TSTP Solution File: SEU163+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU163+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 : n008.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 12:07:26 EDT 2022
% Result : Theorem 0.71s 1.00s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 131
% Syntax : Number of formulae : 1307 ( 702 unt; 38 typ; 0 def)
% Number of atoms : 8195 (3249 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 17781 (3194 ~;2797 |; 188 &;11479 @)
% ( 64 <=>; 59 =>; 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 : 41 ( 38 usr; 7 con; 0-4 aty)
% Number of variables : 3812 ( 0 ^3798 !; 14 ?;3812 :)
% 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_D,type,
sK10_D: $i > $i > $i > $i ).
thf(tp_sK11_C,type,
sK11_C: $i > $i > $i ).
thf(tp_sK12_E,type,
sK12_E: $i > $i > $i > $i > $i ).
thf(tp_sK13_SY192,type,
sK13_SY192: $i > $i > $i > $i > $i ).
thf(tp_sK14_D,type,
sK14_D: $i > $i > $i > $i ).
thf(tp_sK15_SY195,type,
sK15_SY195: $i > $i > $i > $i ).
thf(tp_sK16_SY197,type,
sK16_SY197: $i > $i > $i > $i ).
thf(tp_sK17_D,type,
sK17_D: $i > $i > $i > $i ).
thf(tp_sK18_D,type,
sK18_D: $i > $i > $i > $i ).
thf(tp_sK19_C,type,
sK19_C: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_B,type,
sK20_B: $i > $i ).
thf(tp_sK21_C,type,
sK21_C: $i > $i > $i ).
thf(tp_sK22_C,type,
sK22_C: $i > $i > $i ).
thf(tp_sK23_C,type,
sK23_C: $i > $i > $i ).
thf(tp_sK2_SY189,type,
sK2_SY189: $i ).
thf(tp_sK3_C,type,
sK3_C: $i > $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_D,type,
sK6_D: $i > $i > $i > $i ).
thf(tp_sK7_D,type,
sK7_D: $i > $i > $i > $i ).
thf(tp_sK8_C,type,
sK8_C: $i > $i > $i ).
thf(tp_sK9_SY191,type,
sK9_SY191: $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/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(5,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(7,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(8,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(11,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(12,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(19,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(41,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(53,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(55,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(58,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(59,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/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(64,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(71,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(74,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(77,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(80,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(90,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(92,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(93,conjecture,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(94,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[93]) ).
thf(95,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[94]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(98,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(99,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(100,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(101,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(102,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(103,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(106,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(107,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(114,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(115,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(116,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(117,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(118,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(119,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(120,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(121,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(122,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(123,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(124,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(125,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(126,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(127,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(128,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(129,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(130,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(131,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(132,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(133,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(134,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(135,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(136,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(137,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(138,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(139,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(141,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(142,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(143,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(144,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(145,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(146,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(147,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(148,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(149,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(150,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(151,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(152,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(153,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(154,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)],[59]) ).
thf(155,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(156,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(157,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(158,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(159,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(160,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)],[65]) ).
thf(161,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(162,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(163,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)],[68]) ).
thf(164,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(165,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(166,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(167,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)],[72]) ).
thf(168,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)],[73]) ).
thf(169,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(170,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(171,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)],[76]) ).
thf(172,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(173,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(174,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)],[79]) ).
thf(175,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(176,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(177,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)],[82]) ).
thf(178,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)],[83]) ).
thf(179,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(180,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(181,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)],[86]) ).
thf(182,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(183,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(184,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(185,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(186,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(187,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(188,plain,
( ( ! [SY189: $i] :
( ( in @ sK1_A @ SY189 )
=> ( subset @ sK1_A @ ( union @ SY189 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[95]) ).
thf(189,plain,
( ( ( in @ sK1_A @ sK2_SY189 )
=> ( subset @ sK1_A @ ( union @ sK2_SY189 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[188]) ).
thf(190,plain,
( ( in @ sK1_A @ sK2_SY189 )
= $true ),
inference(standard_cnf,[status(thm)],[189]) ).
thf(191,plain,
( ( subset @ sK1_A @ ( union @ sK2_SY189 ) )
= $false ),
inference(standard_cnf,[status(thm)],[189]) ).
thf(192,plain,
( ( ~ ( subset @ sK1_A @ ( union @ sK2_SY189 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[191]) ).
thf(193,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(194,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(195,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(196,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_C @ B @ A ) @ A )
| ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
& ( ( in @ ( sK3_C @ B @ A ) @ A )
| ( in @ ( sK3_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(197,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(198,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(199,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(200,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(201,plain,
( ( ! [A: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(202,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(203,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(204,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(205,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[112]) ).
thf(206,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)],[125]) ).
thf(207,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)],[126]) ).
thf(208,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ( in @ ( sK6_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)],[128]) ).
thf(209,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY190: $i] :
( ~ ( in @ ( sK8_C @ B @ A ) @ SY190 )
| ~ ( in @ SY190 @ A ) )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK8_C @ B @ A ) @ ( sK9_SY191 @ B @ A ) )
& ( in @ ( sK9_SY191 @ B @ A ) @ A ) )
| ( in @ ( sK8_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 @ ( sK7_D @ C @ B @ A ) )
& ( in @ ( sK7_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[129]) ).
thf(210,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK10_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK10_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK10_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK10_D @ C @ B @ A ) @ A )
| ( in @ ( sK10_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK10_D @ C @ B @ A ) @ B )
| ( in @ ( sK10_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)],[130]) ).
thf(211,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK11_C @ B @ A ) @ A )
& ~ ( in @ ( sK11_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)],[131]) ).
