )
| ~ ~ ( ~ ! [SY519: $i] :
( ~ ( in @ SY519 @ SY636 )
| ( in @ SY519 @ SV314 ) )
| ~ ! [SY639: $i] :
( ~ ( in @ SY639 @ SY636 )
| ( in @ SY639 @ SV421 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(1789,plain,
! [SV385: $i,SV422: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
| ~ ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 ) )
| ~ ( ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
| ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 ) ) )
| ( SV422
= ( powerset @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(1790,plain,
! [SV386: $i,SV423: $i] :
( ( ( SV423
!= ( powerset @ SV386 ) )
| ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ SV423 )
| ( subset @ SY640 @ SV386 ) )
| ~ ! [SY641: $i] :
( ~ ( subset @ SY641 @ SV386 )
| ( in @ SY641 @ SV423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(1791,plain,
! [SV315: $i,SV360: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
| ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 ) ) )
= $false )
| ( ( SV315 = SV360 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1719]) ).
thf(1792,plain,
! [SV315: $i,SV360: $i] :
( ( ( ~ ( ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
| ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 ) ) )
= $false )
| ( ( SV315 = SV360 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1719]) ).
thf(1793,plain,
! [SV424: $i,SV387: $i] :
( ( ( ( set_difference @ SV387 @ SV424 )
!= SV387 )
| ( disjoint @ SV387 @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(1794,plain,
! [SV425: $i,SV388: $i] :
( ( ~ ( disjoint @ SV388 @ SV425 )
| ( ( set_difference @ SV388 @ SV425 )
= SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(1795,plain,
! [SV361: $i,SV316: $i] :
( ( ! [SY581: $i] :
( ! [SY582: $i] :
( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SY581 @ SY582 ) )
| ( SV316 = SY581 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1722]) ).
thf(1796,plain,
! [SV361: $i,SV316: $i] :
( ( ! [SY583: $i,SY584: $i] :
( ( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SY583 @ SY584 ) )
| ( SV361 = SY584 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1723]) ).
thf(1797,plain,
! [SV317: $i,SV426: $i] :
( ( ! [SY642: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SY642 @ SV426 @ SV317 ) @ SY642 )
| ~ ( in @ ( sK19_D @ SY642 @ SV426 @ SV317 ) @ SV317 ) )
| ~ ( ~ ( in @ ( sK19_D @ SY642 @ SV426 @ SV317 ) @ SY642 )
| ~ ( in @ ( sK19_D @ SY642 @ SV426 @ SV317 ) @ SV426 ) ) )
| ~ ( ( in @ ( sK19_D @ SY642 @ SV426 @ SV317 ) @ SY642 )
| ( in @ ( sK19_D @ SY642 @ SV426 @ SV317 ) @ SV317 )
| ( in @ ( sK19_D @ SY642 @ SV426 @ SV317 ) @ SV426 ) ) )
| ( SY642
= ( set_union2 @ SV317 @ SV426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(1798,plain,
! [SV427: $i,SV317: $i] :
( ( ! [SY643: $i] :
( ( SY643
!= ( set_union2 @ SV317 @ SV427 ) )
| ~ ( ~ ! [SY644: $i] :
( ~ ( in @ SY644 @ SY643 )
| ( in @ SY644 @ SV317 )
| ( in @ SY644 @ SV427 ) )
| ~ ~ ( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV317 )
| ( in @ SY532 @ SY643 ) )
| ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV427 )
| ( in @ SY646 @ SY643 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(1799,plain,
! [SV428: $i,SV389: $i] :
( ( ~ ( subset @ SV389 @ SV428 )
| ~ ( subset @ SV428 @ SV389 )
| ( SV389 = SV428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(1800,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1727]) ).
thf(1801,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1727]) ).
thf(1802,plain,
! [SV429: $i,SV318: $i] :
( ( ! [SY647: $i] :
( ~ ( in @ SV318 @ SY647 )
| ~ ( in @ SV429 @ SY647 )
| ( subset @ ( unordered_pair @ SV318 @ SV429 ) @ SY647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(1803,plain,
! [SV318: $i] :
( ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY536 ) @ SY537 )
| ( in @ SV318 @ SY537 ) )
| ~ ! [SY538: $i,SY539: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY538 ) @ SY539 )
| ( in @ SY538 @ SY539 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(1804,plain,
! [SV319: $i,SV430: $i] :
( ( ! [SY648: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SY648 @ SV430 @ SV319 ) @ SY648 )
| ( ( sK20_D @ SY648 @ SV430 @ SV319 )
!= SV319 ) )
| ~ ( ~ ( in @ ( sK20_D @ SY648 @ SV430 @ SV319 ) @ SY648 )
| ( ( sK20_D @ SY648 @ SV430 @ SV319 )
!= SV430 ) ) )
| ~ ( ( in @ ( sK20_D @ SY648 @ SV430 @ SV319 ) @ SY648 )
| ( ( sK20_D @ SY648 @ SV430 @ SV319 )
= SV319 )
| ( ( sK20_D @ SY648 @ SV430 @ SV319 )
= SV430 ) ) )
| ( SY648
= ( unordered_pair @ SV319 @ SV430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(1805,plain,
! [SV431: $i,SV319: $i] :
( ( ! [SY649: $i] :
( ( SY649
!= ( unordered_pair @ SV319 @ SV431 ) )
| ~ ( ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SY649 )
| ( SY650 = SV319 )
| ( SY650 = SV431 ) )
| ~ ~ ( ~ ! [SY545: $i] :
( ( SY545 != SV319 )
| ( in @ SY545 @ SY649 ) )
| ~ ! [SY652: $i] :
( ( SY652 != SV431 )
| ( in @ SY652 @ SY649 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(1806,plain,
! [SV390: $i] :
( ( ( in @ ( sK22_B @ SV390 ) @ SV390 )
= $true )
| ( ( SV390 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1732]) ).
thf(1807,plain,
! [SV391: $i] :
( ( ( ( SV391 != empty_set ) )
= $true )
| ( ( ! [SY613: $i] :
~ ( in @ SY613 @ SV391 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1733]) ).
thf(1808,plain,
( ( ~ ( in @ sK1_A @ sK3_SY197 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(1809,plain,
( ( ~ ( in @ sK2_SY194 @ sK4_SY199 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1734]) ).
thf(1810,plain,
! [SV320: $i,SV432: $i] :
( ( ! [SY653: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_D @ SY653 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SY653 @ SV432 @ SV320 ) @ SV432 )
| ~ ( in @ ( sK8_D @ SY653 @ SV432 @ SV320 ) @ SY653 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SY653 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SY653 @ SV432 @ SV320 ) @ SY653 ) )
| ~ ( ~ ( in @ ( sK8_D @ SY653 @ SV432 @ SV320 ) @ SV432 )
| ( in @ ( sK8_D @ SY653 @ SV432 @ SV320 ) @ SY653 ) ) ) )
| ( SY653
= ( set_difference @ SV320 @ SV432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(1811,plain,
! [SV433: $i,SV320: $i] :
( ( ! [SY654: $i] :
( ( SY654
!= ( set_difference @ SV320 @ SV433 ) )
| ~ ( ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ SV320 )
| ( in @ SY655 @ SV433 )
| ( in @ SY655 @ SY654 ) )
| ~ ~ ( ~ ! [SY552: $i] :
( ~ ( in @ SY552 @ SY654 )
| ( in @ SY552 @ SV320 ) )
| ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SY654 )
| ~ ( in @ SY657 @ SV433 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(1812,plain,
! [SV434: $i,SV392: $i] :
( ( ( ( set_difference @ SV392 @ SV434 )
!= empty_set )
| ( subset @ SV392 @ SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(1813,plain,
! [SV435: $i,SV393: $i] :
( ( ~ ( subset @ SV393 @ SV435 )
| ( ( set_difference @ SV393 @ SV435 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(1814,plain,
! [SV436: $i,SV394: $i] :
( ( ( disjoint @ SV394 @ SV436 )
| ( in @ ( sK24_C @ SV436 @ SV394 ) @ ( set_intersection2 @ SV394 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(1815,plain,
! [SV437: $i,SV395: $i] :
( ( ! [SY658: $i] :
~ ( in @ SY658 @ ( set_intersection2 @ SV395 @ SV437 ) )
| ~ ( disjoint @ SV395 @ SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(1816,plain,
! [SV438: $i,SV396: $i] :
( ( ~ ( subset @ SV396 @ ( singleton @ SV438 ) )
| ( SV396 = empty_set )
| ( SV396
= ( singleton @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(1817,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1743]) ).
thf(1818,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1743]) ).
thf(1819,plain,
! [SV439: $i,SV397: $i] :
( ( ~ ( subset @ SV397 @ ( singleton @ SV439 ) )
| ( SV397 = empty_set )
| ( SV397
= ( singleton @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(1820,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1745]) ).
thf(1821,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1745]) ).
thf(1822,plain,
! [SV440: $i,SV398: $i] :
( ( ~ ( in @ SV398 @ SV440 )
| ( subset @ ( singleton @ SV398 ) @ SV440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(1823,plain,
! [SV441: $i,SV399: $i] :
( ( ~ ( subset @ ( singleton @ SV399 ) @ SV441 )
| ( in @ SV399 @ SV441 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(1824,plain,
! [SV442: $i,SV400: $i] :
( ( ( ( set_difference @ SV400 @ SV442 )
!= empty_set )
| ( subset @ SV400 @ SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(1825,plain,
! [SV443: $i,SV401: $i] :
( ( ~ ( subset @ SV401 @ SV443 )
| ( ( set_difference @ SV401 @ SV443 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(1826,plain,
! [SV444: $i,SV402: $i] :
( ( ( disjoint @ SV402 @ SV444 )
| ~ ( ~ ( in @ ( sK25_C @ SV444 @ SV402 ) @ SV402 )
| ~ ( in @ ( sK25_C @ SV444 @ SV402 ) @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(1827,plain,
! [SV445: $i,SV403: $i] :
( ( ! [SY659: $i] :
( ~ ( in @ SY659 @ SV403 )
| ~ ( in @ SY659 @ SV445 ) )
| ~ ( disjoint @ SV403 @ SV445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(1828,plain,
! [SV446: $i,SV321: $i] :
( ( ! [SY660: $i] :
( ~ ( ~ ( ! [SY661: $i,SY662: $i] :
( ~ ( in @ SY661 @ SV321 )
| ~ ( in @ SY662 @ SV446 )
| ( ( sK16_D @ SY660 @ SV446 @ SV321 )
!= ( ordered_pair @ SY661 @ SY662 ) ) )
| ~ ( in @ ( sK16_D @ SY660 @ SV446 @ SV321 ) @ SY660 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SY660 @ SV446 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SY660 @ SV446 @ SV321 ) @ SV446 ) )
| ( ( sK16_D @ SY660 @ SV446 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SY660 @ SV446 @ SV321 ) @ ( sK18_SY207 @ SY660 @ SV446 @ SV321 ) ) ) )
| ( in @ ( sK16_D @ SY660 @ SV446 @ SV321 ) @ SY660 ) ) )
| ( SY660
= ( cartesian_product2 @ SV321 @ SV446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(1829,plain,
! [SV447: $i,SV321: $i] :
( ( ! [SY663: $i] :
( ( SY663
!= ( cartesian_product2 @ SV321 @ SV447 ) )
| ~ ( ~ ! [SY664: $i] :
( ! [SY665: $i,SY666: $i] :
( ~ ( in @ SY665 @ SV321 )
| ~ ( in @ SY666 @ SV447 )
| ( SY664
!= ( ordered_pair @ SY665 @ SY666 ) ) )
| ( in @ SY664 @ SY663 ) )
| ~ ! [SY667: $i] :
( ~ ( in @ SY667 @ SY663 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY667 @ SY663 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SY667 @ SY663 @ SV447 @ SV321 ) @ SV447 ) )
| ( SY667
!= ( ordered_pair @ ( sK14_E @ SY667 @ SY663 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SY667 @ SY663 @ SV447 @ SV321 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(1830,plain,
! [SV325: $i,SV264: $i,SV404: $i] :
( ( ( in @ SV404 @ SV264 )
= $true )
| ( ( subset @ SV264 @ ( set_difference @ SV325 @ ( singleton @ SV404 ) ) )
= $true )
| ( ( subset @ SV264 @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1831,plain,
! [SV370: $i,SV327: $i,SV362: $i,SV266: $i] :
( ( ( SV266 = SV362 )
= $true )
| ( ( ( ( unordered_pair @ SV266 @ SV327 )
!= ( unordered_pair @ SV362 @ SV370 ) ) )
= $true )
| ( ( SV266 = SV370 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(1832,plain,
! [SV363: $i,SV330: $i,SV269: $i] :
( ( ( subset @ SV269 @ SV330 )
= $false )
| ( ( ~ ( subset @ SV269 @ SV363 ) )
= $true )
| ( ( subset @ SV269 @ ( set_intersection2 @ SV330 @ SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1833,plain,
! [SV364: $i,SV331: $i,SV270: $i] :
( ( ( subset @ SV270 @ SV331 )
= $false )
| ( ( ~ ( subset @ SV331 @ SV364 ) )
= $true )
| ( ( subset @ SV270 @ SV364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1834,plain,
! [SV283: $i,SV365: $i,SV342: $i] :
( ( ( disjoint @ SV342 @ SV365 )
= $false )
| ( ( ~ ( subset @ SV283 @ SV342 ) )
= $true )
| ( ( disjoint @ SV283 @ SV365 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1762]) ).
thf(1835,plain,
! [SV366: $i,SV345: $i,SV287: $i] :
( ( ( subset @ SV287 @ SV345 )
= $false )
| ( ( ~ ( subset @ SV366 @ SV345 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV287 @ SV366 ) @ SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1836,plain,
! [SV312: $i,SV358: $i] :
( ( ( empty @ SV358 )
= $false )
| ( ( SV312 = SV358 )
= $true )
| ( ( empty @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1837,plain,
! [SV372: $i,SV407: $i] :
( ( ( ~ ( ~ ( ! [SY628: $i] :
( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SY628 )
| ~ ( in @ SY628 @ SV372 ) )
| ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ ( sK11_SY201 @ SV407 @ SV372 ) )
| ~ ( in @ ( sK11_SY201 @ SV407 @ SV372 ) @ SV372 ) )
| ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) ) ) )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(1838,plain,
! [SV373: $i,SV408: $i] :
( ( ( ( SV408
!= ( union @ SV373 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY629: $i] :
( ! [SY590: $i] :
( ~ ( in @ SY629 @ SY590 )
| ~ ( in @ SY590 @ SV373 ) )
| ( in @ SY629 @ SV408 ) )
| ~ ! [SY631: $i] :
( ~ ( in @ SY631 @ SV408 )
| ~ ( ~ ( in @ SY631 @ ( sK9_D @ SY631 @ SV408 @ SV373 ) )
| ~ ( in @ ( sK9_D @ SY631 @ SV408 @ SV373 ) @ SV373 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(1839,plain,
! [SV409: $i,SV374: $i] :
( ( ( ( ( set_difference @ SV374 @ ( singleton @ SV409 ) )
!= SV374 ) )
= $true )
| ( ( ~ ( in @ SV409 @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(1840,plain,
! [SV375: $i,SV410: $i] :
( ( ( in @ SV410 @ SV375 )
= $true )
| ( ( ( set_difference @ SV375 @ ( singleton @ SV410 ) )
= SV375 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(1841,plain,
! [SV376: $i,SV411: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_C @ SV411 @ SV376 ) @ SV376 )
| ~ ~ ( in @ ( sK13_C @ SV411 @ SV376 ) @ SV411 ) ) )
= $true )
| ( ( subset @ SV376 @ SV411 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(1842,plain,
! [SV412: $i,SV377: $i] :
( ( ( ~ ( subset @ SV377 @ SV412 ) )
= $true )
| ( ( ! [SY632: $i] :
( ~ ( in @ SY632 @ SV377 )
| ( in @ SY632 @ SV412 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(1843,plain,
! [SV378: $i,SV413: $i] :
( ( ( ~ ( ~ ( ( ( sK23_C @ SV413 @ SV378 )
!= SV378 )
| ~ ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 ) )
| ~ ( ( ( sK23_C @ SV413 @ SV378 )
= SV378 )
| ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 ) ) ) )
= $true )
| ( ( SV413
= ( singleton @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1776]) ).