thf(212,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY193: $i,SY194: $i] :
( ~ ( in @ SY193 @ A )
| ~ ( in @ SY194 @ B )
| ( ( sK14_D @ C @ B @ A )
!= ( ordered_pair @ SY193 @ SY194 ) ) )
| ~ ( in @ ( sK14_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK15_SY195 @ C @ B @ A ) @ A )
& ( in @ ( sK16_SY197 @ C @ B @ A ) @ B )
& ( ( sK14_D @ C @ B @ A )
= ( ordered_pair @ ( sK15_SY195 @ C @ B @ A ) @ ( sK16_SY197 @ C @ B @ A ) ) ) )
| ( in @ ( sK14_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 @ ( sK12_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK13_SY192 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK12_E @ D @ C @ B @ A ) @ ( sK13_SY192 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(213,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK17_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK17_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK17_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK17_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK17_D @ C @ B @ A ) @ C )
| ( in @ ( sK17_D @ C @ B @ A ) @ A )
| ( in @ ( sK17_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)],[133]) ).
thf(214,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK18_D @ C @ B @ A ) @ C )
| ( ( sK18_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK18_D @ C @ B @ A ) @ C )
| ( ( sK18_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK18_D @ C @ B @ A ) @ C )
| ( ( sK18_D @ C @ B @ A )
= A )
| ( ( sK18_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)],[134]) ).
thf(215,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK19_C @ B @ A ) @ B )
| ~ ( subset @ ( sK19_C @ B @ A ) @ A ) )
& ( ( in @ ( sK19_C @ B @ A ) @ B )
| ( subset @ ( sK19_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)],[135]) ).
thf(216,plain,
( ( ! [A: $i] :
( ( in @ ( sK20_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[136]) ).
thf(217,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK21_C @ B @ A )
!= A )
| ~ ( in @ ( sK21_C @ B @ A ) @ B ) )
& ( ( ( sK21_C @ B @ A )
= A )
| ( in @ ( sK21_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)],[137]) ).
thf(218,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)],[138]) ).
thf(219,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(220,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(221,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(223,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)],[146]) ).
thf(224,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)],[147]) ).
thf(225,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(226,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)],[151]) ).
thf(227,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(228,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK22_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)],[154]) ).
thf(230,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[156]) ).
thf(231,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(232,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(233,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK23_C @ B @ A ) @ A )
& ( in @ ( sK23_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)],[160]) ).
thf(234,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)],[161]) ).
thf(235,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)],[163]) ).
thf(236,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)],[164]) ).
thf(237,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)],[165]) ).
thf(238,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)],[167]) ).
thf(239,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)],[168]) ).
thf(240,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[170]) ).
thf(241,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)],[171]) ).
thf(242,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[173]) ).
thf(243,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)],[174]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(245,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)],[177]) ).
thf(246,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)],[178]) ).
thf(247,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(248,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)],[180]) ).
thf(249,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)],[181]) ).
thf(250,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)],[182]) ).
thf(251,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)],[183]) ).
thf(252,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[184]) ).
thf(253,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[185]) ).
thf(254,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(255,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[187]) ).
thf(256,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(257,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(258,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(260,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)],[251]) ).
thf(261,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)],[250]) ).
thf(262,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)],[249]) ).
thf(263,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)],[248]) ).
thf(264,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(265,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)],[246]) ).
thf(266,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)],[245]) ).
thf(267,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(268,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(269,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(270,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(271,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(272,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(273,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(274,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(276,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)],[238]) ).
thf(277,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(278,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)],[237]) ).
thf(279,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)],[236]) ).
thf(280,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)],[235]) ).
thf(281,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(282,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)],[234]) ).
thf(283,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK23_C @ B @ A ) @ A )
& ( in @ ( sK23_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(284,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(285,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(286,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(287,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(288,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(289,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK22_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)],[229]) ).
thf(290,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(291,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(292,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)],[226]) ).
thf(293,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(294,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(295,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(296,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)],[224]) ).
thf(297,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(298,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(299,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(301,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(302,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(303,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(304,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(305,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)],[218]) ).
thf(306,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK21_C @ B @ A )
!= A )
| ~ ( in @ ( sK21_C @ B @ A ) @ B ) )
& ( ( ( sK21_C @ B @ A )
= A )
| ( in @ ( sK21_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)],[217]) ).
thf(307,plain,
( ( ! [A: $i] :
( ( in @ ( sK20_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(308,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK19_C @ B @ A ) @ B )
| ~ ( subset @ ( sK19_C @ B @ A ) @ A ) )
& ( ( in @ ( sK19_C @ B @ A ) @ B )
| ( subset @ ( sK19_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)],[215]) ).
thf(309,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK18_D @ C @ B @ A ) @ C )
| ( ( sK18_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK18_D @ C @ B @ A ) @ C )
| ( ( sK18_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK18_D @ C @ B @ A ) @ C )
| ( ( sK18_D @ C @ B @ A )
= A )
| ( ( sK18_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)],[214]) ).
thf(310,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK17_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK17_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK17_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK17_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK17_D @ C @ B @ A ) @ C )
| ( in @ ( sK17_D @ C @ B @ A ) @ A )
| ( in @ ( sK17_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)],[213]) ).
thf(311,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY193: $i,SY194: $i] :
( ~ ( in @ SY193 @ A )
| ~ ( in @ SY194 @ B )
| ( ( sK14_D @ C @ B @ A )
!= ( ordered_pair @ SY193 @ SY194 ) ) )
| ~ ( in @ ( sK14_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK15_SY195 @ C @ B @ A ) @ A )
& ( in @ ( sK16_SY197 @ C @ B @ A ) @ B )
& ( ( sK14_D @ C @ B @ A )
= ( ordered_pair @ ( sK15_SY195 @ C @ B @ A ) @ ( sK16_SY197 @ C @ B @ A ) ) ) )
| ( in @ ( sK14_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 @ ( sK12_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK13_SY192 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK12_E @ D @ C @ B @ A ) @ ( sK13_SY192 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(312,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK11_C @ B @ A ) @ A )
& ~ ( in @ ( sK11_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)],[211]) ).
thf(313,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK10_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK10_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK10_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK10_D @ C @ B @ A ) @ A )
| ( in @ ( sK10_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK10_D @ C @ B @ A ) @ B )
| ( in @ ( sK10_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)],[210]) ).
thf(314,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY190: $i] :
( ~ ( in @ ( sK8_C @ B @ A ) @ SY190 )
| ~ ( in @ SY190 @ A ) )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK8_C @ B @ A ) @ ( sK9_SY191 @ B @ A ) )
& ( in @ ( sK9_SY191 @ B @ A ) @ A ) )
| ( in @ ( sK8_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 @ ( sK7_D @ C @ B @ A ) )
& ( in @ ( sK7_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(315,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ( in @ ( sK6_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)],[208]) ).
thf(316,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(317,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)],[207]) ).
thf(318,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)],[206]) ).
thf(319,plain,
$true = $true,
inference(copy,[status(thm)],[124]) ).
thf(320,plain,
$true = $true,
inference(copy,[status(thm)],[123]) ).
thf(321,plain,
$true = $true,
inference(copy,[status(thm)],[122]) ).
thf(322,plain,
$true = $true,
inference(copy,[status(thm)],[121]) ).
thf(323,plain,
$true = $true,
inference(copy,[status(thm)],[120]) ).
thf(324,plain,
$true = $true,
inference(copy,[status(thm)],[119]) ).
thf(325,plain,
$true = $true,
inference(copy,[status(thm)],[118]) ).
thf(326,plain,
$true = $true,
inference(copy,[status(thm)],[117]) ).
thf(327,plain,
$true = $true,
inference(copy,[status(thm)],[116]) ).
thf(328,plain,
$true = $true,
inference(copy,[status(thm)],[115]) ).
thf(329,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(330,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(331,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(332,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(333,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(334,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(335,plain,
( ( ! [A: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(336,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(337,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(338,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(339,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(340,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(341,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(342,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_C @ B @ A ) @ A )
| ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
& ( ( in @ ( sK3_C @ B @ A ) @ A )
| ( in @ ( sK3_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(343,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(344,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(345,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(346,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(347,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(348,plain,
( ( in @ sK1_A @ sK2_SY189 )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(349,plain,
( ( ~ ( subset @ sK1_A @ ( union @ sK2_SY189 ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(350,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)],[263]) ).
thf(351,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)],[265]) ).
thf(352,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)],[282]) ).
thf(353,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK14_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK14_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK16_SY197 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK14_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK15_SY195 @ SX2 @ SX1 @ SX0 ) @ ( sK16_SY197 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK14_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 @ ( sK12_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK13_SY192 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK12_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY192 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(354,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)],[260]) ).
thf(355,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)],[278]) ).
thf(356,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK11_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)],[312]) ).
thf(357,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK18_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK18_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK18_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK18_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK18_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK18_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)],[309]) ).
thf(358,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)],[261]) ).
thf(359,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK20_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(360,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)],[296]) ).
thf(361,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK21_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK21_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK21_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)],[306]) ).
thf(362,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)],[318]) ).
thf(363,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK23_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)],[283]) ).
thf(364,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(365,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK19_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK19_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)],[308]) ).
thf(366,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ ( sK9_SY191 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_SY191 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK8_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 @ ( sK7_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(367,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK17_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK17_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)],[310]) ).
thf(368,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK6_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)],[315]) ).
thf(369,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)],[276]) ).
thf(370,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)],[292]) ).
thf(371,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)],[280]) ).
thf(372,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)],[317]) ).
thf(373,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK22_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)],[289]) ).
thf(374,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK10_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)],[313]) ).
thf(375,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)],[279]) ).
thf(376,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)],[305]) ).
thf(377,plain,
! [SV1: $i] :
( ( ( ( singleton @ SV1 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(378,plain,
! [SV2: $i] :
( ( ! [SY198: $i] :
( ~ ( in @ SV2 @ SY198 )
| ( ( set_union2 @ ( singleton @ SV2 ) @ SY198 )
= SY198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(379,plain,
! [SV3: $i] :
( ( ! [SY199: $i] :
( ~ ( disjoint @ ( singleton @ SV3 ) @ SY199 )
| ~ ( in @ SV3 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(380,plain,
! [SV4: $i] :
( ( ! [SY200: $i] :
( ( in @ SV4 @ SY200 )
| ( disjoint @ ( singleton @ SV4 ) @ SY200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(381,plain,