thf(1844,plain,
! [SV379: $i,SV414: $i] :
( ( ( ( SV414
!= ( singleton @ SV379 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY633: $i] :
( ( SY633 != SV379 )
| ( in @ SY633 @ SV414 ) )
| ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV414 )
| ( SY634 = SV379 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1845,plain,
! [SV415: $i,SV380: $i] :
( ( ( ( ( set_intersection2 @ SV380 @ SV415 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV380 @ SV415 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(1846,plain,
! [SV416: $i,SV381: $i] :
( ( ( ~ ( disjoint @ SV381 @ SV416 ) )
= $true )
| ( ( ( set_intersection2 @ SV381 @ SV416 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(1847,plain,
! [SV417: $i,SV382: $i] :
( ( ( ( SV382 = SV417 )
| ~ ( subset @ SV382 @ SV417 ) )
= $true )
| ( ( proper_subset @ SV382 @ SV417 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1780]) ).
thf(1848,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1781]) ).
thf(1849,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1782]) ).
thf(1850,plain,
! [SV359: $i,SV448: $i,SV313: $i] :
( ( ! [SY668: $i] :
( ~ ( in @ SV313 @ SV448 )
| ~ ( in @ SV359 @ SY668 )
| ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV448 @ SY668 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(1851,plain,
! [SV359: $i,SV313: $i] :
( ( ~ ! [SY577: $i] :
( ! [SY578: $i] :
~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY577 @ SY578 ) )
| ( in @ SV313 @ SY577 ) )
| ~ ! [SY579: $i,SY580: $i] :
( ~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY579 @ SY580 ) )
| ( in @ SV359 @ SY580 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(1852,plain,
! [SV418: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ SV418 ) )
= $true )
| ( ( subset @ ( singleton @ SV383 ) @ SV418 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1785]) ).
thf(1853,plain,
! [SV419: $i,SV384: $i] :
( ( ( ~ ( subset @ ( singleton @ SV384 ) @ SV419 ) )
= $true )
| ( ( in @ SV384 @ SV419 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1786]) ).
thf(1854,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
| ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) ) ) )
| ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(1855,plain,
! [SV421: $i,SV314: $i,SV450: $i] :
( ( ( SV450
!= ( set_intersection2 @ SV314 @ SV421 ) )
| ~ ( ~ ! [SY669: $i] :
( ~ ( in @ SY669 @ SV314 )
| ~ ( in @ SY669 @ SV421 )
| ( in @ SY669 @ SV450 ) )
| ~ ~ ( ~ ! [SY670: $i] :
( ~ ( in @ SY670 @ SV450 )
| ( in @ SY670 @ SV314 ) )
| ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ SV450 )
| ( in @ SY671 @ SV421 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(1856,plain,
! [SV385: $i,SV422: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
| ~ ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 ) )
| ~ ( ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
| ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 ) ) ) )
= $true )
| ( ( SV422
= ( powerset @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(1857,plain,
! [SV386: $i,SV423: $i] :
( ( ( ( SV423
!= ( powerset @ SV386 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ SV423 )
| ( subset @ SY640 @ SV386 ) )
| ~ ! [SY641: $i] :
( ~ ( subset @ SY641 @ SV386 )
| ( in @ SY641 @ SV423 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(1858,plain,
! [SV315: $i,SV360: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
| ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 ) )
= $true )
| ( ( SV315 = SV360 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1859,plain,
! [SV315: $i,SV360: $i] :
( ( ( ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
| ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 ) )
= $true )
| ( ( SV315 = SV360 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1792]) ).
thf(1860,plain,
! [SV424: $i,SV387: $i] :
( ( ( ( ( set_difference @ SV387 @ SV424 )
!= SV387 ) )
= $true )
| ( ( disjoint @ SV387 @ SV424 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(1861,plain,
! [SV425: $i,SV388: $i] :
( ( ( ~ ( disjoint @ SV388 @ SV425 ) )
= $true )
| ( ( ( set_difference @ SV388 @ SV425 )
= SV388 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1862,plain,
! [SV451: $i,SV361: $i,SV316: $i] :
( ( ! [SY672: $i] :
( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SV451 @ SY672 ) )
| ( SV316 = SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(1863,plain,
! [SV452: $i,SV361: $i,SV316: $i] :
( ( ! [SY673: $i] :
( ( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SV452 @ SY673 ) )
| ( SV361 = SY673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(1864,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 ) )
| ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) ) )
| ~ ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 )
| ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) ) )
| ( SV453
= ( set_union2 @ SV317 @ SV426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(1865,plain,
! [SV427: $i,SV317: $i,SV454: $i] :
( ( ( SV454
!= ( set_union2 @ SV317 @ SV427 ) )
| ~ ( ~ ! [SY674: $i] :
( ~ ( in @ SY674 @ SV454 )
| ( in @ SY674 @ SV317 )
| ( in @ SY674 @ SV427 ) )
| ~ ~ ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV317 )
| ( in @ SY675 @ SV454 ) )
| ~ ! [SY676: $i] :
( ~ ( in @ SY676 @ SV427 )
| ( in @ SY676 @ SV454 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(1866,plain,
! [SV428: $i,SV389: $i] :
( ( ( ~ ( subset @ SV389 @ SV428 )
| ~ ( subset @ SV428 @ SV389 ) )
= $true )
| ( ( SV389 = SV428 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1799]) ).
thf(1867,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1868,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1869,plain,
! [SV429: $i,SV455: $i,SV318: $i] :
( ( ~ ( in @ SV318 @ SV455 )
| ~ ( in @ SV429 @ SV455 )
| ( subset @ ( unordered_pair @ SV318 @ SV429 ) @ SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(1870,plain,
! [SV318: $i] :
( ( ~ ! [SY536: $i,SY537: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY536 ) @ SY537 )
| ( in @ SV318 @ SY537 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1803]) ).
thf(1871,plain,
! [SV318: $i] :
( ( ~ ! [SY538: $i,SY539: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY538 ) @ SY539 )
| ( in @ SY538 @ SY539 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1803]) ).
thf(1872,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV319 ) )
| ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV430 ) ) )
| ~ ( ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV319 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV430 ) ) )
| ( SV456
= ( unordered_pair @ SV319 @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(1873,plain,
! [SV431: $i,SV319: $i,SV457: $i] :
( ( ( SV457
!= ( unordered_pair @ SV319 @ SV431 ) )
| ~ ( ~ ! [SY677: $i] :
( ~ ( in @ SY677 @ SV457 )
| ( SY677 = SV319 )
| ( SY677 = SV431 ) )
| ~ ~ ( ~ ! [SY678: $i] :
( ( SY678 != SV319 )
| ( in @ SY678 @ SV457 ) )
| ~ ! [SY679: $i] :
( ( SY679 != SV431 )
| ( in @ SY679 @ SV457 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(1874,plain,
! [SV391: $i] :
( ( ( SV391 = empty_set )
= $false )
| ( ( ! [SY613: $i] :
~ ( in @ SY613 @ SV391 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1807]) ).
thf(1875,plain,
( ( in @ sK1_A @ sK3_SY197 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1808]) ).
thf(1876,plain,
( ( in @ sK2_SY194 @ sK4_SY199 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1809]) ).
thf(1877,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
| ~ ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) ) ) )
| ( SV458
= ( set_difference @ SV320 @ SV432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(1878,plain,
! [SV433: $i,SV320: $i,SV459: $i] :
( ( ( SV459
!= ( set_difference @ SV320 @ SV433 ) )
| ~ ( ~ ! [SY680: $i] :
( ~ ( in @ SY680 @ SV320 )
| ( in @ SY680 @ SV433 )
| ( in @ SY680 @ SV459 ) )
| ~ ~ ( ~ ! [SY681: $i] :
( ~ ( in @ SY681 @ SV459 )
| ( in @ SY681 @ SV320 ) )
| ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV459 )
| ~ ( in @ SY682 @ SV433 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(1879,plain,
! [SV434: $i,SV392: $i] :
( ( ( ( ( set_difference @ SV392 @ SV434 )
!= empty_set ) )
= $true )
| ( ( subset @ SV392 @ SV434 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1812]) ).
thf(1880,plain,
! [SV435: $i,SV393: $i] :
( ( ( ~ ( subset @ SV393 @ SV435 ) )
= $true )
| ( ( ( set_difference @ SV393 @ SV435 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1813]) ).
thf(1881,plain,
! [SV436: $i,SV394: $i] :
( ( ( disjoint @ SV394 @ SV436 )
= $true )
| ( ( in @ ( sK24_C @ SV436 @ SV394 ) @ ( set_intersection2 @ SV394 @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1814]) ).
thf(1882,plain,
! [SV437: $i,SV395: $i] :
( ( ( ! [SY658: $i] :
~ ( in @ SY658 @ ( set_intersection2 @ SV395 @ SV437 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV395 @ SV437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1815]) ).
thf(1883,plain,
! [SV438: $i,SV396: $i] :
( ( ( ~ ( subset @ SV396 @ ( singleton @ SV438 ) ) )
= $true )
| ( ( ( SV396 = empty_set )
| ( SV396
= ( singleton @ SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(1884,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1885,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1886,plain,
! [SV439: $i,SV397: $i] :
( ( ( ~ ( subset @ SV397 @ ( singleton @ SV439 ) ) )
= $true )
| ( ( ( SV397 = empty_set )
| ( SV397
= ( singleton @ SV439 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(1887,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1820]) ).
thf(1888,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1821]) ).
thf(1889,plain,
! [SV440: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ SV440 ) )
= $true )
| ( ( subset @ ( singleton @ SV398 ) @ SV440 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(1890,plain,
! [SV441: $i,SV399: $i] :
( ( ( ~ ( subset @ ( singleton @ SV399 ) @ SV441 ) )
= $true )
| ( ( in @ SV399 @ SV441 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1823]) ).
thf(1891,plain,
! [SV442: $i,SV400: $i] :
( ( ( ( ( set_difference @ SV400 @ SV442 )
!= empty_set ) )
= $true )
| ( ( subset @ SV400 @ SV442 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1824]) ).
thf(1892,plain,
! [SV443: $i,SV401: $i] :
( ( ( ~ ( subset @ SV401 @ SV443 ) )
= $true )
| ( ( ( set_difference @ SV401 @ SV443 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(1893,plain,
! [SV444: $i,SV402: $i] :
( ( ( disjoint @ SV402 @ SV444 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK25_C @ SV444 @ SV402 ) @ SV402 )
| ~ ( in @ ( sK25_C @ SV444 @ SV402 ) @ SV444 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(1894,plain,
! [SV445: $i,SV403: $i] :
( ( ( ! [SY659: $i] :
( ~ ( in @ SY659 @ SV403 )
| ~ ( in @ SY659 @ SV445 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV403 @ SV445 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(1895,plain,
! [SV460: $i,SV446: $i,SV321: $i] :
( ( ~ ( ~ ( ! [SY683: $i,SY684: $i] :
( ~ ( in @ SY683 @ SV321 )
| ~ ( in @ SY684 @ SV446 )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ SY683 @ SY684 ) ) )
| ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) @ SV446 ) )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) ) ) )
| ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) ) )
| ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(1896,plain,
! [SV447: $i,SV321: $i,SV461: $i] :
( ( ( SV461
!= ( cartesian_product2 @ SV321 @ SV447 ) )
| ~ ( ~ ! [SY685: $i] :
( ! [SY665: $i,SY666: $i] :
( ~ ( in @ SY665 @ SV321 )
| ~ ( in @ SY666 @ SV447 )
| ( SY685
!= ( ordered_pair @ SY665 @ SY666 ) ) )
| ( in @ SY685 @ SV461 ) )
| ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SV461 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY688 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SY688 @ SV461 @ SV447 @ SV321 ) @ SV447 ) )
| ( SY688
!= ( ordered_pair @ ( sK14_E @ SY688 @ SV461 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SY688 @ SV461 @ SV447 @ SV321 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(1897,plain,
! [SV370: $i,SV362: $i,SV327: $i,SV266: $i] :
( ( ( ( unordered_pair @ SV266 @ SV327 )
= ( unordered_pair @ SV362 @ SV370 ) )
= $false )
| ( ( SV266 = SV362 )
= $true )
| ( ( SV266 = SV370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(1898,plain,
! [SV330: $i,SV363: $i,SV269: $i] :
( ( ( subset @ SV269 @ SV363 )
= $false )
| ( ( subset @ SV269 @ SV330 )
= $false )
| ( ( subset @ SV269 @ ( set_intersection2 @ SV330 @ SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(1899,plain,
! [SV270: $i,SV364: $i,SV331: $i] :
( ( ( subset @ SV331 @ SV364 )
= $false )
| ( ( subset @ SV270 @ SV331 )
= $false )
| ( ( subset @ SV270 @ SV364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(1900,plain,
! [SV365: $i,SV342: $i,SV283: $i] :
( ( ( subset @ SV283 @ SV342 )
= $false )
| ( ( disjoint @ SV342 @ SV365 )
= $false )
| ( ( disjoint @ SV283 @ SV365 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1901,plain,
! [SV287: $i,SV345: $i,SV366: $i] :
( ( ( subset @ SV366 @ SV345 )
= $false )
| ( ( subset @ SV287 @ SV345 )
= $false )
| ( ( subset @ ( set_union2 @ SV287 @ SV366 ) @ SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(1902,plain,
! [SV372: $i,SV407: $i] :
( ( ( ~ ( ! [SY628: $i] :
( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SY628 )
| ~ ( in @ SY628 @ SV372 ) )
| ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) )
| ~ ( ~ ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ ( sK11_SY201 @ SV407 @ SV372 ) )
| ~ ( in @ ( sK11_SY201 @ SV407 @ SV372 ) @ SV372 ) )
| ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) ) )
= $false )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1903,plain,
! [SV373: $i,SV408: $i] :
( ( ( SV408
= ( union @ SV373 ) )
= $false )
| ( ( ~ ( ~ ! [SY629: $i] :
( ! [SY590: $i] :
( ~ ( in @ SY629 @ SY590 )
| ~ ( in @ SY590 @ SV373 ) )
| ( in @ SY629 @ SV408 ) )
| ~ ! [SY631: $i] :
( ~ ( in @ SY631 @ SV408 )
| ~ ( ~ ( in @ SY631 @ ( sK9_D @ SY631 @ SV408 @ SV373 ) )
| ~ ( in @ ( sK9_D @ SY631 @ SV408 @ SV373 ) @ SV373 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(1904,plain,
! [SV409: $i,SV374: $i] :
( ( ( ( set_difference @ SV374 @ ( singleton @ SV409 ) )
= SV374 )
= $false )
| ( ( ~ ( in @ SV409 @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(1905,plain,
! [SV376: $i,SV411: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV411 @ SV376 ) @ SV376 )
| ~ ~ ( in @ ( sK13_C @ SV411 @ SV376 ) @ SV411 ) )
= $false )
| ( ( subset @ SV376 @ SV411 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1841]) ).
thf(1906,plain,
! [SV412: $i,SV377: $i] :
( ( ( subset @ SV377 @ SV412 )
= $false )
| ( ( ! [SY632: $i] :
( ~ ( in @ SY632 @ SV377 )
| ( in @ SY632 @ SV412 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(1907,plain,
! [SV378: $i,SV413: $i] :
( ( ( ~ ( ( ( sK23_C @ SV413 @ SV378 )
!= SV378 )
| ~ ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 ) )
| ~ ( ( ( sK23_C @ SV413 @ SV378 )
= SV378 )
| ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 ) ) )
= $false )
| ( ( SV413
= ( singleton @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(1908,plain,
! [SV379: $i,SV414: $i] :
( ( ( SV414
= ( singleton @ SV379 ) )
= $false )
| ( ( ~ ( ~ ! [SY633: $i] :
( ( SY633 != SV379 )
| ( in @ SY633 @ SV414 ) )
| ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV414 )
| ( SY634 = SV379 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(1909,plain,
! [SV415: $i,SV380: $i] :
( ( ( ( set_intersection2 @ SV380 @ SV415 )
= empty_set )
= $false )
| ( ( disjoint @ SV380 @ SV415 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1910,plain,
! [SV416: $i,SV381: $i] :
( ( ( disjoint @ SV381 @ SV416 )
= $false )
| ( ( ( set_intersection2 @ SV381 @ SV416 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1911,plain,
! [SV417: $i,SV382: $i] :
( ( ( SV382 = SV417 )
= $true )
| ( ( ~ ( subset @ SV382 @ SV417 ) )
= $true )
| ( ( proper_subset @ SV382 @ SV417 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(1912,plain,
! [SV462: $i] :
( ( ! [SY689: $i] :
( ~ ( proper_subset @ SV462 @ SY689 )
| ( SV462 != SY689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(1913,plain,
! [SV463: $i] :
( ( ! [SY690: $i] :
( ~ ( proper_subset @ SV463 @ SY690 )
| ( subset @ SV463 @ SY690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(1914,plain,
! [SV464: $i,SV359: $i,SV448: $i,SV313: $i] :
( ( ~ ( in @ SV313 @ SV448 )
| ~ ( in @ SV359 @ SV464 )
| ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV448 @ SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(1915,plain,
! [SV359: $i,SV313: $i] :
( ( ~ ! [SY577: $i] :
( ! [SY578: $i] :
~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY577 @ SY578 ) )
| ( in @ SV313 @ SY577 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1851]) ).
thf(1916,plain,
! [SV359: $i,SV313: $i] :
( ( ~ ! [SY579: $i,SY580: $i] :
( ~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY579 @ SY580 ) )
| ( in @ SV359 @ SY580 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1851]) ).
thf(1917,plain,
! [SV418: $i,SV383: $i] :
( ( ( in @ SV383 @ SV418 )
= $false )
| ( ( subset @ ( singleton @ SV383 ) @ SV418 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(1918,plain,
! [SV419: $i,SV384: $i] :
( ( ( subset @ ( singleton @ SV384 ) @ SV419 )
= $false )
| ( ( in @ SV384 @ SV419 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1919,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
| ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) ) ) ) )
= $true )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(1920,plain,
! [SV421: $i,SV314: $i,SV450: $i] :
( ( ( ( SV450
!= ( set_intersection2 @ SV314 @ SV421 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY669: $i] :
( ~ ( in @ SY669 @ SV314 )
| ~ ( in @ SY669 @ SV421 )
| ( in @ SY669 @ SV450 ) )
| ~ ~ ( ~ ! [SY670: $i] :
( ~ ( in @ SY670 @ SV450 )
| ( in @ SY670 @ SV314 ) )
| ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ SV450 )
| ( in @ SY671 @ SV421 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(1921,plain,
! [SV385: $i,SV422: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
| ~ ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 ) )
| ~ ( ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
| ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 ) ) )
= $false )
| ( ( SV422
= ( powerset @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(1922,plain,
! [SV386: $i,SV423: $i] :
( ( ( SV423
= ( powerset @ SV386 ) )
= $false )
| ( ( ~ ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ SV423 )
| ( subset @ SY640 @ SV386 ) )
| ~ ! [SY641: $i] :
( ~ ( subset @ SY641 @ SV386 )
| ( in @ SY641 @ SV423 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1923,plain,
! [SV315: $i,SV360: $i] :
( ( ( ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 ) )
= $true )
| ( ( ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 ) )
= $true )
| ( ( SV315 = SV360 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(1924,plain,
! [SV315: $i,SV360: $i] :
( ( ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
= $true )
| ( ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 )
= $true )
| ( ( SV315 = SV360 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(1925,plain,
! [SV424: $i,SV387: $i] :
( ( ( ( set_difference @ SV387 @ SV424 )
= SV387 )
= $false )
| ( ( disjoint @ SV387 @ SV424 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(1926,plain,
! [SV425: $i,SV388: $i] :
( ( ( disjoint @ SV388 @ SV425 )
= $false )
| ( ( ( set_difference @ SV388 @ SV425 )
= SV388 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1927,plain,
! [SV451: $i,SV361: $i,SV316: $i] :
( ( ( ! [SY672: $i] :
( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SV451 @ SY672 ) ) )
= $true )
| ( ( SV316 = SV451 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(1928,plain,
! [SV465: $i,SV452: $i,SV361: $i,SV316: $i] :
( ( ( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SV452 @ SV465 ) )
| ( SV361 = SV465 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(1929,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 ) )
| ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) ) )
| ~ ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 )
| ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) ) ) )
= $true )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1864]) ).
thf(1930,plain,
! [SV427: $i,SV317: $i,SV454: $i] :
( ( ( ( SV454
!= ( set_union2 @ SV317 @ SV427 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY674: $i] :
( ~ ( in @ SY674 @ SV454 )
| ( in @ SY674 @ SV317 )
| ( in @ SY674 @ SV427 ) )
| ~ ~ ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV317 )
| ( in @ SY675 @ SV454 ) )
| ~ ! [SY676: $i] :
( ~ ( in @ SY676 @ SV427 )
| ( in @ SY676 @ SV454 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(1931,plain,
! [SV428: $i,SV389: $i] :
( ( ( ~ ( subset @ SV389 @ SV428 ) )
= $true )
| ( ( ~ ( subset @ SV428 @ SV389 ) )
= $true )
| ( ( SV389 = SV428 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(1932,plain,
! [SV466: $i] :
( ( ! [SY691: $i] :
( ( SV466 != SY691 )
| ( subset @ SV466 @ SY691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(1933,plain,
! [SV467: $i] :
( ( ! [SY692: $i] :
( ( SV467 != SY692 )
| ( subset @ SY692 @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(1934,plain,
! [SV429: $i,SV455: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV455 )
| ~ ( in @ SV429 @ SV455 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV318 @ SV429 ) @ SV455 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(1935,plain,
! [SV318: $i] :
( ( ! [SY536: $i,SY537: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY536 ) @ SY537 )
| ( in @ SV318 @ SY537 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1870]) ).
thf(1936,plain,
! [SV318: $i] :
( ( ! [SY538: $i,SY539: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SY538 ) @ SY539 )
| ( in @ SY538 @ SY539 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1871]) ).
thf(1937,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV319 ) )
| ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV430 ) ) )
| ~ ( ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV319 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV430 ) ) ) )
= $true )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(1938,plain,
! [SV431: $i,SV319: $i,SV457: $i] :
( ( ( ( SV457
!= ( unordered_pair @ SV319 @ SV431 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY677: $i] :
( ~ ( in @ SY677 @ SV457 )
| ( SY677 = SV319 )
| ( SY677 = SV431 ) )
| ~ ~ ( ~ ! [SY678: $i] :
( ( SY678 != SV319 )
| ( in @ SY678 @ SV457 ) )
| ~ ! [SY679: $i] :
( ( SY679 != SV431 )
| ( in @ SY679 @ SV457 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(1939,plain,
! [SV391: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV391 ) )
= $true )
| ( ( SV391 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(1940,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
| ~ ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) ) ) ) )
= $true )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(1941,plain,
! [SV433: $i,SV320: $i,SV459: $i] :
( ( ( ( SV459
!= ( set_difference @ SV320 @ SV433 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY680: $i] :
( ~ ( in @ SY680 @ SV320 )
| ( in @ SY680 @ SV433 )
| ( in @ SY680 @ SV459 ) )
| ~ ~ ( ~ ! [SY681: $i] :
( ~ ( in @ SY681 @ SV459 )
| ( in @ SY681 @ SV320 ) )
| ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV459 )
| ~ ( in @ SY682 @ SV433 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1878]) ).
thf(1942,plain,
! [SV434: $i,SV392: $i] :
( ( ( ( set_difference @ SV392 @ SV434 )
= empty_set )
= $false )
| ( ( subset @ SV392 @ SV434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1943,plain,
! [SV435: $i,SV393: $i] :
( ( ( subset @ SV393 @ SV435 )
= $false )
| ( ( ( set_difference @ SV393 @ SV435 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(1944,plain,
! [SV437: $i,SV395: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ ( set_intersection2 @ SV395 @ SV437 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV395 @ SV437 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(1945,plain,
! [SV438: $i,SV396: $i] :
( ( ( subset @ SV396 @ ( singleton @ SV438 ) )
= $false )
| ( ( ( SV396 = empty_set )
| ( SV396
= ( singleton @ SV438 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1883]) ).
thf(1946,plain,
! [SV470: $i] :
( ( ( SV470 != empty_set )
| ! [SY693: $i] : ( subset @ SV470 @ ( singleton @ SY693 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(1947,plain,
! [SV471: $i] :
( ( ! [SY694: $i] :
( ( SV471
!= ( singleton @ SY694 ) )
| ( subset @ SV471 @ ( singleton @ SY694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(1948,plain,
! [SV439: $i,SV397: $i] :
( ( ( subset @ SV397 @ ( singleton @ SV439 ) )
= $false )
| ( ( ( SV397 = empty_set )
| ( SV397
= ( singleton @ SV439 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(1949,plain,
! [SV472: $i] :
( ( ( SV472 != empty_set )
| ! [SY695: $i] : ( subset @ SV472 @ ( singleton @ SY695 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(1950,plain,
! [SV473: $i] :
( ( ! [SY696: $i] :
( ( SV473
!= ( singleton @ SY696 ) )
| ( subset @ SV473 @ ( singleton @ SY696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(1951,plain,
! [SV440: $i,SV398: $i] :
( ( ( in @ SV398 @ SV440 )
= $false )
| ( ( subset @ ( singleton @ SV398 ) @ SV440 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1952,plain,
! [SV441: $i,SV399: $i] :
( ( ( subset @ ( singleton @ SV399 ) @ SV441 )
= $false )
| ( ( in @ SV399 @ SV441 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1890]) ).
thf(1953,plain,
! [SV442: $i,SV400: $i] :
( ( ( ( set_difference @ SV400 @ SV442 )
= empty_set )
= $false )
| ( ( subset @ SV400 @ SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(1954,plain,
! [SV443: $i,SV401: $i] :
( ( ( subset @ SV401 @ SV443 )
= $false )
| ( ( ( set_difference @ SV401 @ SV443 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(1955,plain,
! [SV402: $i,SV444: $i] :
( ( ( ~ ( in @ ( sK25_C @ SV444 @ SV402 ) @ SV402 )
| ~ ( in @ ( sK25_C @ SV444 @ SV402 ) @ SV444 ) )
= $false )
| ( ( disjoint @ SV402 @ SV444 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(1956,plain,
! [SV445: $i,SV403: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ SV403 )
| ~ ( in @ SV474 @ SV445 ) )
= $true )
| ( ( ~ ( disjoint @ SV403 @ SV445 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(1957,plain,
! [SV460: $i,SV446: $i,SV321: $i] :
( ( ( ~ ( ~ ( ! [SY683: $i,SY684: $i] :
( ~ ( in @ SY683 @ SV321 )
| ~ ( in @ SY684 @ SV446 )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ SY683 @ SY684 ) ) )
| ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) @ SV446 ) )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) ) ) )
| ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) ) ) )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(1958,plain,
! [SV447: $i,SV321: $i,SV461: $i] :
( ( ( ( SV461
!= ( cartesian_product2 @ SV321 @ SV447 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY685: $i] :
( ! [SY665: $i,SY666: $i] :
( ~ ( in @ SY665 @ SV321 )
| ~ ( in @ SY666 @ SV447 )
| ( SY685
!= ( ordered_pair @ SY665 @ SY666 ) ) )
| ( in @ SY685 @ SV461 ) )
| ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SV461 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY688 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SY688 @ SV461 @ SV447 @ SV321 ) @ SV447 ) )
| ( SY688
!= ( ordered_pair @ ( sK14_E @ SY688 @ SV461 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SY688 @ SV461 @ SV447 @ SV321 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1896]) ).
thf(1959,plain,
! [SV372: $i,SV407: $i] :
( ( ( ~ ( ! [SY628: $i] :
( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SY628 )
| ~ ( in @ SY628 @ SV372 ) )
| ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) ) )
= $false )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1902]) ).
thf(1960,plain,
! [SV372: $i,SV407: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ ( sK11_SY201 @ SV407 @ SV372 ) )
| ~ ( in @ ( sK11_SY201 @ SV407 @ SV372 ) @ SV372 ) )
| ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) ) )
= $false )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1902]) ).
thf(1961,plain,
! [SV408: $i,SV373: $i] :
( ( ( ~ ! [SY629: $i] :
( ! [SY590: $i] :
( ~ ( in @ SY629 @ SY590 )
| ~ ( in @ SY590 @ SV373 ) )
| ( in @ SY629 @ SV408 ) )
| ~ ! [SY631: $i] :
( ~ ( in @ SY631 @ SV408 )
| ~ ( ~ ( in @ SY631 @ ( sK9_D @ SY631 @ SV408 @ SV373 ) )
| ~ ( in @ ( sK9_D @ SY631 @ SV408 @ SV373 ) @ SV373 ) ) ) )
= $false )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(1962,plain,
! [SV374: $i,SV409: $i] :
( ( ( in @ SV409 @ SV374 )
= $false )
| ( ( ( set_difference @ SV374 @ ( singleton @ SV409 ) )
= SV374 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(1963,plain,
! [SV376: $i,SV411: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV411 @ SV376 ) @ SV376 ) )
= $false )
| ( ( subset @ SV376 @ SV411 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1905]) ).
thf(1964,plain,
! [SV376: $i,SV411: $i] :
( ( ( ~ ~ ( in @ ( sK13_C @ SV411 @ SV376 ) @ SV411 ) )
= $false )
| ( ( subset @ SV376 @ SV411 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1905]) ).
thf(1965,plain,
! [SV412: $i,SV377: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV377 )
| ( in @ SV475 @ SV412 ) )
= $true )
| ( ( subset @ SV377 @ SV412 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(1966,plain,
! [SV378: $i,SV413: $i] :
( ( ( ~ ( ( ( sK23_C @ SV413 @ SV378 )
!= SV378 )
| ~ ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 ) ) )
= $false )
| ( ( SV413
= ( singleton @ SV378 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1907]) ).
thf(1967,plain,
! [SV378: $i,SV413: $i] :
( ( ( ~ ( ( ( sK23_C @ SV413 @ SV378 )
= SV378 )
| ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 ) ) )
= $false )
| ( ( SV413
= ( singleton @ SV378 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1907]) ).
thf(1968,plain,
! [SV414: $i,SV379: $i] :
( ( ( ~ ! [SY633: $i] :
( ( SY633 != SV379 )
| ( in @ SY633 @ SV414 ) )
| ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV414 )
| ( SY634 = SV379 ) ) )
= $false )
| ( ( SV414
= ( singleton @ SV379 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(1969,plain,
! [SV417: $i,SV382: $i] :
( ( ( subset @ SV382 @ SV417 )
= $false )
| ( ( SV382 = SV417 )
= $true )
| ( ( proper_subset @ SV382 @ SV417 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(1970,plain,
! [SV476: $i,SV462: $i] :
( ( ~ ( proper_subset @ SV462 @ SV476 )
| ( SV462 != SV476 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(1971,plain,
! [SV477: $i,SV463: $i] :
( ( ~ ( proper_subset @ SV463 @ SV477 )
| ( subset @ SV463 @ SV477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(1972,plain,
! [SV464: $i,SV359: $i,SV448: $i,SV313: $i] :
( ( ( ~ ( in @ SV313 @ SV448 )
| ~ ( in @ SV359 @ SV464 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV448 @ SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(1973,plain,
! [SV359: $i,SV313: $i] :
( ( ! [SY577: $i] :
( ! [SY578: $i] :
~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY577 @ SY578 ) )
| ( in @ SV313 @ SY577 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1915]) ).
thf(1974,plain,
! [SV359: $i,SV313: $i] :
( ( ! [SY579: $i,SY580: $i] :
( ~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SY579 @ SY580 ) )
| ( in @ SV359 @ SY580 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1916]) ).