! [SV5: $i] :
( ( ! [SY201: $i] :
( ~ ( subset @ SV5 @ SY201 )
| ! [SY202: $i] :
( ( in @ SY202 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SY201 @ ( singleton @ SY202 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(382,plain,
! [SV6: $i] :
( ( ! [SY203: $i] :
( ~ ( in @ SV6 @ SY203 )
| ( subset @ SV6 @ ( union @ SY203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(383,plain,
! [SV7: $i] :
( ( ! [SY204: $i,SY205: $i,SY206: $i] :
( ( SV7 = SY206 )
| ( SV7 = SY205 )
| ( ( unordered_pair @ SV7 @ SY204 )
!= ( unordered_pair @ SY205 @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(384,plain,
! [SV8: $i] :
( ( ! [SY207: $i] :
( ~ ( subset @ SV8 @ SY207 )
| ( ( set_union2 @ SV8 @ SY207 )
= SY207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(385,plain,
! [SV9: $i] :
( ( ! [SY208: $i] : ( subset @ ( set_intersection2 @ SV9 @ SY208 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(386,plain,
! [SV10: $i] :
( ( ! [SY209: $i,SY210: $i] :
( ~ ( subset @ SV10 @ SY209 )
| ~ ( subset @ SV10 @ SY210 )
| ( subset @ SV10 @ ( set_intersection2 @ SY209 @ SY210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(387,plain,
! [SV11: $i] :
( ( ! [SY211: $i,SY212: $i] :
( ~ ( subset @ SV11 @ SY211 )
| ~ ( subset @ SY211 @ SY212 )
| ( subset @ SV11 @ SY212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(388,plain,
! [SV12: $i] :
( ( ! [SY213: $i] :
( ~ ( subset @ SV12 @ SY213 )
| ! [SY214: $i] : ( subset @ ( set_intersection2 @ SV12 @ SY214 ) @ ( set_intersection2 @ SY213 @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(389,plain,
! [SV13: $i] :
( ( ! [SY215: $i] :
( ~ ( subset @ SV13 @ SY215 )
| ( ( set_intersection2 @ SV13 @ SY215 )
= SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(390,plain,
! [SV14: $i] :
( ( subset @ empty_set @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(391,plain,
! [SV15: $i] :
( ( ! [SY216: $i] :
( ~ ( subset @ SV15 @ SY216 )
| ! [SY217: $i] : ( subset @ ( set_difference @ SV15 @ SY217 ) @ ( set_difference @ SY216 @ SY217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(392,plain,
! [SV16: $i] :
( ( ! [SY218: $i] : ( subset @ ( set_difference @ SV16 @ SY218 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(393,plain,
! [SV17: $i] :
( ( ! [SY219: $i] :
( ( set_union2 @ SV17 @ ( set_difference @ SY219 @ SV17 ) )
= ( set_union2 @ SV17 @ SY219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(394,plain,
! [SV18: $i] :
( ( ~ ( subset @ SV18 @ empty_set )
| ( SV18 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(395,plain,
! [SV19: $i] :
( ( ! [SY220: $i] :
( ( set_difference @ ( set_union2 @ SV19 @ SY220 ) @ SY220 )
= ( set_difference @ SV19 @ SY220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(396,plain,
! [SV20: $i] :
( ( ! [SY221: $i] :
( ~ ( subset @ SV20 @ SY221 )
| ( SY221
= ( set_union2 @ SV20 @ ( set_difference @ SY221 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(397,plain,
! [SV21: $i] :
( ( ! [SY222: $i] :
( ~ ( in @ SV21 @ SY222 )
| ( ( set_union2 @ ( singleton @ SV21 ) @ SY222 )
= SY222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(398,plain,
! [SV22: $i] :
( ( ! [SY223: $i] :
( ( set_difference @ SV22 @ ( set_difference @ SV22 @ SY223 ) )
= ( set_intersection2 @ SV22 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(399,plain,
! [SV23: $i] :
( ( ! [SY224: $i] :
( ~ ( proper_subset @ SY224 @ SV23 )
| ~ ( subset @ SV23 @ SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(400,plain,
! [SV24: $i] :
( ( ! [SY225: $i,SY226: $i] :
( ~ ( disjoint @ SY225 @ SY226 )
| ~ ( subset @ SV24 @ SY225 )
| ( disjoint @ SV24 @ SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(401,plain,
! [SV25: $i] :
( ( ( unordered_pair @ SV25 @ SV25 )
= ( singleton @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(402,plain,
! [SV26: $i] :
( ( ! [SY227: $i] :
( ~ ( subset @ ( singleton @ SV26 ) @ ( singleton @ SY227 ) )
| ( SV26 = SY227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(403,plain,
! [SV27: $i] :
( ( ! [SY228: $i] : ( subset @ SV27 @ ( set_union2 @ SV27 @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(404,plain,
! [SV28: $i] :
( ( ! [SY229: $i,SY230: $i] :
( ~ ( subset @ SV28 @ SY229 )
| ~ ( subset @ SY230 @ SY229 )
| ( subset @ ( set_union2 @ SV28 @ SY230 ) @ SY229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(405,plain,
! [SV29: $i] :
( ( ! [SY231: $i] :
( ! [SY232: $i] :
( ( singleton @ SV29 )
!= ( unordered_pair @ SY231 @ SY232 ) )
| ( SV29 = SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(406,plain,
! [SV30: $i] :
( ( ! [SY233: $i,SY234: $i] :
( ( ( singleton @ SV30 )
!= ( unordered_pair @ SY233 @ SY234 ) )
| ( SY233 = SY234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(407,plain,
! [SV31: $i] :
( ( ! [SY235: $i] :
( ~ ( in @ SV31 @ SY235 )
| ~ ( in @ SY235 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(408,plain,
! [SV32: $i] :
( ( ! [SY236: $i] :
( ~ ( proper_subset @ SV32 @ SY236 )
| ~ ( proper_subset @ SY236 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(409,plain,
! [SV33: $i] :
( ( ! [SY237: $i] :
( ( unordered_pair @ SV33 @ SY237 )
= ( unordered_pair @ SY237 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(410,plain,
! [SV34: $i] :
( ( ! [SY238: $i] :
( ( set_union2 @ SV34 @ SY238 )
= ( set_union2 @ SY238 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(411,plain,
! [SV35: $i] :
( ( ! [SY239: $i] :
( ( set_intersection2 @ SV35 @ SY239 )
= ( set_intersection2 @ SY239 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(412,plain,
! [SV36: $i] :
( ( ! [SY240: $i] :
( ( ordered_pair @ SV36 @ SY240 )
= ( unordered_pair @ ( unordered_pair @ SV36 @ SY240 ) @ ( singleton @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(413,plain,
! [SV37: $i] :
( ( ! [SY241: $i] :
~ ( empty @ ( ordered_pair @ SV37 @ SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(414,plain,
! [SV38: $i] :
( ( ( empty @ SV38 )
| ! [SY242: $i] :
~ ( empty @ ( set_union2 @ SV38 @ SY242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(415,plain,
! [SV39: $i] :
( ( ( empty @ SV39 )
| ! [SY243: $i] :
~ ( empty @ ( set_union2 @ SY243 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(416,plain,
! [SV40: $i] :
( ( ( set_union2 @ SV40 @ SV40 )
= SV40 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(417,plain,
! [SV41: $i] :
( ( ( set_intersection2 @ SV41 @ SV41 )
= SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(418,plain,
! [SV42: $i] :
( ( ~ ( proper_subset @ SV42 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(419,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(420,plain,
! [SV43: $i] :
( ( subset @ SV43 @ SV43 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(421,plain,
! [SV44: $i] :
( ( ! [SY244: $i] :
( ~ ( disjoint @ SV44 @ SY244 )
| ( disjoint @ SY244 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(422,plain,
! [SV45: $i] :
( ( ( set_union2 @ SV45 @ empty_set )
= SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(423,plain,
! [SV46: $i] :
( ( ( set_intersection2 @ SV46 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(424,plain,
! [SV47: $i] :
( ( ( set_difference @ SV47 @ empty_set )
= SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(425,plain,
! [SV48: $i] :
( ( ( set_difference @ empty_set @ SV48 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(426,plain,
! [SV49: $i] :
( ( ~ ( empty @ SV49 )
| ( SV49 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(427,plain,
! [SV50: $i] :
( ( ! [SY245: $i] :
( ~ ( empty @ SY245 )
| ~ ( in @ SV50 @ SY245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(428,plain,
! [SV51: $i] :
( ( ! [SY246: $i] :
( ( SV51 = SY246 )
| ~ ( empty @ SV51 )
| ~ ( empty @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(429,plain,
( ( subset @ sK1_A @ ( union @ sK2_SY189 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(430,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)],[350]) ).