thf(1975,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
| ~ ~ ( ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
| ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) ) ) )
= $false )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(1976,plain,
! [SV421: $i,SV314: $i,SV450: $i] :
( ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false )
| ( ( ~ ( ~ ! [SY669: $i] :
( ~ ( in @ SY669 @ SV314 )
| ~ ( in @ SY669 @ SV421 )
| ( in @ SY669 @ SV450 ) )
| ~ ~ ( ~ ! [SY670: $i] :
( ~ ( in @ SY670 @ SV450 )
| ( in @ SY670 @ SV314 ) )
| ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ SV450 )
| ( in @ SY671 @ SV421 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(1977,plain,
! [SV385: $i,SV422: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
| ~ ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 ) ) )
= $false )
| ( ( SV422
= ( powerset @ SV385 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(1978,plain,
! [SV385: $i,SV422: $i] :
( ( ( ~ ( ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
| ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 ) ) )
= $false )
| ( ( SV422
= ( powerset @ SV385 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(1979,plain,
! [SV386: $i,SV423: $i] :
( ( ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ SV423 )
| ( subset @ SY640 @ SV386 ) )
| ~ ! [SY641: $i] :
( ~ ( subset @ SY641 @ SV386 )
| ( in @ SY641 @ SV423 ) ) )
= $false )
| ( ( SV423
= ( powerset @ SV386 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(1980,plain,
! [SV315: $i,SV360: $i] :
( ( ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
= $false )
| ( ( ~ ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 ) )
= $true )
| ( ( SV315 = SV360 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(1981,plain,
! [SV478: $i,SV451: $i,SV361: $i,SV316: $i] :
( ( ( ( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SV451 @ SV478 ) ) )
= $true )
| ( ( SV316 = SV451 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(1982,plain,
! [SV465: $i,SV452: $i,SV361: $i,SV316: $i] :
( ( ( ( ( ordered_pair @ SV316 @ SV361 )
!= ( ordered_pair @ SV452 @ SV465 ) ) )
= $true )
| ( ( SV361 = SV465 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(1983,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 ) )
| ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) ) )
| ~ ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 )
| ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) ) )
= $false )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(1984,plain,
! [SV427: $i,SV317: $i,SV454: $i] :
( ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false )
| ( ( ~ ( ~ ! [SY674: $i] :
( ~ ( in @ SY674 @ SV454 )
| ( in @ SY674 @ SV317 )
| ( in @ SY674 @ SV427 ) )
| ~ ~ ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV317 )
| ( in @ SY675 @ SV454 ) )
| ~ ! [SY676: $i] :
( ~ ( in @ SY676 @ SV427 )
| ( in @ SY676 @ SV454 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(1985,plain,
! [SV428: $i,SV389: $i] :
( ( ( subset @ SV389 @ SV428 )
= $false )
| ( ( ~ ( subset @ SV428 @ SV389 ) )
= $true )
| ( ( SV389 = SV428 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(1986,plain,
! [SV479: $i,SV466: $i] :
( ( ( SV466 != SV479 )
| ( subset @ SV466 @ SV479 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(1987,plain,
! [SV480: $i,SV467: $i] :
( ( ( SV467 != SV480 )
| ( subset @ SV480 @ SV467 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(1988,plain,
! [SV429: $i,SV455: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV455 ) )
= $true )
| ( ( ~ ( in @ SV429 @ SV455 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV318 @ SV429 ) @ SV455 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(1989,plain,
! [SV481: $i,SV318: $i] :
( ( ! [SY697: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SV481 ) @ SY697 )
| ( in @ SV318 @ SY697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(1990,plain,
! [SV482: $i,SV318: $i] :
( ( ! [SY698: $i] :
( ~ ( subset @ ( unordered_pair @ SV318 @ SV482 ) @ SY698 )
| ( in @ SV482 @ SY698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(1991,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV319 ) )
| ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV430 ) ) )
| ~ ( ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV319 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV430 ) ) )
= $false )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(1992,plain,
! [SV431: $i,SV319: $i,SV457: $i] :
( ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false )
| ( ( ~ ( ~ ! [SY677: $i] :
( ~ ( in @ SY677 @ SV457 )
| ( SY677 = SV319 )
| ( SY677 = SV431 ) )
| ~ ~ ( ~ ! [SY678: $i] :
( ( SY678 != SV319 )
| ( in @ SY678 @ SV457 ) )
| ~ ! [SY679: $i] :
( ( SY679 != SV431 )
| ( in @ SY679 @ SV457 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(1993,plain,
! [SV391: $i,SV468: $i] :
( ( ( in @ SV468 @ SV391 )
= $false )
| ( ( SV391 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(1994,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
| ~ ~ ( ~ ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
| ~ ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) ) ) )
= $false )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(1995,plain,
! [SV433: $i,SV320: $i,SV459: $i] :
( ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false )
| ( ( ~ ( ~ ! [SY680: $i] :
( ~ ( in @ SY680 @ SV320 )
| ( in @ SY680 @ SV433 )
| ( in @ SY680 @ SV459 ) )
| ~ ~ ( ~ ! [SY681: $i] :
( ~ ( in @ SY681 @ SV459 )
| ( in @ SY681 @ SV320 ) )
| ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV459 )
| ~ ( in @ SY682 @ SV433 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(1996,plain,
! [SV437: $i,SV395: $i,SV469: $i] :
( ( ( in @ SV469 @ ( set_intersection2 @ SV395 @ SV437 ) )
= $false )
| ( ( ~ ( disjoint @ SV395 @ SV437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(1997,plain,
! [SV438: $i,SV396: $i] :
( ( ( SV396 = empty_set )
= $true )
| ( ( SV396
= ( singleton @ SV438 ) )
= $true )
| ( ( subset @ SV396 @ ( singleton @ SV438 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(1998,plain,
! [SV470: $i] :
( ( ( ( SV470 != empty_set ) )
= $true )
| ( ( ! [SY693: $i] : ( subset @ SV470 @ ( singleton @ SY693 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(1999,plain,
! [SV483: $i,SV471: $i] :
( ( ( SV471
!= ( singleton @ SV483 ) )
| ( subset @ SV471 @ ( singleton @ SV483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2000,plain,
! [SV439: $i,SV397: $i] :
( ( ( SV397 = empty_set )
= $true )
| ( ( SV397
= ( singleton @ SV439 ) )
= $true )
| ( ( subset @ SV397 @ ( singleton @ SV439 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2001,plain,
! [SV472: $i] :
( ( ( ( SV472 != empty_set ) )
= $true )
| ( ( ! [SY695: $i] : ( subset @ SV472 @ ( singleton @ SY695 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1949]) ).
thf(2002,plain,
! [SV484: $i,SV473: $i] :
( ( ( SV473
!= ( singleton @ SV484 ) )
| ( subset @ SV473 @ ( singleton @ SV484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2003,plain,
! [SV402: $i,SV444: $i] :
( ( ( ~ ( in @ ( sK25_C @ SV444 @ SV402 ) @ SV402 ) )
= $false )
| ( ( disjoint @ SV402 @ SV444 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2004,plain,
! [SV402: $i,SV444: $i] :
( ( ( ~ ( in @ ( sK25_C @ SV444 @ SV402 ) @ SV444 ) )
= $false )
| ( ( disjoint @ SV402 @ SV444 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2005,plain,
! [SV445: $i,SV403: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ SV403 ) )
= $true )
| ( ( ~ ( in @ SV474 @ SV445 ) )
= $true )
| ( ( ~ ( disjoint @ SV403 @ SV445 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(2006,plain,
! [SV460: $i,SV446: $i,SV321: $i] :
( ( ( ~ ( ! [SY683: $i,SY684: $i] :
( ~ ( in @ SY683 @ SV321 )
| ~ ( in @ SY684 @ SV446 )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ SY683 @ SY684 ) ) )
| ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) @ SV446 ) )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) ) ) )
| ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) ) )
= $false )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2007,plain,
! [SV447: $i,SV321: $i,SV461: $i] :
( ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false )
| ( ( ~ ( ~ ! [SY685: $i] :
( ! [SY665: $i,SY666: $i] :
( ~ ( in @ SY665 @ SV321 )
| ~ ( in @ SY666 @ SV447 )
| ( SY685
!= ( ordered_pair @ SY665 @ SY666 ) ) )
| ( in @ SY685 @ SV461 ) )
| ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SV461 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY688 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SY688 @ SV461 @ SV447 @ SV321 ) @ SV447 ) )
| ( SY688
!= ( ordered_pair @ ( sK14_E @ SY688 @ SV461 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SY688 @ SV461 @ SV447 @ SV321 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2008,plain,
! [SV372: $i,SV407: $i] :
( ( ( ! [SY628: $i] :
( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SY628 )
| ~ ( in @ SY628 @ SV372 ) )
| ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1959]) ).
thf(2009,plain,
! [SV372: $i,SV407: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ ( sK11_SY201 @ SV407 @ SV372 ) )
| ~ ( in @ ( sK11_SY201 @ SV407 @ SV372 ) @ SV372 ) )
| ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1960]) ).
thf(2010,plain,
! [SV408: $i,SV373: $i] :
( ( ( ~ ! [SY629: $i] :
( ! [SY590: $i] :
( ~ ( in @ SY629 @ SY590 )
| ~ ( in @ SY590 @ SV373 ) )
| ( in @ SY629 @ SV408 ) ) )
= $false )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1961]) ).
thf(2011,plain,
! [SV373: $i,SV408: $i] :
( ( ( ~ ! [SY631: $i] :
( ~ ( in @ SY631 @ SV408 )
| ~ ( ~ ( in @ SY631 @ ( sK9_D @ SY631 @ SV408 @ SV373 ) )
| ~ ( in @ ( sK9_D @ SY631 @ SV408 @ SV373 ) @ SV373 ) ) ) )
= $false )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1961]) ).
thf(2012,plain,
! [SV376: $i,SV411: $i] :
( ( ( in @ ( sK13_C @ SV411 @ SV376 ) @ SV376 )
= $true )
| ( ( subset @ SV376 @ SV411 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1963]) ).
thf(2013,plain,
! [SV376: $i,SV411: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV411 @ SV376 ) @ SV411 ) )
= $true )
| ( ( subset @ SV376 @ SV411 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1964]) ).
thf(2014,plain,
! [SV412: $i,SV377: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV377 ) )
= $true )
| ( ( in @ SV475 @ SV412 )
= $true )
| ( ( subset @ SV377 @ SV412 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2015,plain,
! [SV378: $i,SV413: $i] :
( ( ( ( ( sK23_C @ SV413 @ SV378 )
!= SV378 )
| ~ ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 ) )
= $true )
| ( ( SV413
= ( singleton @ SV378 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1966]) ).
thf(2016,plain,
! [SV378: $i,SV413: $i] :
( ( ( ( ( sK23_C @ SV413 @ SV378 )
= SV378 )
| ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 ) )
= $true )
| ( ( SV413
= ( singleton @ SV378 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1967]) ).
thf(2017,plain,
! [SV414: $i,SV379: $i] :
( ( ( ~ ! [SY633: $i] :
( ( SY633 != SV379 )
| ( in @ SY633 @ SV414 ) ) )
= $false )
| ( ( SV414
= ( singleton @ SV379 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1968]) ).
thf(2018,plain,
! [SV379: $i,SV414: $i] :
( ( ( ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV414 )
| ( SY634 = SV379 ) ) )
= $false )
| ( ( SV414
= ( singleton @ SV379 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1968]) ).
thf(2019,plain,
! [SV476: $i,SV462: $i] :
( ( ( ~ ( proper_subset @ SV462 @ SV476 ) )
= $true )
| ( ( ( SV462 != SV476 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1970]) ).
thf(2020,plain,
! [SV477: $i,SV463: $i] :
( ( ( ~ ( proper_subset @ SV463 @ SV477 ) )
= $true )
| ( ( subset @ SV463 @ SV477 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1971]) ).
thf(2021,plain,
! [SV464: $i,SV359: $i,SV448: $i,SV313: $i] :
( ( ( ~ ( in @ SV313 @ SV448 ) )
= $true )
| ( ( ~ ( in @ SV359 @ SV464 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV448 @ SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1972]) ).
thf(2022,plain,
! [SV485: $i,SV359: $i,SV313: $i] :
( ( ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV485 @ SY699 ) )
| ( in @ SV313 @ SV485 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2023,plain,
! [SV486: $i,SV359: $i,SV313: $i] :
( ( ! [SY700: $i] :
( ~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV486 @ SY700 ) )
| ( in @ SV359 @ SY700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2024,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) ) )
= $false )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1975]) ).
thf(2025,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
| ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) ) ) )
= $false )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1975]) ).
thf(2026,plain,
! [SV450: $i,SV421: $i,SV314: $i] :
( ( ( ~ ! [SY669: $i] :
( ~ ( in @ SY669 @ SV314 )
| ~ ( in @ SY669 @ SV421 )
| ( in @ SY669 @ SV450 ) )
| ~ ~ ( ~ ! [SY670: $i] :
( ~ ( in @ SY670 @ SV450 )
| ( in @ SY670 @ SV314 ) )
| ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ SV450 )
| ( in @ SY671 @ SV421 ) ) ) )
= $false )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2027,plain,
! [SV385: $i,SV422: $i] :
( ( ( ~ ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
| ~ ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 ) )
= $true )
| ( ( SV422
= ( powerset @ SV385 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1977]) ).
thf(2028,plain,
! [SV385: $i,SV422: $i] :
( ( ( ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
| ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 ) )
= $true )
| ( ( SV422
= ( powerset @ SV385 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1978]) ).
thf(2029,plain,
! [SV386: $i,SV423: $i] :
( ( ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ SV423 )
| ( subset @ SY640 @ SV386 ) ) )
= $false )
| ( ( SV423
= ( powerset @ SV386 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1979]) ).
thf(2030,plain,
! [SV423: $i,SV386: $i] :
( ( ( ~ ! [SY641: $i] :
( ~ ( subset @ SY641 @ SV386 )
| ( in @ SY641 @ SV423 ) ) )
= $false )
| ( ( SV423
= ( powerset @ SV386 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1979]) ).
thf(2031,plain,
! [SV315: $i,SV360: $i] :
( ( ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV360 )
= $false )
| ( ( in @ ( sK5_C @ SV360 @ SV315 ) @ SV315 )
= $false )
| ( ( SV315 = SV360 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2032,plain,
! [SV478: $i,SV451: $i,SV361: $i,SV316: $i] :
( ( ( ( ordered_pair @ SV316 @ SV361 )
= ( ordered_pair @ SV451 @ SV478 ) )
= $false )
| ( ( SV316 = SV451 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2033,plain,
! [SV465: $i,SV452: $i,SV361: $i,SV316: $i] :
( ( ( ( ordered_pair @ SV316 @ SV361 )
= ( ordered_pair @ SV452 @ SV465 ) )
= $false )
| ( ( SV361 = SV465 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2034,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 ) )
| ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) ) ) )
= $false )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1983]) ).
thf(2035,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ~ ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 )
| ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) ) )
= $false )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1983]) ).
thf(2036,plain,
! [SV427: $i,SV317: $i,SV454: $i] :
( ( ( ~ ! [SY674: $i] :
( ~ ( in @ SY674 @ SV454 )
| ( in @ SY674 @ SV317 )
| ( in @ SY674 @ SV427 ) )
| ~ ~ ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV317 )
| ( in @ SY675 @ SV454 ) )
| ~ ! [SY676: $i] :
( ~ ( in @ SY676 @ SV427 )
| ( in @ SY676 @ SV454 ) ) ) )
= $false )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2037,plain,
! [SV389: $i,SV428: $i] :
( ( ( subset @ SV428 @ SV389 )
= $false )
| ( ( subset @ SV389 @ SV428 )
= $false )
| ( ( SV389 = SV428 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2038,plain,
! [SV479: $i,SV466: $i] :
( ( ( ( SV466 != SV479 ) )
= $true )
| ( ( subset @ SV466 @ SV479 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1986]) ).
thf(2039,plain,
! [SV480: $i,SV467: $i] :
( ( ( ( SV467 != SV480 ) )
= $true )
| ( ( subset @ SV480 @ SV467 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1987]) ).