thf(431,plain,
! [SV52: $i] :
( ( ! [SY247: $i] :
~ ( ~ ! [SY248: $i,SY249: $i] :
( ~ ( in @ SV52 @ SY248 )
| ~ ( in @ SY247 @ SY249 )
| ( in @ ( ordered_pair @ SV52 @ SY247 ) @ ( cartesian_product2 @ SY248 @ SY249 ) ) )
| ~ ~ ( ~ ! [SY250: $i] :
( ! [SY251: $i] :
~ ( in @ ( ordered_pair @ SV52 @ SY247 ) @ ( cartesian_product2 @ SY250 @ SY251 ) )
| ( in @ SV52 @ SY250 ) )
| ~ ! [SY252: $i,SY253: $i] :
( ~ ( in @ ( ordered_pair @ SV52 @ SY247 ) @ ( cartesian_product2 @ SY252 @ SY253 ) )
| ( in @ SY247 @ SY253 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(432,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)],[352]) ).
thf(433,plain,
! [SV53: $i] :
( ( ~ ( ~ ! [SY254: $i,SY255: $i] :
( ~ ( ~ ( ! [SY256: $i,SY257: $i] :
( ~ ( in @ SY256 @ SV53 )
| ~ ( in @ SY257 @ SY254 )
| ( ( sK14_D @ SY255 @ SY254 @ SV53 )
!= ( ordered_pair @ SY256 @ SY257 ) ) )
| ~ ( in @ ( sK14_D @ SY255 @ SY254 @ SV53 ) @ SY255 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SY255 @ SY254 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SY255 @ SY254 @ SV53 ) @ SY254 ) )
| ( ( sK14_D @ SY255 @ SY254 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SY255 @ SY254 @ SV53 ) @ ( sK16_SY197 @ SY255 @ SY254 @ SV53 ) ) ) )
| ( in @ ( sK14_D @ SY255 @ SY254 @ SV53 ) @ SY255 ) ) )
| ( SY255
= ( cartesian_product2 @ SV53 @ SY254 ) ) )
| ~ ! [SY258: $i,SY259: $i] :
( ( SY259
!= ( cartesian_product2 @ SV53 @ SY258 ) )
| ~ ( ~ ! [SY260: $i] :
( ! [SY261: $i,SY262: $i] :
( ~ ( in @ SY261 @ SV53 )
| ~ ( in @ SY262 @ SY258 )
| ( SY260
!= ( ordered_pair @ SY261 @ SY262 ) ) )
| ( in @ SY260 @ SY259 ) )
| ~ ! [SY263: $i] :
( ~ ( in @ SY263 @ SY259 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY263 @ SY259 @ SY258 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SY263 @ SY259 @ SY258 @ SV53 ) @ SY258 ) )
| ( SY263
!= ( ordered_pair @ ( sK12_E @ SY263 @ SY259 @ SY258 @ SV53 ) @ ( sK13_SY192 @ SY263 @ SY259 @ SY258 @ SV53 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(434,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)],[354]) ).
thf(435,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)],[355]) ).
thf(436,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK11_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)],[356]) ).
thf(437,plain,
! [SV54: $i] :
( ( ~ ( ~ ! [SY264: $i,SY265: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY265 @ SY264 @ SV54 ) @ SY265 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
!= SV54 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY265 @ SY264 @ SV54 ) @ SY265 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
!= SY264 ) ) )
| ~ ( ( in @ ( sK18_D @ SY265 @ SY264 @ SV54 ) @ SY265 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
= SV54 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
= SY264 ) ) )
| ( SY265
= ( unordered_pair @ SV54 @ SY264 ) ) )
| ~ ! [SY266: $i,SY267: $i] :
( ( SY267
!= ( unordered_pair @ SV54 @ SY266 ) )
| ~ ( ~ ! [SY268: $i] :
( ~ ( in @ SY268 @ SY267 )
| ( SY268 = SV54 )
| ( SY268 = SY266 ) )
| ~ ~ ( ~ ! [SY269: $i] :
( ( SY269 != SV54 )
| ( in @ SY269 @ SY267 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY266 )
| ( in @ SX3 @ SY267 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(438,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)],[358]) ).
thf(439,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK20_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(440,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)],[360]) ).
thf(441,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK21_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK21_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK21_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)],[361]) ).
thf(442,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)],[362]) ).
thf(443,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK23_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)],[363]) ).
thf(444,plain,
! [SV55: $i] :
( ( ! [SY271: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SY271 @ SV55 ) @ SV55 )
| ~ ( in @ ( sK3_C @ SY271 @ SV55 ) @ SY271 ) )
| ~ ( ( in @ ( sK3_C @ SY271 @ SV55 ) @ SV55 )
| ( in @ ( sK3_C @ SY271 @ SV55 ) @ SY271 ) ) )
| ( SV55 = SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(445,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK19_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK19_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)],[365]) ).
thf(446,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ ( sK9_SY191 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_SY191 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK8_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 @ ( sK7_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(447,plain,
! [SV56: $i] :
( ( ~ ( ~ ! [SY272: $i,SY273: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY273 )
| ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY273 )
| ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY272 ) ) )
| ~ ( ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY273 )
| ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY272 ) ) )
| ( SY273
= ( set_union2 @ SV56 @ SY272 ) ) )
| ~ ! [SY274: $i,SY275: $i] :
( ( SY275
!= ( set_union2 @ SV56 @ SY274 ) )
| ~ ( ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SY275 )
| ( in @ SY276 @ SV56 )
| ( in @ SY276 @ SY274 ) )
| ~ ~ ( ~ ! [SY277: $i] :
( ~ ( in @ SY277 @ SV56 )
| ( in @ SY277 @ SY275 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY274 )
| ( in @ SX3 @ SY275 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(448,plain,
! [SV57: $i] :
( ( ~ ( ~ ! [SY279: $i,SY280: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY279 )
| ~ ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY280 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY280 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY279 )
| ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY280 ) ) ) )
| ( SY280
= ( set_difference @ SV57 @ SY279 ) ) )
| ~ ! [SY281: $i,SY282: $i] :
( ( SY282
!= ( set_difference @ SV57 @ SY281 ) )
| ~ ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SV57 )
| ( in @ SY283 @ SY281 )
| ( in @ SY283 @ SY282 ) )
| ~ ~ ( ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ SY282 )
| ( in @ SY284 @ SV57 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY282 )
| ~ ( in @ SX3 @ SY281 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(449,plain,
! [SV58: $i] :
( ( ! [SY286: $i] :
~ ( ~ ! [SY287: $i] :
( ! [SY288: $i] :
( ( ordered_pair @ SV58 @ SY286 )
!= ( ordered_pair @ SY287 @ SY288 ) )
| ( SV58 = SY287 ) )
| ~ ! [SY289: $i,SY290: $i] :
( ( ( ordered_pair @ SV58 @ SY286 )
!= ( ordered_pair @ SY289 @ SY290 ) )
| ( SY286 = SY290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(450,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)],[370]) ).
thf(451,plain,
! [SV59: $i] :
( ( ~ ( ~ ! [SY291: $i,SY292: $i] :
( ~ ( in @ SV59 @ SY292 )
| ~ ( in @ SY291 @ SY292 )
| ( subset @ ( unordered_pair @ SV59 @ SY291 ) @ SY292 ) )
| ~ ~ ( ~ ! [SY293: $i,SY294: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY293 ) @ SY294 )
| ( in @ SV59 @ SY294 ) )
| ~ ! [SY295: $i,SY296: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY295 ) @ SY296 )
| ( in @ SY295 @ SY296 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(452,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)],[372]) ).
thf(453,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK22_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)],[373]) ).
thf(454,plain,
! [SV60: $i] :
( ( ~ ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY297 )
| ~ ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY298 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY298 ) )
| ~ ( ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY297 )
| ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY298 ) ) ) )
| ( SY298
= ( set_intersection2 @ SV60 @ SY297 ) ) )
| ~ ! [SY299: $i,SY300: $i] :
( ( SY300
!= ( set_intersection2 @ SV60 @ SY299 ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV60 )
| ~ ( in @ SY301 @ SY299 )
| ( in @ SY301 @ SY300 ) )
| ~ ~ ( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SY300 )
| ( in @ SY302 @ SV60 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY300 )
| ( in @ SX3 @ SY299 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(455,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)],[375]) ).
thf(456,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)],[376]) ).
thf(457,plain,
! [SV1: $i] :
( ( ( singleton @ SV1 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(458,plain,
! [SV61: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV61 )
| ( ( set_union2 @ ( singleton @ SV2 ) @ SV61 )
= SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(459,plain,
! [SV62: $i,SV3: $i] :
( ( ~ ( disjoint @ ( singleton @ SV3 ) @ SV62 )
| ~ ( in @ SV3 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(460,plain,
! [SV63: $i,SV4: $i] :
( ( ( in @ SV4 @ SV63 )
| ( disjoint @ ( singleton @ SV4 ) @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(461,plain,
! [SV64: $i,SV5: $i] :
( ( ~ ( subset @ SV5 @ SV64 )
| ! [SY304: $i] :
( ( in @ SY304 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV64 @ ( singleton @ SY304 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(462,plain,
! [SV65: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV65 )
| ( subset @ SV6 @ ( union @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(463,plain,
! [SV66: $i,SV7: $i] :
( ( ! [SY305: $i,SY306: $i] :
( ( SV7 = SY306 )
| ( SV7 = SY305 )
| ( ( unordered_pair @ SV7 @ SV66 )
!= ( unordered_pair @ SY305 @ SY306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(464,plain,
! [SV67: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ SV67 )