thf(2040,plain,
! [SV429: $i,SV455: $i,SV318: $i] :
( ( ( in @ SV318 @ SV455 )
= $false )
| ( ( ~ ( in @ SV429 @ SV455 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV318 @ SV429 ) @ SV455 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2041,plain,
! [SV487: $i,SV481: $i,SV318: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV318 @ SV481 ) @ SV487 )
| ( in @ SV318 @ SV487 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2042,plain,
! [SV488: $i,SV482: $i,SV318: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV318 @ SV482 ) @ SV488 )
| ( in @ SV482 @ SV488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2043,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV319 ) )
| ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV430 ) ) ) )
= $false )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2044,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ~ ( ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV319 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV430 ) ) )
= $false )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1991]) ).
thf(2045,plain,
! [SV431: $i,SV319: $i,SV457: $i] :
( ( ( ~ ! [SY677: $i] :
( ~ ( in @ SY677 @ SV457 )
| ( SY677 = SV319 )
| ( SY677 = SV431 ) )
| ~ ~ ( ~ ! [SY678: $i] :
( ( SY678 != SV319 )
| ( in @ SY678 @ SV457 ) )
| ~ ! [SY679: $i] :
( ( SY679 != SV431 )
| ( in @ SY679 @ SV457 ) ) ) )
= $false )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2046,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) ) )
= $false )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2047,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
| ~ ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) ) ) )
= $false )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1994]) ).
thf(2048,plain,
! [SV459: $i,SV433: $i,SV320: $i] :
( ( ( ~ ! [SY680: $i] :
( ~ ( in @ SY680 @ SV320 )
| ( in @ SY680 @ SV433 )
| ( in @ SY680 @ SV459 ) )
| ~ ~ ( ~ ! [SY681: $i] :
( ~ ( in @ SY681 @ SV459 )
| ( in @ SY681 @ SV320 ) )
| ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV459 )
| ~ ( in @ SY682 @ SV433 ) ) ) )
= $false )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2049,plain,
! [SV469: $i,SV437: $i,SV395: $i] :
( ( ( disjoint @ SV395 @ SV437 )
= $false )
| ( ( in @ SV469 @ ( set_intersection2 @ SV395 @ SV437 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2050,plain,
! [SV470: $i] :
( ( ( SV470 = empty_set )
= $false )
| ( ( ! [SY693: $i] : ( subset @ SV470 @ ( singleton @ SY693 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2051,plain,
! [SV483: $i,SV471: $i] :
( ( ( ( SV471
!= ( singleton @ SV483 ) ) )
= $true )
| ( ( subset @ SV471 @ ( singleton @ SV483 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1999]) ).
thf(2052,plain,
! [SV472: $i] :
( ( ( SV472 = empty_set )
= $false )
| ( ( ! [SY695: $i] : ( subset @ SV472 @ ( singleton @ SY695 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2053,plain,
! [SV484: $i,SV473: $i] :
( ( ( ( SV473
!= ( singleton @ SV484 ) ) )
= $true )
| ( ( subset @ SV473 @ ( singleton @ SV484 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2002]) ).
thf(2054,plain,
! [SV402: $i,SV444: $i] :
( ( ( in @ ( sK25_C @ SV444 @ SV402 ) @ SV402 )
= $true )
| ( ( disjoint @ SV402 @ SV444 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2003]) ).
thf(2055,plain,
! [SV402: $i,SV444: $i] :
( ( ( in @ ( sK25_C @ SV444 @ SV402 ) @ SV444 )
= $true )
| ( ( disjoint @ SV402 @ SV444 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2004]) ).
thf(2056,plain,
! [SV445: $i,SV403: $i,SV474: $i] :
( ( ( in @ SV474 @ SV403 )
= $false )
| ( ( ~ ( in @ SV474 @ SV445 ) )
= $true )
| ( ( ~ ( disjoint @ SV403 @ SV445 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2057,plain,
! [SV460: $i,SV446: $i,SV321: $i] :
( ( ( ~ ( ! [SY683: $i,SY684: $i] :
( ~ ( in @ SY683 @ SV321 )
| ~ ( in @ SY684 @ SV446 )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ SY683 @ SY684 ) ) )
| ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) ) )
= $false )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2006]) ).
thf(2058,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) @ SV446 ) )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) ) ) )
| ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) ) )
= $false )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2006]) ).
thf(2059,plain,
! [SV461: $i,SV447: $i,SV321: $i] :
( ( ( ~ ! [SY685: $i] :
( ! [SY665: $i,SY666: $i] :
( ~ ( in @ SY665 @ SV321 )
| ~ ( in @ SY666 @ SV447 )
| ( SY685
!= ( ordered_pair @ SY665 @ SY666 ) ) )
| ( in @ SY685 @ SV461 ) )
| ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SV461 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY688 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SY688 @ SV461 @ SV447 @ SV321 ) @ SV447 ) )
| ( SY688
!= ( ordered_pair @ ( sK14_E @ SY688 @ SV461 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SY688 @ SV461 @ SV447 @ SV321 ) ) ) ) ) )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2060,plain,
! [SV372: $i,SV407: $i] :
( ( ( ! [SY628: $i] :
( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SY628 )
| ~ ( in @ SY628 @ SV372 ) ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2061,plain,
! [SV372: $i,SV407: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ ( sK11_SY201 @ SV407 @ SV372 ) )
| ~ ( in @ ( sK11_SY201 @ SV407 @ SV372 ) @ SV372 ) ) )
= $true )
| ( ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2062,plain,
! [SV408: $i,SV373: $i] :
( ( ( ! [SY629: $i] :
( ! [SY590: $i] :
( ~ ( in @ SY629 @ SY590 )
| ~ ( in @ SY590 @ SV373 ) )
| ( in @ SY629 @ SV408 ) ) )
= $true )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2063,plain,
! [SV373: $i,SV408: $i] :
( ( ( ! [SY631: $i] :
( ~ ( in @ SY631 @ SV408 )
| ~ ( ~ ( in @ SY631 @ ( sK9_D @ SY631 @ SV408 @ SV373 ) )
| ~ ( in @ ( sK9_D @ SY631 @ SV408 @ SV373 ) @ SV373 ) ) ) )
= $true )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2011]) ).
thf(2064,plain,
! [SV376: $i,SV411: $i] :
( ( ( in @ ( sK13_C @ SV411 @ SV376 ) @ SV411 )
= $false )
| ( ( subset @ SV376 @ SV411 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2065,plain,
! [SV412: $i,SV377: $i,SV475: $i] :
( ( ( in @ SV475 @ SV377 )
= $false )
| ( ( in @ SV475 @ SV412 )
= $true )
| ( ( subset @ SV377 @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2066,plain,
! [SV378: $i,SV413: $i] :
( ( ( ( ( sK23_C @ SV413 @ SV378 )
!= SV378 ) )
= $true )
| ( ( ~ ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 ) )
= $true )
| ( ( SV413
= ( singleton @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2015]) ).
thf(2067,plain,
! [SV378: $i,SV413: $i] :
( ( ( ( sK23_C @ SV413 @ SV378 )
= SV378 )
= $true )
| ( ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 )
= $true )
| ( ( SV413
= ( singleton @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2068,plain,
! [SV414: $i,SV379: $i] :
( ( ( ! [SY633: $i] :
( ( SY633 != SV379 )
| ( in @ SY633 @ SV414 ) ) )
= $true )
| ( ( SV414
= ( singleton @ SV379 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2069,plain,
! [SV379: $i,SV414: $i] :
( ( ( ! [SY634: $i] :
( ~ ( in @ SY634 @ SV414 )
| ( SY634 = SV379 ) ) )
= $true )
| ( ( SV414
= ( singleton @ SV379 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2018]) ).
thf(2070,plain,
! [SV476: $i,SV462: $i] :
( ( ( proper_subset @ SV462 @ SV476 )
= $false )
| ( ( ( SV462 != SV476 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2071,plain,
! [SV477: $i,SV463: $i] :
( ( ( proper_subset @ SV463 @ SV477 )
= $false )
| ( ( subset @ SV463 @ SV477 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2072,plain,
! [SV464: $i,SV359: $i,SV448: $i,SV313: $i] :
( ( ( in @ SV313 @ SV448 )
= $false )
| ( ( ~ ( in @ SV359 @ SV464 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV448 @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2073,plain,
! [SV485: $i,SV359: $i,SV313: $i] :
( ( ( ! [SY699: $i] :
~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV485 @ SY699 ) ) )
= $true )
| ( ( in @ SV313 @ SV485 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2022]) ).
thf(2074,plain,
! [SV489: $i,SV486: $i,SV359: $i,SV313: $i] :
( ( ~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV486 @ SV489 ) )
| ( in @ SV359 @ SV489 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2075,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
= $true )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2024]) ).
thf(2076,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
| ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) ) ) )
= $true )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2025]) ).
thf(2077,plain,
! [SV450: $i,SV421: $i,SV314: $i] :
( ( ( ~ ! [SY669: $i] :
( ~ ( in @ SY669 @ SV314 )
| ~ ( in @ SY669 @ SV421 )
| ( in @ SY669 @ SV450 ) ) )
= $false )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2026]) ).
thf(2078,plain,
! [SV421: $i,SV314: $i,SV450: $i] :
( ( ( ~ ~ ( ~ ! [SY670: $i] :
( ~ ( in @ SY670 @ SV450 )
| ( in @ SY670 @ SV314 ) )
| ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ SV450 )
| ( in @ SY671 @ SV421 ) ) ) )
= $false )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2026]) ).
thf(2079,plain,
! [SV385: $i,SV422: $i] :
( ( ( ~ ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 ) )
= $true )
| ( ( ~ ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 ) )
= $true )
| ( ( SV422
= ( powerset @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2027]) ).
thf(2080,plain,
! [SV385: $i,SV422: $i] :
( ( ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
= $true )
| ( ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 )
= $true )
| ( ( SV422
= ( powerset @ SV385 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2028]) ).
thf(2081,plain,
! [SV386: $i,SV423: $i] :
( ( ( ! [SY640: $i] :
( ~ ( in @ SY640 @ SV423 )
| ( subset @ SY640 @ SV386 ) ) )
= $true )
| ( ( SV423
= ( powerset @ SV386 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2029]) ).
thf(2082,plain,
! [SV423: $i,SV386: $i] :
( ( ( ! [SY641: $i] :
( ~ ( subset @ SY641 @ SV386 )
| ( in @ SY641 @ SV423 ) ) )
= $true )
| ( ( SV423
= ( powerset @ SV386 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2030]) ).
thf(2083,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 ) )
| ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) ) ) )
= $true )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2034]) ).
thf(2084,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 )
| ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) )
= $true )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2035]) ).
thf(2085,plain,
! [SV427: $i,SV317: $i,SV454: $i] :
( ( ( ~ ! [SY674: $i] :
( ~ ( in @ SY674 @ SV454 )
| ( in @ SY674 @ SV317 )
| ( in @ SY674 @ SV427 ) ) )
= $false )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2036]) ).
thf(2086,plain,
! [SV427: $i,SV454: $i,SV317: $i] :
( ( ( ~ ~ ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV317 )
| ( in @ SY675 @ SV454 ) )
| ~ ! [SY676: $i] :
( ~ ( in @ SY676 @ SV427 )
| ( in @ SY676 @ SV454 ) ) ) )
= $false )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2036]) ).
thf(2087,plain,
! [SV479: $i,SV466: $i] :
( ( ( SV466 = SV479 )
= $false )
| ( ( subset @ SV466 @ SV479 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2088,plain,
! [SV480: $i,SV467: $i] :
( ( ( SV467 = SV480 )
= $false )
| ( ( subset @ SV480 @ SV467 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2089,plain,
! [SV318: $i,SV455: $i,SV429: $i] :
( ( ( in @ SV429 @ SV455 )
= $false )
| ( ( in @ SV318 @ SV455 )
= $false )
| ( ( subset @ ( unordered_pair @ SV318 @ SV429 ) @ SV455 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2090,plain,
! [SV487: $i,SV481: $i,SV318: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV318 @ SV481 ) @ SV487 ) )
= $true )
| ( ( in @ SV318 @ SV487 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2041]) ).
thf(2091,plain,
! [SV488: $i,SV482: $i,SV318: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV318 @ SV482 ) @ SV488 ) )
= $true )
| ( ( in @ SV482 @ SV488 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2092,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV319 ) )
| ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV430 ) ) ) )
= $true )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2043]) ).
thf(2093,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV319 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV430 ) )
= $true )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2044]) ).
thf(2094,plain,
! [SV431: $i,SV319: $i,SV457: $i] :
( ( ( ~ ! [SY677: $i] :
( ~ ( in @ SY677 @ SV457 )
| ( SY677 = SV319 )
| ( SY677 = SV431 ) ) )
= $false )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2095,plain,
! [SV431: $i,SV457: $i,SV319: $i] :
( ( ( ~ ~ ( ~ ! [SY678: $i] :
( ( SY678 != SV319 )
| ( in @ SY678 @ SV457 ) )
| ~ ! [SY679: $i] :
( ( SY679 != SV431 )
| ( in @ SY679 @ SV457 ) ) ) )
= $false )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2045]) ).
thf(2096,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
= $true )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2046]) ).
thf(2097,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
| ~ ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) ) ) )
= $true )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2047]) ).
thf(2098,plain,
! [SV459: $i,SV433: $i,SV320: $i] :
( ( ( ~ ! [SY680: $i] :
( ~ ( in @ SY680 @ SV320 )
| ( in @ SY680 @ SV433 )
| ( in @ SY680 @ SV459 ) ) )
= $false )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2048]) ).
thf(2099,plain,
! [SV433: $i,SV320: $i,SV459: $i] :
( ( ( ~ ~ ( ~ ! [SY681: $i] :
( ~ ( in @ SY681 @ SV459 )
| ( in @ SY681 @ SV320 ) )
| ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV459 )
| ~ ( in @ SY682 @ SV433 ) ) ) )
= $false )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2048]) ).
thf(2100,plain,
! [SV490: $i,SV470: $i] :
( ( ( subset @ SV470 @ ( singleton @ SV490 ) )
= $true )
| ( ( SV470 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2101,plain,
! [SV483: $i,SV471: $i] :
( ( ( SV471
= ( singleton @ SV483 ) )
= $false )
| ( ( subset @ SV471 @ ( singleton @ SV483 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2051]) ).
thf(2102,plain,
! [SV491: $i,SV472: $i] :
( ( ( subset @ SV472 @ ( singleton @ SV491 ) )
= $true )
| ( ( SV472 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2103,plain,
! [SV484: $i,SV473: $i] :
( ( ( SV473
= ( singleton @ SV484 ) )
= $false )
| ( ( subset @ SV473 @ ( singleton @ SV484 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2104,plain,
! [SV403: $i,SV445: $i,SV474: $i] :
( ( ( in @ SV474 @ SV445 )
= $false )
| ( ( in @ SV474 @ SV403 )
= $false )
| ( ( ~ ( disjoint @ SV403 @ SV445 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2105,plain,
! [SV460: $i,SV446: $i,SV321: $i] :
( ( ( ! [SY683: $i,SY684: $i] :
( ~ ( in @ SY683 @ SV321 )
| ~ ( in @ SY684 @ SV446 )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ SY683 @ SY684 ) ) )
| ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2057]) ).
thf(2106,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) @ SV446 ) )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) ) ) )
| ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2107,plain,
! [SV461: $i,SV447: $i,SV321: $i] :
( ( ( ~ ! [SY685: $i] :
( ! [SY665: $i,SY666: $i] :
( ~ ( in @ SY665 @ SV321 )
| ~ ( in @ SY666 @ SV447 )
| ( SY685
!= ( ordered_pair @ SY665 @ SY666 ) ) )
| ( in @ SY685 @ SV461 ) ) )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2059]) ).
thf(2108,plain,
! [SV321: $i,SV447: $i,SV461: $i] :
( ( ( ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SV461 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY688 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SY688 @ SV461 @ SV447 @ SV321 ) @ SV447 ) )
| ( SY688
!= ( ordered_pair @ ( sK14_E @ SY688 @ SV461 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SY688 @ SV461 @ SV447 @ SV321 ) ) ) ) ) )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2059]) ).
thf(2109,plain,
! [SV492: $i,SV372: $i,SV407: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV492 )
| ~ ( in @ SV492 @ SV372 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2110,plain,
! [SV372: $i,SV407: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ ( sK11_SY201 @ SV407 @ SV372 ) )
| ~ ( in @ ( sK11_SY201 @ SV407 @ SV372 ) @ SV372 ) )
= $false )
| ( ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2061]) ).
thf(2111,plain,
! [SV408: $i,SV373: $i,SV493: $i] :
( ( ( ! [SY701: $i] :
( ~ ( in @ SV493 @ SY701 )
| ~ ( in @ SY701 @ SV373 ) )
| ( in @ SV493 @ SV408 ) )
= $true )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2112,plain,
! [SV373: $i,SV408: $i,SV494: $i] :
( ( ( ~ ( in @ SV494 @ SV408 )
| ~ ( ~ ( in @ SV494 @ ( sK9_D @ SV494 @ SV408 @ SV373 ) )
| ~ ( in @ ( sK9_D @ SV494 @ SV408 @ SV373 ) @ SV373 ) ) )
= $true )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2113,plain,
! [SV378: $i,SV413: $i] :
( ( ( ( sK23_C @ SV413 @ SV378 )
= SV378 )
= $false )
| ( ( ~ ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 ) )
= $true )
| ( ( SV413
= ( singleton @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2114,plain,
! [SV414: $i,SV379: $i,SV495: $i] :
( ( ( ( SV495 != SV379 )
| ( in @ SV495 @ SV414 ) )
= $true )
| ( ( SV414
= ( singleton @ SV379 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2115,plain,
! [SV379: $i,SV414: $i,SV496: $i] :
( ( ( ~ ( in @ SV496 @ SV414 )
| ( SV496 = SV379 ) )
= $true )
| ( ( SV414
= ( singleton @ SV379 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2116,plain,
! [SV476: $i,SV462: $i] :
( ( ( SV462 = SV476 )
= $false )
| ( ( proper_subset @ SV462 @ SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2117,plain,
! [SV448: $i,SV313: $i,SV464: $i,SV359: $i] :
( ( ( in @ SV359 @ SV464 )
= $false )
| ( ( in @ SV313 @ SV448 )
= $false )
| ( ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV448 @ SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2118,plain,
! [SV497: $i,SV485: $i,SV359: $i,SV313: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV485 @ SV497 ) ) )
= $true )
| ( ( in @ SV313 @ SV485 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2119,plain,
! [SV489: $i,SV486: $i,SV359: $i,SV313: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV486 @ SV489 ) ) )
= $true )
| ( ( in @ SV359 @ SV489 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2074]) ).
thf(2120,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 ) )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
= $true )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2075]) ).
thf(2121,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
| ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) ) )
= $false )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2122,plain,
! [SV450: $i,SV421: $i,SV314: $i] :
( ( ( ! [SY669: $i] :
( ~ ( in @ SY669 @ SV314 )
| ~ ( in @ SY669 @ SV421 )
| ( in @ SY669 @ SV450 ) ) )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2077]) ).
thf(2123,plain,
! [SV421: $i,SV314: $i,SV450: $i] :
( ( ( ~ ( ~ ! [SY670: $i] :
( ~ ( in @ SY670 @ SV450 )
| ( in @ SY670 @ SV314 ) )
| ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ SV450 )
| ( in @ SY671 @ SV421 ) ) ) )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2078]) ).
thf(2124,plain,
! [SV385: $i,SV422: $i] :
( ( ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
= $false )
| ( ( ~ ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 ) )
= $true )
| ( ( SV422
= ( powerset @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2079]) ).
thf(2125,plain,
! [SV386: $i,SV423: $i,SV498: $i] :
( ( ( ~ ( in @ SV498 @ SV423 )
| ( subset @ SV498 @ SV386 ) )
= $true )
| ( ( SV423
= ( powerset @ SV386 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2126,plain,
! [SV423: $i,SV386: $i,SV499: $i] :
( ( ( ~ ( subset @ SV499 @ SV386 )
| ( in @ SV499 @ SV423 ) )
= $true )
| ( ( SV423
= ( powerset @ SV386 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2127,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 ) )
| ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) ) )
= $false )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2128,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
= $true )
| ( ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 )
| ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) )
= $true )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2084]) ).
thf(2129,plain,
! [SV427: $i,SV317: $i,SV454: $i] :
( ( ( ! [SY674: $i] :
( ~ ( in @ SY674 @ SV454 )
| ( in @ SY674 @ SV317 )
| ( in @ SY674 @ SV427 ) ) )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2085]) ).
thf(2130,plain,
! [SV427: $i,SV454: $i,SV317: $i] :
( ( ( ~ ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV317 )
| ( in @ SY675 @ SV454 ) )
| ~ ! [SY676: $i] :
( ~ ( in @ SY676 @ SV427 )
| ( in @ SY676 @ SV454 ) ) ) )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2086]) ).
thf(2131,plain,
! [SV487: $i,SV481: $i,SV318: $i] :
( ( ( subset @ ( unordered_pair @ SV318 @ SV481 ) @ SV487 )
= $false )
| ( ( in @ SV318 @ SV487 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2132,plain,
! [SV488: $i,SV482: $i,SV318: $i] :
( ( ( subset @ ( unordered_pair @ SV318 @ SV482 ) @ SV488 )
= $false )
| ( ( in @ SV482 @ SV488 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2133,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV319 ) )
| ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV430 ) ) )
= $false )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2134,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
= $true )
| ( ( ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV319 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV430 ) )
= $true )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2093]) ).
thf(2135,plain,
! [SV431: $i,SV319: $i,SV457: $i] :
( ( ( ! [SY677: $i] :
( ~ ( in @ SY677 @ SV457 )
| ( SY677 = SV319 )
| ( SY677 = SV431 ) ) )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2094]) ).
thf(2136,plain,
! [SV431: $i,SV457: $i,SV319: $i] :
( ( ( ~ ( ~ ! [SY678: $i] :
( ( SY678 != SV319 )
| ( in @ SY678 @ SV457 ) )
| ~ ! [SY679: $i] :
( ( SY679 != SV431 )
| ( in @ SY679 @ SV457 ) ) ) )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2095]) ).
thf(2137,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 ) )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
= $true )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2138,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
| ~ ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) ) )
= $false )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2139,plain,
! [SV459: $i,SV433: $i,SV320: $i] :
( ( ( ! [SY680: $i] :
( ~ ( in @ SY680 @ SV320 )
| ( in @ SY680 @ SV433 )
| ( in @ SY680 @ SV459 ) ) )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2098]) ).
thf(2140,plain,
! [SV433: $i,SV320: $i,SV459: $i] :
( ( ( ~ ( ~ ! [SY681: $i] :
( ~ ( in @ SY681 @ SV459 )
| ( in @ SY681 @ SV320 ) )
| ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV459 )
| ~ ( in @ SY682 @ SV433 ) ) ) )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2099]) ).
thf(2141,plain,
! [SV474: $i,SV445: $i,SV403: $i] :
( ( ( disjoint @ SV403 @ SV445 )
= $false )
| ( ( in @ SV474 @ SV403 )
= $false )
| ( ( in @ SV474 @ SV445 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2142,plain,
! [SV460: $i,SV446: $i,SV321: $i] :
( ( ( ! [SY683: $i,SY684: $i] :
( ~ ( in @ SY683 @ SV321 )
| ~ ( in @ SY684 @ SV446 )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ SY683 @ SY684 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2105]) ).
thf(2143,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) @ SV446 ) )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) ) ) ) )
= $true )
| ( ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2106]) ).
thf(2144,plain,
! [SV461: $i,SV447: $i,SV321: $i] :
( ( ( ! [SY685: $i] :
( ! [SY665: $i,SY666: $i] :
( ~ ( in @ SY665 @ SV321 )
| ~ ( in @ SY666 @ SV447 )
| ( SY685
!= ( ordered_pair @ SY665 @ SY666 ) ) )
| ( in @ SY685 @ SV461 ) ) )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2107]) ).
thf(2145,plain,
! [SV321: $i,SV447: $i,SV461: $i] :
( ( ( ! [SY688: $i] :
( ~ ( in @ SY688 @ SV461 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SY688 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SY688 @ SV461 @ SV447 @ SV321 ) @ SV447 ) )
| ( SY688
!= ( ordered_pair @ ( sK14_E @ SY688 @ SV461 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SY688 @ SV461 @ SV447 @ SV321 ) ) ) ) ) )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2108]) ).
thf(2146,plain,
! [SV492: $i,SV372: $i,SV407: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV492 ) )
= $true )
| ( ( ~ ( in @ SV492 @ SV372 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2147,plain,
! [SV372: $i,SV407: $i] :
( ( ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ ( sK11_SY201 @ SV407 @ SV372 ) ) )
= $false )
| ( ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2110]) ).
thf(2148,plain,
! [SV372: $i,SV407: $i] :
( ( ( ~ ( in @ ( sK11_SY201 @ SV407 @ SV372 ) @ SV372 ) )
= $false )
| ( ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2110]) ).
thf(2149,plain,
! [SV408: $i,SV373: $i,SV493: $i] :
( ( ( ! [SY701: $i] :
( ~ ( in @ SV493 @ SY701 )
| ~ ( in @ SY701 @ SV373 ) ) )
= $true )
| ( ( in @ SV493 @ SV408 )
= $true )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2111]) ).
thf(2150,plain,
! [SV373: $i,SV408: $i,SV494: $i] :
( ( ( ~ ( in @ SV494 @ SV408 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV494 @ ( sK9_D @ SV494 @ SV408 @ SV373 ) )
| ~ ( in @ ( sK9_D @ SV494 @ SV408 @ SV373 ) @ SV373 ) ) )
= $true )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2151,plain,
! [SV378: $i,SV413: $i] :
( ( ( in @ ( sK23_C @ SV413 @ SV378 ) @ SV413 )
= $false )
| ( ( ( sK23_C @ SV413 @ SV378 )
= SV378 )
= $false )
| ( ( SV413
= ( singleton @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2152,plain,
! [SV414: $i,SV379: $i,SV495: $i] :
( ( ( ( SV495 != SV379 ) )
= $true )
| ( ( in @ SV495 @ SV414 )
= $true )
| ( ( SV414
= ( singleton @ SV379 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2114]) ).
thf(2153,plain,
! [SV379: $i,SV414: $i,SV496: $i] :
( ( ( ~ ( in @ SV496 @ SV414 ) )
= $true )
| ( ( SV496 = SV379 )
= $true )
| ( ( SV414
= ( singleton @ SV379 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2154,plain,
! [SV497: $i,SV485: $i,SV359: $i,SV313: $i] :
( ( ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV485 @ SV497 ) )
= $false )
| ( ( in @ SV313 @ SV485 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2155,plain,
! [SV489: $i,SV486: $i,SV359: $i,SV313: $i] :
( ( ( in @ ( ordered_pair @ SV313 @ SV359 ) @ ( cartesian_product2 @ SV486 @ SV489 ) )
= $false )
| ( ( in @ SV359 @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2156,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 ) )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 ) )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
= $true )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2120]) ).
thf(2157,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) ) )
= $false )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2121]) ).
thf(2158,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ~ ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) ) )
= $false )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2121]) ).
thf(2159,plain,
! [SV450: $i,SV421: $i,SV314: $i,SV500: $i] :
( ( ( ~ ( in @ SV500 @ SV314 )
| ~ ( in @ SV500 @ SV421 )
| ( in @ SV500 @ SV450 ) )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2160,plain,
! [SV421: $i,SV314: $i,SV450: $i] :
( ( ( ~ ! [SY670: $i] :
( ~ ( in @ SY670 @ SV450 )
| ( in @ SY670 @ SV314 ) )
| ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ SV450 )
| ( in @ SY671 @ SV421 ) ) )
= $false )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2161,plain,
! [SV385: $i,SV422: $i] :
( ( ( subset @ ( sK21_C @ SV422 @ SV385 ) @ SV385 )
= $false )
| ( ( in @ ( sK21_C @ SV422 @ SV385 ) @ SV422 )
= $false )
| ( ( SV422
= ( powerset @ SV385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2124]) ).
thf(2162,plain,
! [SV386: $i,SV423: $i,SV498: $i] :
( ( ( ~ ( in @ SV498 @ SV423 ) )
= $true )
| ( ( subset @ SV498 @ SV386 )
= $true )
| ( ( SV423
= ( powerset @ SV386 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2125]) ).
thf(2163,plain,
! [SV423: $i,SV386: $i,SV499: $i] :
( ( ( ~ ( subset @ SV499 @ SV386 ) )
= $true )
| ( ( in @ SV499 @ SV423 )
= $true )
| ( ( SV423
= ( powerset @ SV386 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2126]) ).
thf(2164,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 ) ) )
= $false )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2127]) ).
thf(2165,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) ) )
= $false )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2127]) ).
thf(2166,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 )
= $true )
| ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 )
= $true )
| ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
= $true )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2167,plain,
! [SV427: $i,SV317: $i,SV454: $i,SV501: $i] :
( ( ( ~ ( in @ SV501 @ SV454 )
| ( in @ SV501 @ SV317 )
| ( in @ SV501 @ SV427 ) )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2168,plain,
! [SV427: $i,SV454: $i,SV317: $i] :
( ( ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV317 )
| ( in @ SY675 @ SV454 ) )
| ~ ! [SY676: $i] :
( ~ ( in @ SY676 @ SV427 )
| ( in @ SY676 @ SV454 ) ) )
= $false )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2130]) ).
thf(2169,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV319 ) ) )
= $false )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2133]) ).
thf(2170,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV430 ) ) )
= $false )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2133]) ).
thf(2171,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV319 )
= $true )
| ( ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV430 )
= $true )
| ( ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
= $true )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2172,plain,
! [SV431: $i,SV319: $i,SV457: $i,SV502: $i] :
( ( ( ~ ( in @ SV502 @ SV457 )
| ( SV502 = SV319 )
| ( SV502 = SV431 ) )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2173,plain,
! [SV431: $i,SV457: $i,SV319: $i] :
( ( ( ~ ! [SY678: $i] :
( ( SY678 != SV319 )
| ( in @ SY678 @ SV457 ) )
| ~ ! [SY679: $i] :
( ( SY679 != SV431 )
| ( in @ SY679 @ SV457 ) ) )
= $false )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2174,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 ) )
= $true )
| ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
= $true )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2137]) ).
thf(2175,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) ) )
= $false )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2138]) ).
thf(2176,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) ) )
= $false )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2138]) ).
thf(2177,plain,
! [SV459: $i,SV433: $i,SV320: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV320 )
| ( in @ SV503 @ SV433 )
| ( in @ SV503 @ SV459 ) )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2178,plain,
! [SV433: $i,SV320: $i,SV459: $i] :
( ( ( ~ ! [SY681: $i] :
( ~ ( in @ SY681 @ SV459 )
| ( in @ SY681 @ SV320 ) )
| ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV459 )
| ~ ( in @ SY682 @ SV433 ) ) )
= $false )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2179,plain,
! [SV460: $i,SV446: $i,SV321: $i,SV504: $i] :
( ( ( ! [SY702: $i] :
( ~ ( in @ SV504 @ SV321 )
| ~ ( in @ SY702 @ SV446 )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ SV504 @ SY702 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2180,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) @ SV446 ) )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) ) ) )
= $false )
| ( ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2181,plain,
! [SV461: $i,SV505: $i,SV447: $i,SV321: $i] :
( ( ( ! [SY703: $i,SY704: $i] :
( ~ ( in @ SY703 @ SV321 )
| ~ ( in @ SY704 @ SV447 )
| ( SV505
!= ( ordered_pair @ SY703 @ SY704 ) ) )
| ( in @ SV505 @ SV461 ) )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2182,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( ~ ( in @ SV506 @ SV461 )
| ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV447 ) )
| ( SV506
!= ( ordered_pair @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) ) ) ) )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2183,plain,
! [SV492: $i,SV372: $i,SV407: $i] :
( ( ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV492 )
= $false )
| ( ( ~ ( in @ SV492 @ SV372 ) )
= $true )
| ( ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2184,plain,
! [SV372: $i,SV407: $i] :
( ( ( in @ ( sK10_C @ SV407 @ SV372 ) @ ( sK11_SY201 @ SV407 @ SV372 ) )
= $true )
| ( ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2147]) ).