| ( ( set_union2 @ SV8 @ SV67 )
= SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(465,plain,
! [SV68: $i,SV9: $i] :
( ( subset @ ( set_intersection2 @ SV9 @ SV68 ) @ SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(466,plain,
! [SV69: $i,SV10: $i] :
( ( ! [SY307: $i] :
( ~ ( subset @ SV10 @ SV69 )
| ~ ( subset @ SV10 @ SY307 )
| ( subset @ SV10 @ ( set_intersection2 @ SV69 @ SY307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(467,plain,
! [SV70: $i,SV11: $i] :
( ( ! [SY308: $i] :
( ~ ( subset @ SV11 @ SV70 )
| ~ ( subset @ SV70 @ SY308 )
| ( subset @ SV11 @ SY308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(468,plain,
! [SV71: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV71 )
| ! [SY309: $i] : ( subset @ ( set_intersection2 @ SV12 @ SY309 ) @ ( set_intersection2 @ SV71 @ SY309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(469,plain,
! [SV72: $i,SV13: $i] :
( ( ~ ( subset @ SV13 @ SV72 )
| ( ( set_intersection2 @ SV13 @ SV72 )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(470,plain,
! [SV73: $i,SV15: $i] :
( ( ~ ( subset @ SV15 @ SV73 )
| ! [SY310: $i] : ( subset @ ( set_difference @ SV15 @ SY310 ) @ ( set_difference @ SV73 @ SY310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(471,plain,
! [SV74: $i,SV16: $i] :
( ( subset @ ( set_difference @ SV16 @ SV74 ) @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(472,plain,
! [SV75: $i,SV17: $i] :
( ( ( set_union2 @ SV17 @ ( set_difference @ SV75 @ SV17 ) )
= ( set_union2 @ SV17 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(473,plain,
! [SV18: $i] :
( ( ( ~ ( subset @ SV18 @ empty_set ) )
= $true )
| ( ( SV18 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(474,plain,
! [SV76: $i,SV19: $i] :
( ( ( set_difference @ ( set_union2 @ SV19 @ SV76 ) @ SV76 )
= ( set_difference @ SV19 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(475,plain,
! [SV77: $i,SV20: $i] :
( ( ~ ( subset @ SV20 @ SV77 )
| ( SV77
= ( set_union2 @ SV20 @ ( set_difference @ SV77 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(476,plain,
! [SV78: $i,SV21: $i] :
( ( ~ ( in @ SV21 @ SV78 )
| ( ( set_union2 @ ( singleton @ SV21 ) @ SV78 )
= SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(477,plain,
! [SV79: $i,SV22: $i] :
( ( ( set_difference @ SV22 @ ( set_difference @ SV22 @ SV79 ) )
= ( set_intersection2 @ SV22 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(478,plain,
! [SV23: $i,SV80: $i] :
( ( ~ ( proper_subset @ SV80 @ SV23 )
| ~ ( subset @ SV23 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(479,plain,
! [SV24: $i,SV81: $i] :
( ( ! [SY311: $i] :
( ~ ( disjoint @ SV81 @ SY311 )
| ~ ( subset @ SV24 @ SV81 )
| ( disjoint @ SV24 @ SY311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(480,plain,
! [SV82: $i,SV26: $i] :
( ( ~ ( subset @ ( singleton @ SV26 ) @ ( singleton @ SV82 ) )
| ( SV26 = SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(481,plain,
! [SV83: $i,SV27: $i] :
( ( subset @ SV27 @ ( set_union2 @ SV27 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(482,plain,
! [SV84: $i,SV28: $i] :
( ( ! [SY312: $i] :
( ~ ( subset @ SV28 @ SV84 )
| ~ ( subset @ SY312 @ SV84 )
| ( subset @ ( set_union2 @ SV28 @ SY312 ) @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(483,plain,
! [SV85: $i,SV29: $i] :
( ( ! [SY313: $i] :
( ( singleton @ SV29 )
!= ( unordered_pair @ SV85 @ SY313 ) )
| ( SV29 = SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(484,plain,
! [SV86: $i,SV30: $i] :
( ( ! [SY314: $i] :
( ( ( singleton @ SV30 )
!= ( unordered_pair @ SV86 @ SY314 ) )
| ( SV86 = SY314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(485,plain,
! [SV87: $i,SV31: $i] :
( ( ~ ( in @ SV31 @ SV87 )
| ~ ( in @ SV87 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(486,plain,
! [SV88: $i,SV32: $i] :
( ( ~ ( proper_subset @ SV32 @ SV88 )
| ~ ( proper_subset @ SV88 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(487,plain,
! [SV89: $i,SV33: $i] :
( ( ( unordered_pair @ SV33 @ SV89 )
= ( unordered_pair @ SV89 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(488,plain,
! [SV90: $i,SV34: $i] :
( ( ( set_union2 @ SV34 @ SV90 )
= ( set_union2 @ SV90 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(489,plain,
! [SV91: $i,SV35: $i] :
( ( ( set_intersection2 @ SV35 @ SV91 )
= ( set_intersection2 @ SV91 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(490,plain,
! [SV92: $i,SV36: $i] :
( ( ( ordered_pair @ SV36 @ SV92 )
= ( unordered_pair @ ( unordered_pair @ SV36 @ SV92 ) @ ( singleton @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(491,plain,
! [SV93: $i,SV37: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV37 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(492,plain,
! [SV38: $i] :
( ( ( empty @ SV38 )
= $true )
| ( ( ! [SY242: $i] :
~ ( empty @ ( set_union2 @ SV38 @ SY242 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(493,plain,
! [SV39: $i] :
( ( ( empty @ SV39 )
= $true )
| ( ( ! [SY243: $i] :
~ ( empty @ ( set_union2 @ SY243 @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(494,plain,
! [SV42: $i] :
( ( proper_subset @ SV42 @ SV42 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(495,plain,
! [SV94: $i,SV44: $i] :
( ( ~ ( disjoint @ SV44 @ SV94 )
| ( disjoint @ SV94 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(496,plain,
! [SV49: $i] :
( ( ( ~ ( empty @ SV49 ) )
= $true )
| ( ( SV49 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(497,plain,
! [SV50: $i,SV95: $i] :
( ( ~ ( empty @ SV95 )
| ~ ( in @ SV50 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(498,plain,
! [SV96: $i,SV51: $i] :
( ( ( SV51 = SV96 )
| ~ ( empty @ SV51 )
| ~ ( empty @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(499,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(500,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)],[430]) ).