thf(2185,plain,
! [SV372: $i,SV407: $i] :
( ( ( in @ ( sK11_SY201 @ SV407 @ SV372 ) @ SV372 )
= $true )
| ( ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2148]) ).
thf(2186,plain,
! [SV408: $i,SV373: $i,SV507: $i,SV493: $i] :
( ( ( ~ ( in @ SV493 @ SV507 )
| ~ ( in @ SV507 @ SV373 ) )
= $true )
| ( ( in @ SV493 @ SV408 )
= $true )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2187,plain,
! [SV373: $i,SV408: $i,SV494: $i] :
( ( ( in @ SV494 @ SV408 )
= $false )
| ( ( ~ ( ~ ( in @ SV494 @ ( sK9_D @ SV494 @ SV408 @ SV373 ) )
| ~ ( in @ ( sK9_D @ SV494 @ SV408 @ SV373 ) @ SV373 ) ) )
= $true )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2188,plain,
! [SV414: $i,SV379: $i,SV495: $i] :
( ( ( SV495 = SV379 )
= $false )
| ( ( in @ SV495 @ SV414 )
= $true )
| ( ( SV414
= ( singleton @ SV379 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2189,plain,
! [SV379: $i,SV414: $i,SV496: $i] :
( ( ( in @ SV496 @ SV414 )
= $false )
| ( ( SV496 = SV379 )
= $true )
| ( ( SV414
= ( singleton @ SV379 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2190,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
= $false )
| ( ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 ) )
= $true )
| ( ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
= $true )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2191,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
= $true )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2157]) ).
thf(2192,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
| ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
= $true )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2158]) ).
thf(2193,plain,
! [SV450: $i,SV421: $i,SV314: $i,SV500: $i] :
( ( ( ~ ( in @ SV500 @ SV314 )
| ~ ( in @ SV500 @ SV421 ) )
= $true )
| ( ( in @ SV500 @ SV450 )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2159]) ).
thf(2194,plain,
! [SV421: $i,SV314: $i,SV450: $i] :
( ( ( ~ ! [SY670: $i] :
( ~ ( in @ SY670 @ SV450 )
| ( in @ SY670 @ SV314 ) ) )
= $false )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2160]) ).
thf(2195,plain,
! [SV314: $i,SV421: $i,SV450: $i] :
( ( ( ~ ! [SY671: $i] :
( ~ ( in @ SY671 @ SV450 )
| ( in @ SY671 @ SV421 ) ) )
= $false )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2160]) ).
thf(2196,plain,
! [SV386: $i,SV423: $i,SV498: $i] :
( ( ( in @ SV498 @ SV423 )
= $false )
| ( ( subset @ SV498 @ SV386 )
= $true )
| ( ( SV423
= ( powerset @ SV386 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2197,plain,
! [SV423: $i,SV386: $i,SV499: $i] :
( ( ( subset @ SV499 @ SV386 )
= $false )
| ( ( in @ SV499 @ SV423 )
= $true )
| ( ( SV423
= ( powerset @ SV386 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2198,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 ) )
= $true )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2199,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
| ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) )
= $true )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2165]) ).
thf(2200,plain,
! [SV427: $i,SV317: $i,SV454: $i,SV501: $i] :
( ( ( ~ ( in @ SV501 @ SV454 ) )
= $true )
| ( ( ( in @ SV501 @ SV317 )
| ( in @ SV501 @ SV427 ) )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2167]) ).
thf(2201,plain,
! [SV427: $i,SV454: $i,SV317: $i] :
( ( ( ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV317 )
| ( in @ SY675 @ SV454 ) ) )
= $false )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2168]) ).
thf(2202,plain,
! [SV317: $i,SV454: $i,SV427: $i] :
( ( ( ~ ! [SY676: $i] :
( ~ ( in @ SY676 @ SV427 )
| ( in @ SY676 @ SV454 ) ) )
= $false )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2168]) ).
thf(2203,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV319 ) )
= $true )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2169]) ).
thf(2204,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
| ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV430 ) )
= $true )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2170]) ).
thf(2205,plain,
! [SV431: $i,SV319: $i,SV457: $i,SV502: $i] :
( ( ( ~ ( in @ SV502 @ SV457 ) )
= $true )
| ( ( ( SV502 = SV319 )
| ( SV502 = SV431 ) )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2172]) ).
thf(2206,plain,
! [SV431: $i,SV457: $i,SV319: $i] :
( ( ( ~ ! [SY678: $i] :
( ( SY678 != SV319 )
| ( in @ SY678 @ SV457 ) ) )
= $false )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2207,plain,
! [SV319: $i,SV457: $i,SV431: $i] :
( ( ( ~ ! [SY679: $i] :
( ( SY679 != SV431 )
| ( in @ SY679 @ SV457 ) ) )
= $false )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2173]) ).
thf(2208,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
= $false )
| ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
= $true )
| ( ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
= $true )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2209,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
= $true )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2210,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
| ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 ) )
= $true )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2176]) ).
thf(2211,plain,
! [SV459: $i,SV433: $i,SV320: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV320 )
| ( in @ SV503 @ SV433 ) )
= $true )
| ( ( in @ SV503 @ SV459 )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2177]) ).
thf(2212,plain,
! [SV433: $i,SV320: $i,SV459: $i] :
( ( ( ~ ! [SY681: $i] :
( ~ ( in @ SY681 @ SV459 )
| ( in @ SY681 @ SV320 ) ) )
= $false )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2178]) ).
thf(2213,plain,
! [SV320: $i,SV433: $i,SV459: $i] :
( ( ( ~ ! [SY682: $i] :
( ~ ( in @ SY682 @ SV459 )
| ~ ( in @ SY682 @ SV433 ) ) )
= $false )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2178]) ).
thf(2214,plain,
! [SV460: $i,SV446: $i,SV508: $i,SV321: $i,SV504: $i] :
( ( ( ~ ( in @ SV504 @ SV321 )
| ~ ( in @ SV508 @ SV446 )
| ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ SV504 @ SV508 ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2215,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) @ SV446 ) ) )
= $false )
| ( ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2180]) ).
thf(2216,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) ) ) )
= $false )
| ( ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2180]) ).
thf(2217,plain,
! [SV461: $i,SV505: $i,SV447: $i,SV321: $i] :
( ( ( ! [SY703: $i,SY704: $i] :
( ~ ( in @ SY703 @ SV321 )
| ~ ( in @ SY704 @ SV447 )
| ( SV505
!= ( ordered_pair @ SY703 @ SY704 ) ) ) )
= $true )
| ( ( in @ SV505 @ SV461 )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2218,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( ~ ( in @ SV506 @ SV461 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV447 ) )
| ( SV506
!= ( ordered_pair @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) ) ) ) )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2219,plain,
! [SV407: $i,SV372: $i,SV492: $i] :
( ( ( in @ SV492 @ SV372 )
= $false )
| ( ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV492 )
= $false )
| ( ( ~ ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 ) )
= $true )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2183]) ).
thf(2220,plain,
! [SV408: $i,SV373: $i,SV507: $i,SV493: $i] :
( ( ( ~ ( in @ SV493 @ SV507 ) )
= $true )
| ( ( ~ ( in @ SV507 @ SV373 ) )
= $true )
| ( ( in @ SV493 @ SV408 )
= $true )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2186]) ).
thf(2221,plain,
! [SV373: $i,SV408: $i,SV494: $i] :
( ( ( ~ ( in @ SV494 @ ( sK9_D @ SV494 @ SV408 @ SV373 ) )
| ~ ( in @ ( sK9_D @ SV494 @ SV408 @ SV373 ) @ SV373 ) )
= $false )
| ( ( in @ SV494 @ SV408 )
= $false )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2222,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
= $false )
| ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
= $false )
| ( ( ~ ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 ) )
= $true )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2223,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
= $true )
| ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 )
= $true )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2191]) ).
thf(2224,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
= $true )
| ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 )
= $true )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2192]) ).
thf(2225,plain,
! [SV450: $i,SV421: $i,SV314: $i,SV500: $i] :
( ( ( ~ ( in @ SV500 @ SV314 ) )
= $true )
| ( ( ~ ( in @ SV500 @ SV421 ) )
= $true )
| ( ( in @ SV500 @ SV450 )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2193]) ).
thf(2226,plain,
! [SV421: $i,SV314: $i,SV450: $i] :
( ( ( ! [SY670: $i] :
( ~ ( in @ SY670 @ SV450 )
| ( in @ SY670 @ SV314 ) ) )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2194]) ).
thf(2227,plain,
! [SV314: $i,SV421: $i,SV450: $i] :
( ( ( ! [SY671: $i] :
( ~ ( in @ SY671 @ SV450 )
| ( in @ SY671 @ SV421 ) ) )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2195]) ).
thf(2228,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 ) )
= $true )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2229,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) )
= $true )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2199]) ).
thf(2230,plain,
! [SV427: $i,SV317: $i,SV454: $i,SV501: $i] :
( ( ( in @ SV501 @ SV454 )
= $false )
| ( ( ( in @ SV501 @ SV317 )
| ( in @ SV501 @ SV427 ) )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2231,plain,
! [SV427: $i,SV454: $i,SV317: $i] :
( ( ( ! [SY675: $i] :
( ~ ( in @ SY675 @ SV317 )
| ( in @ SY675 @ SV454 ) ) )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2201]) ).
thf(2232,plain,
! [SV317: $i,SV454: $i,SV427: $i] :
( ( ( ! [SY676: $i] :
( ~ ( in @ SY676 @ SV427 )
| ( in @ SY676 @ SV454 ) ) )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2202]) ).
thf(2233,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 ) )
= $true )
| ( ( ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV319 ) )
= $true )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2234,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ~ ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 ) )
= $true )
| ( ( ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV430 ) )
= $true )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2235,plain,
! [SV431: $i,SV319: $i,SV457: $i,SV502: $i] :
( ( ( in @ SV502 @ SV457 )
= $false )
| ( ( ( SV502 = SV319 )
| ( SV502 = SV431 ) )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2236,plain,
! [SV431: $i,SV457: $i,SV319: $i] :
( ( ( ! [SY678: $i] :
( ( SY678 != SV319 )
| ( in @ SY678 @ SV457 ) ) )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2206]) ).
thf(2237,plain,
! [SV319: $i,SV457: $i,SV431: $i] :
( ( ( ! [SY679: $i] :
( ( SY679 != SV431 )
| ( in @ SY679 @ SV457 ) ) )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2207]) ).
thf(2238,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 )
= $false )
| ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
= $true )
| ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
= $false )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2239,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV320 )
= $true )
| ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 )
= $true )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2240,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( ~ ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 ) )
= $true )
| ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 )
= $true )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2241,plain,
! [SV459: $i,SV433: $i,SV320: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV320 ) )
= $true )
| ( ( in @ SV503 @ SV433 )
= $true )
| ( ( in @ SV503 @ SV459 )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2211]) ).
thf(2242,plain,
! [SV433: $i,SV320: $i,SV459: $i] :
( ( ( ! [SY681: $i] :
( ~ ( in @ SY681 @ SV459 )
| ( in @ SY681 @ SV320 ) ) )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2212]) ).
thf(2243,plain,
! [SV320: $i,SV433: $i,SV459: $i] :
( ( ( ! [SY682: $i] :
( ~ ( in @ SY682 @ SV459 )
| ~ ( in @ SY682 @ SV433 ) ) )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2213]) ).
thf(2244,plain,
! [SV460: $i,SV446: $i,SV508: $i,SV321: $i,SV504: $i] :
( ( ( ~ ( in @ SV504 @ SV321 )
| ~ ( in @ SV508 @ SV446 ) )
= $true )
| ( ( ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ SV504 @ SV508 ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2245,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) @ SV446 ) ) )
= $true )
| ( ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2215]) ).
thf(2246,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( ( sK16_D @ SV460 @ SV446 @ SV321 )
= ( ordered_pair @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) ) )
= $true )
| ( ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2216]) ).
thf(2247,plain,
! [SV461: $i,SV505: $i,SV447: $i,SV321: $i,SV509: $i] :
( ( ( ! [SY705: $i] :
( ~ ( in @ SV509 @ SV321 )
| ~ ( in @ SY705 @ SV447 )
| ( SV505
!= ( ordered_pair @ SV509 @ SY705 ) ) ) )
= $true )
| ( ( in @ SV505 @ SV461 )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2248,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( in @ SV506 @ SV461 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV447 ) )
| ( SV506
!= ( ordered_pair @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) ) ) ) )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2249,plain,
! [SV492: $i,SV372: $i,SV407: $i] :
( ( ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV407 )
= $false )
| ( ( in @ ( sK10_C @ SV407 @ SV372 ) @ SV492 )
= $false )
| ( ( in @ SV492 @ SV372 )
= $false )
| ( ( SV407
= ( union @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2250,plain,
! [SV408: $i,SV373: $i,SV507: $i,SV493: $i] :
( ( ( in @ SV493 @ SV507 )
= $false )
| ( ( ~ ( in @ SV507 @ SV373 ) )
= $true )
| ( ( in @ SV493 @ SV408 )
= $true )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2251,plain,
! [SV373: $i,SV408: $i,SV494: $i] :
( ( ( ~ ( in @ SV494 @ ( sK9_D @ SV494 @ SV408 @ SV373 ) ) )
= $false )
| ( ( in @ SV494 @ SV408 )
= $false )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2221]) ).
thf(2252,plain,
! [SV373: $i,SV408: $i,SV494: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV494 @ SV408 @ SV373 ) @ SV373 ) )
= $false )
| ( ( in @ SV494 @ SV408 )
= $false )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2221]) ).
thf(2253,plain,
! [SV314: $i,SV420: $i,SV449: $i] :
( ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV449 )
= $false )
| ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV314 )
= $false )
| ( ( in @ ( sK12_D @ SV449 @ SV420 @ SV314 ) @ SV420 )
= $false )
| ( ( SV449
= ( set_intersection2 @ SV314 @ SV420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2254,plain,
! [SV450: $i,SV421: $i,SV314: $i,SV500: $i] :
( ( ( in @ SV500 @ SV314 )
= $false )
| ( ( ~ ( in @ SV500 @ SV421 ) )
= $true )
| ( ( in @ SV500 @ SV450 )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2225]) ).
thf(2255,plain,
! [SV421: $i,SV314: $i,SV450: $i,SV510: $i] :
( ( ( ~ ( in @ SV510 @ SV450 )
| ( in @ SV510 @ SV314 ) )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2256,plain,
! [SV314: $i,SV421: $i,SV450: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ SV450 )
| ( in @ SV511 @ SV421 ) )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2257,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 ) )
= $true )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2258,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 ) )
= $true )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2259,plain,
! [SV454: $i,SV427: $i,SV317: $i,SV501: $i] :
( ( ( in @ SV501 @ SV317 )
= $true )
| ( ( in @ SV501 @ SV427 )
= $true )
| ( ( in @ SV501 @ SV454 )
= $false )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2230]) ).
thf(2260,plain,
! [SV427: $i,SV454: $i,SV317: $i,SV512: $i] :
( ( ( ~ ( in @ SV512 @ SV317 )
| ( in @ SV512 @ SV454 ) )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2261,plain,
! [SV317: $i,SV454: $i,SV427: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV427 )
| ( in @ SV513 @ SV454 ) )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2262,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
= $false )
| ( ( ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV319 ) )
= $true )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2263,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
= $false )
| ( ( ( ( sK20_D @ SV456 @ SV430 @ SV319 )
!= SV430 ) )
= $true )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2264,plain,
! [SV457: $i,SV431: $i,SV319: $i,SV502: $i] :
( ( ( SV502 = SV319 )
= $true )
| ( ( SV502 = SV431 )
= $true )
| ( ( in @ SV502 @ SV457 )
= $false )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2235]) ).
thf(2265,plain,
! [SV431: $i,SV457: $i,SV319: $i,SV514: $i] :
( ( ( ( SV514 != SV319 )
| ( in @ SV514 @ SV457 ) )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2266,plain,
! [SV319: $i,SV457: $i,SV431: $i,SV515: $i] :
( ( ( ( SV515 != SV431 )
| ( in @ SV515 @ SV457 ) )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2267,plain,
! [SV320: $i,SV432: $i,SV458: $i] :
( ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV432 )
= $false )
| ( ( in @ ( sK8_D @ SV458 @ SV432 @ SV320 ) @ SV458 )
= $true )
| ( ( SV458
= ( set_difference @ SV320 @ SV432 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2240]) ).
thf(2268,plain,
! [SV459: $i,SV433: $i,SV320: $i,SV503: $i] :
( ( ( in @ SV503 @ SV320 )
= $false )
| ( ( in @ SV503 @ SV433 )
= $true )
| ( ( in @ SV503 @ SV459 )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2269,plain,
! [SV433: $i,SV320: $i,SV459: $i,SV516: $i] :
( ( ( ~ ( in @ SV516 @ SV459 )
| ( in @ SV516 @ SV320 ) )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2270,plain,
! [SV320: $i,SV433: $i,SV459: $i,SV517: $i] :
( ( ( ~ ( in @ SV517 @ SV459 )
| ~ ( in @ SV517 @ SV433 ) )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2271,plain,
! [SV460: $i,SV446: $i,SV508: $i,SV321: $i,SV504: $i] :
( ( ( ~ ( in @ SV504 @ SV321 ) )
= $true )
| ( ( ~ ( in @ SV508 @ SV446 ) )
= $true )
| ( ( ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ SV504 @ SV508 ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2244]) ).
thf(2272,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( ~ ( in @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) @ SV446 ) )
= $false )
| ( ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2245]) ).
thf(2273,plain,
! [SV461: $i,SV505: $i,SV447: $i,SV518: $i,SV321: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV321 )
| ~ ( in @ SV518 @ SV447 )
| ( SV505
!= ( ordered_pair @ SV509 @ SV518 ) ) )
= $true )
| ( ( in @ SV505 @ SV461 )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2274,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV447 ) )
| ( SV506
!= ( ordered_pair @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) ) ) )
= $false )
| ( ( in @ SV506 @ SV461 )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2275,plain,
! [SV408: $i,SV493: $i,SV373: $i,SV507: $i] :
( ( ( in @ SV507 @ SV373 )
= $false )
| ( ( in @ SV493 @ SV507 )
= $false )
| ( ( in @ SV493 @ SV408 )
= $true )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2276,plain,
! [SV373: $i,SV408: $i,SV494: $i] :
( ( ( in @ SV494 @ ( sK9_D @ SV494 @ SV408 @ SV373 ) )
= $true )
| ( ( in @ SV494 @ SV408 )
= $false )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2251]) ).
thf(2277,plain,
! [SV373: $i,SV408: $i,SV494: $i] :
( ( ( in @ ( sK9_D @ SV494 @ SV408 @ SV373 ) @ SV373 )
= $true )
| ( ( in @ SV494 @ SV408 )
= $false )
| ( ( SV408
= ( union @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2252]) ).
thf(2278,plain,
! [SV450: $i,SV314: $i,SV421: $i,SV500: $i] :
( ( ( in @ SV500 @ SV421 )
= $false )
| ( ( in @ SV500 @ SV314 )
= $false )
| ( ( in @ SV500 @ SV450 )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2279,plain,
! [SV421: $i,SV314: $i,SV450: $i,SV510: $i] :
( ( ( ~ ( in @ SV510 @ SV450 ) )
= $true )
| ( ( in @ SV510 @ SV314 )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2280,plain,
! [SV314: $i,SV421: $i,SV450: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ SV450 ) )
= $true )
| ( ( in @ SV511 @ SV421 )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2281,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV317 )
= $false )
| ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
= $false )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2282,plain,
! [SV317: $i,SV426: $i,SV453: $i] :
( ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV426 )
= $false )
| ( ( in @ ( sK19_D @ SV453 @ SV426 @ SV317 ) @ SV453 )
= $false )
| ( ( SV453
= ( set_union2 @ SV317 @ SV426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2283,plain,
! [SV427: $i,SV454: $i,SV317: $i,SV512: $i] :
( ( ( ~ ( in @ SV512 @ SV317 ) )
= $true )
| ( ( in @ SV512 @ SV454 )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2260]) ).
thf(2284,plain,
! [SV317: $i,SV454: $i,SV427: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV427 ) )
= $true )
| ( ( in @ SV513 @ SV454 )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2285,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV319 )
= $false )
| ( ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
= $false )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2262]) ).
thf(2286,plain,
! [SV319: $i,SV430: $i,SV456: $i] :
( ( ( ( sK20_D @ SV456 @ SV430 @ SV319 )
= SV430 )
= $false )
| ( ( in @ ( sK20_D @ SV456 @ SV430 @ SV319 ) @ SV456 )
= $false )
| ( ( SV456
= ( unordered_pair @ SV319 @ SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2287,plain,
! [SV431: $i,SV457: $i,SV319: $i,SV514: $i] :
( ( ( ( SV514 != SV319 ) )
= $true )
| ( ( in @ SV514 @ SV457 )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2265]) ).
thf(2288,plain,
! [SV319: $i,SV457: $i,SV431: $i,SV515: $i] :
( ( ( ( SV515 != SV431 ) )
= $true )
| ( ( in @ SV515 @ SV457 )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2266]) ).
thf(2289,plain,
! [SV433: $i,SV320: $i,SV459: $i,SV516: $i] :
( ( ( ~ ( in @ SV516 @ SV459 ) )
= $true )
| ( ( in @ SV516 @ SV320 )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2269]) ).
thf(2290,plain,
! [SV320: $i,SV433: $i,SV459: $i,SV517: $i] :
( ( ( ~ ( in @ SV517 @ SV459 ) )
= $true )
| ( ( ~ ( in @ SV517 @ SV433 ) )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2291,plain,
! [SV460: $i,SV446: $i,SV508: $i,SV321: $i,SV504: $i] :
( ( ( in @ SV504 @ SV321 )
= $false )
| ( ( ~ ( in @ SV508 @ SV446 ) )
= $true )
| ( ( ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ SV504 @ SV508 ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2271]) ).
thf(2292,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( ~ ( in @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ SV321 ) )
= $false )
| ( ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2272]) ).
thf(2293,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( ~ ( in @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) @ SV446 ) )
= $false )
| ( ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2272]) ).
thf(2294,plain,
! [SV461: $i,SV505: $i,SV447: $i,SV518: $i,SV321: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV321 )
| ~ ( in @ SV518 @ SV447 ) )
= $true )
| ( ( ( SV505
!= ( ordered_pair @ SV509 @ SV518 ) ) )
= $true )
| ( ( in @ SV505 @ SV461 )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2295,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV447 ) ) )
= $false )
| ( ( in @ SV506 @ SV461 )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2296,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( ( SV506
!= ( ordered_pair @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) ) ) )
= $false )
| ( ( in @ SV506 @ SV461 )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2274]) ).
thf(2297,plain,
! [SV421: $i,SV314: $i,SV450: $i,SV510: $i] :
( ( ( in @ SV510 @ SV450 )
= $false )
| ( ( in @ SV510 @ SV314 )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2279]) ).
thf(2298,plain,
! [SV314: $i,SV421: $i,SV450: $i,SV511: $i] :
( ( ( in @ SV511 @ SV450 )
= $false )
| ( ( in @ SV511 @ SV421 )
= $true )
| ( ( SV450
= ( set_intersection2 @ SV314 @ SV421 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2280]) ).
thf(2299,plain,
! [SV427: $i,SV454: $i,SV317: $i,SV512: $i] :
( ( ( in @ SV512 @ SV317 )
= $false )
| ( ( in @ SV512 @ SV454 )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2283]) ).
thf(2300,plain,
! [SV317: $i,SV454: $i,SV427: $i,SV513: $i] :
( ( ( in @ SV513 @ SV427 )
= $false )
| ( ( in @ SV513 @ SV454 )
= $true )
| ( ( SV454
= ( set_union2 @ SV317 @ SV427 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2301,plain,
! [SV431: $i,SV457: $i,SV319: $i,SV514: $i] :
( ( ( SV514 = SV319 )
= $false )
| ( ( in @ SV514 @ SV457 )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2302,plain,
! [SV319: $i,SV457: $i,SV431: $i,SV515: $i] :
( ( ( SV515 = SV431 )
= $false )
| ( ( in @ SV515 @ SV457 )
= $true )
| ( ( SV457
= ( unordered_pair @ SV319 @ SV431 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2303,plain,
! [SV433: $i,SV320: $i,SV459: $i,SV516: $i] :
( ( ( in @ SV516 @ SV459 )
= $false )
| ( ( in @ SV516 @ SV320 )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2304,plain,
! [SV320: $i,SV433: $i,SV459: $i,SV517: $i] :
( ( ( in @ SV517 @ SV459 )
= $false )
| ( ( ~ ( in @ SV517 @ SV433 ) )
= $true )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2305,plain,
! [SV460: $i,SV321: $i,SV504: $i,SV446: $i,SV508: $i] :
( ( ( in @ SV508 @ SV446 )
= $false )
| ( ( in @ SV504 @ SV321 )
= $false )
| ( ( ( ( sK16_D @ SV460 @ SV446 @ SV321 )
!= ( ordered_pair @ SV504 @ SV508 ) ) )
= $true )
| ( ( ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2291]) ).
thf(2306,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( in @ ( sK17_SY205 @ SV460 @ SV446 @ SV321 ) @ SV321 )
= $true )
| ( ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2292]) ).
thf(2307,plain,
! [SV321: $i,SV446: $i,SV460: $i] :
( ( ( in @ ( sK18_SY207 @ SV460 @ SV446 @ SV321 ) @ SV446 )
= $true )
| ( ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2293]) ).
thf(2308,plain,
! [SV461: $i,SV505: $i,SV447: $i,SV518: $i,SV321: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ SV321 ) )
= $true )
| ( ( ~ ( in @ SV518 @ SV447 ) )
= $true )
| ( ( ( SV505
!= ( ordered_pair @ SV509 @ SV518 ) ) )
= $true )
| ( ( in @ SV505 @ SV461 )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2294]) ).
thf(2309,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV447 ) ) )
= $true )
| ( ( in @ SV506 @ SV461 )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2295]) ).
thf(2310,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( SV506
= ( ordered_pair @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) ) )
= $true )
| ( ( in @ SV506 @ SV461 )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2296]) ).
thf(2311,plain,
! [SV320: $i,SV459: $i,SV433: $i,SV517: $i] :
( ( ( in @ SV517 @ SV433 )
= $false )
| ( ( in @ SV517 @ SV459 )
= $false )
| ( ( SV459
= ( set_difference @ SV320 @ SV433 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2312,plain,
! [SV508: $i,SV504: $i,SV321: $i,SV446: $i,SV460: $i] :
( ( ( ( sK16_D @ SV460 @ SV446 @ SV321 )
= ( ordered_pair @ SV504 @ SV508 ) )
= $false )
| ( ( in @ SV504 @ SV321 )
= $false )
| ( ( in @ SV508 @ SV446 )
= $false )
| ( ( ~ ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 ) )
= $true )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2305]) ).
thf(2313,plain,
! [SV461: $i,SV505: $i,SV447: $i,SV518: $i,SV321: $i,SV509: $i] :
( ( ( in @ SV509 @ SV321 )
= $false )
| ( ( ~ ( in @ SV518 @ SV447 ) )
= $true )
| ( ( ( SV505
!= ( ordered_pair @ SV509 @ SV518 ) ) )
= $true )
| ( ( in @ SV505 @ SV461 )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2314,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( ~ ( in @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV321 )
| ~ ( in @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV447 ) )
= $false )
| ( ( in @ SV506 @ SV461 )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2315,plain,
! [SV504: $i,SV508: $i,SV321: $i,SV446: $i,SV460: $i] :
( ( ( in @ ( sK16_D @ SV460 @ SV446 @ SV321 ) @ SV460 )
= $false )
| ( ( in @ SV508 @ SV446 )
= $false )
| ( ( in @ SV504 @ SV321 )
= $false )
| ( ( ( sK16_D @ SV460 @ SV446 @ SV321 )
= ( ordered_pair @ SV504 @ SV508 ) )
= $false )
| ( ( SV460
= ( cartesian_product2 @ SV321 @ SV446 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2316,plain,
! [SV461: $i,SV505: $i,SV321: $i,SV509: $i,SV447: $i,SV518: $i] :
( ( ( in @ SV518 @ SV447 )
= $false )
| ( ( in @ SV509 @ SV321 )
= $false )
| ( ( ( SV505
!= ( ordered_pair @ SV509 @ SV518 ) ) )
= $true )
| ( ( in @ SV505 @ SV461 )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2317,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( ~ ( in @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV321 ) )
= $false )
| ( ( in @ SV506 @ SV461 )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2318,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( ~ ( in @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV447 ) )
= $false )
| ( ( in @ SV506 @ SV461 )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2319,plain,
! [SV461: $i,SV447: $i,SV321: $i,SV518: $i,SV509: $i,SV505: $i] :
( ( ( SV505
= ( ordered_pair @ SV509 @ SV518 ) )
= $false )
| ( ( in @ SV509 @ SV321 )
= $false )
| ( ( in @ SV518 @ SV447 )
= $false )
| ( ( in @ SV505 @ SV461 )
= $true )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2316]) ).
thf(2320,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( in @ ( sK14_E @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV321 )
= $true )
| ( ( in @ SV506 @ SV461 )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2317]) ).
thf(2321,plain,
! [SV321: $i,SV447: $i,SV461: $i,SV506: $i] :
( ( ( in @ ( sK15_SY202 @ SV506 @ SV461 @ SV447 @ SV321 ) @ SV447 )
= $true )
| ( ( in @ SV506 @ SV461 )
= $false )
| ( ( SV461
= ( cartesian_product2 @ SV321 @ SV447 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2318]) ).
thf(2322,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1308,2321,2320,2319,2315,2311,2310,2307,2306,2303,2302,2301,2300,2299,2298,2297,2286,2285,2282,2281,2278,2277,2276,2275,2268,2267,2264,2259,2253,2249,2246,2239,2238,2224,2223,2197,2196,2189,2188,2185,2184,2171,2166,2161,2155,2154,2151,2141,2132,2131,2117,2116,2103,2102,2101,2100,2089,2088,2087,2080,2071,2067,2065,2064,2055,2054,2049,2037,2033,2032,2031,2012,2000,1997,1993,1969,1962,1954,1953,1952,1951,1943,1942,1926,1925,1924,1918,1917,1910,1909,1901,1900,1899,1898,1897,1881,1876,1875,1840,1836,1830,1806,1768,1767,1766,1765,1764,1761,1760,1759,1754,1735,1696,1695,1694,1690,1687,1684,1683,1681,1677,1675,1672,1616,1612,1600,1590,1536,1532,1531,1530,1529,1522,1518,1515,1513,1512,1506,1498,1466,1465,1464,1463,1461,1460,1458,1457,1446,1440,1429,1375,1368,1367,1366,1365,1364,1363,1362,1361,1360,1359,1358]) ).
thf(2323,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2322,1292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU165+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jun 19 21:35:08 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.39 ..
% 0.21/0.41
% 0.21/0.41 No.of.Axioms: 94
% 0.21/0.41
% 0.21/0.41 Length.of.Defs: 0
% 0.21/0.41
% 0.21/0.41 Contains.Choice.Funs: false
% 0.21/0.45 ..
% 0.21/0.47 (rf:0,axioms:94,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:96,loop_count:0,foatp_calls:0,translation:fof_full)....................................................................................................................................................
% 1.19/1.61
% 1.19/1.61 ********************************
% 1.19/1.61 * All subproblems solved! *
% 1.19/1.61 ********************************
% 1.19/1.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:94,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2322,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.23/3.42
% 3.23/3.42 %**** Beginning of derivation protocol ****
% 3.23/3.42 % SZS output start CNFRefutation
% See solution above
% 3.23/3.43
% 3.23/3.43 %**** End of derivation protocol ****
% 3.23/3.43 %**** no. of clauses in derivation: 2323 ****
% 3.23/3.43 %**** clause counter: 2322 ****
% 3.23/3.43
% 3.23/3.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:94,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2322,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------