thf(501,plain,
! [SV97: $i,SV52: $i] :
( ( ~ ( ~ ! [SY315: $i,SY316: $i] :
( ~ ( in @ SV52 @ SY315 )
| ~ ( in @ SV97 @ SY316 )
| ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY315 @ SY316 ) ) )
| ~ ~ ( ~ ! [SY317: $i] :
( ! [SY318: $i] :
~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY317 @ SY318 ) )
| ( in @ SV52 @ SY317 ) )
| ~ ! [SY319: $i,SY320: $i] :
( ~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY319 @ SY320 ) )
| ( in @ SV97 @ SY320 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(502,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(503,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)],[432]) ).
thf(504,plain,
! [SV53: $i] :
( ( ~ ! [SY254: $i,SY255: $i] :
( ~ ( ~ ( ! [SY256: $i,SY257: $i] :
( ~ ( in @ SY256 @ SV53 )
| ~ ( in @ SY257 @ SY254 )
| ( ( sK14_D @ SY255 @ SY254 @ SV53 )
!= ( ordered_pair @ SY256 @ SY257 ) ) )
| ~ ( in @ ( sK14_D @ SY255 @ SY254 @ SV53 ) @ SY255 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SY255 @ SY254 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SY255 @ SY254 @ SV53 ) @ SY254 ) )
| ( ( sK14_D @ SY255 @ SY254 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SY255 @ SY254 @ SV53 ) @ ( sK16_SY197 @ SY255 @ SY254 @ SV53 ) ) ) )
| ( in @ ( sK14_D @ SY255 @ SY254 @ SV53 ) @ SY255 ) ) )
| ( SY255
= ( cartesian_product2 @ SV53 @ SY254 ) ) )
| ~ ! [SY258: $i,SY259: $i] :
( ( SY259
!= ( cartesian_product2 @ SV53 @ SY258 ) )
| ~ ( ~ ! [SY260: $i] :
( ! [SY261: $i,SY262: $i] :
( ~ ( in @ SY261 @ SV53 )
| ~ ( in @ SY262 @ SY258 )
| ( SY260
!= ( ordered_pair @ SY261 @ SY262 ) ) )
| ( in @ SY260 @ SY259 ) )
| ~ ! [SY263: $i] :
( ~ ( in @ SY263 @ SY259 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY263 @ SY259 @ SY258 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SY263 @ SY259 @ SY258 @ SV53 ) @ SY258 ) )
| ( SY263
!= ( ordered_pair @ ( sK12_E @ SY263 @ SY259 @ SY258 @ SV53 ) @ ( sK13_SY192 @ SY263 @ SY259 @ SY258 @ SV53 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(505,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(506,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(507,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(508,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(509,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(510,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(511,plain,
! [SV54: $i] :
( ( ~ ! [SY264: $i,SY265: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY265 @ SY264 @ SV54 ) @ SY265 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
!= SV54 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY265 @ SY264 @ SV54 ) @ SY265 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
!= SY264 ) ) )
| ~ ( ( in @ ( sK18_D @ SY265 @ SY264 @ SV54 ) @ SY265 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
= SV54 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
= SY264 ) ) )
| ( SY265
= ( unordered_pair @ SV54 @ SY264 ) ) )
| ~ ! [SY266: $i,SY267: $i] :
( ( SY267
!= ( unordered_pair @ SV54 @ SY266 ) )
| ~ ( ~ ! [SY268: $i] :
( ~ ( in @ SY268 @ SY267 )
| ( SY268 = SV54 )
| ( SY268 = SY266 ) )
| ~ ~ ( ~ ! [SY269: $i] :
( ( SY269 != SV54 )
| ( in @ SY269 @ SY267 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY266 )
| ( in @ SX3 @ SY267 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(512,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(513,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(514,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK20_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(515,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(516,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(517,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(518,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK21_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK21_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(519,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)],[441]) ).
thf(520,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(521,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)],[442]) ).
thf(522,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(523,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(524,plain,
! [SV55: $i,SV98: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
| ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 ) )
| ~ ( ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
| ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 ) ) )
| ( SV55 = SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(525,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK19_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK19_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(526,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)],[445]) ).
thf(527,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ ( sK9_SY191 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_SY191 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[446]) ).
thf(528,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 @ ( sK7_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[446]) ).
thf(529,plain,
! [SV56: $i] :
( ( ~ ! [SY272: $i,SY273: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY273 )
| ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY273 )
| ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY272 ) ) )
| ~ ( ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY273 )
| ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY272 ) ) )
| ( SY273
= ( set_union2 @ SV56 @ SY272 ) ) )
| ~ ! [SY274: $i,SY275: $i] :
( ( SY275
!= ( set_union2 @ SV56 @ SY274 ) )
| ~ ( ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SY275 )
| ( in @ SY276 @ SV56 )
| ( in @ SY276 @ SY274 ) )
| ~ ~ ( ~ ! [SY277: $i] :
( ~ ( in @ SY277 @ SV56 )
| ( in @ SY277 @ SY275 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY274 )
| ( in @ SX3 @ SY275 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(530,plain,
! [SV57: $i] :
( ( ~ ! [SY279: $i,SY280: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY279 )
| ~ ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY280 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY280 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY279 )
| ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY280 ) ) ) )
| ( SY280
= ( set_difference @ SV57 @ SY279 ) ) )
| ~ ! [SY281: $i,SY282: $i] :
( ( SY282
!= ( set_difference @ SV57 @ SY281 ) )
| ~ ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SV57 )
| ( in @ SY283 @ SY281 )
| ( in @ SY283 @ SY282 ) )
| ~ ~ ( ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ SY282 )
| ( in @ SY284 @ SV57 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY282 )
| ~ ( in @ SX3 @ SY281 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(531,plain,
! [SV99: $i,SV58: $i] :
( ( ~ ( ~ ! [SY321: $i] :
( ! [SY322: $i] :
( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SY321 @ SY322 ) )
| ( SV58 = SY321 ) )
| ~ ! [SY323: $i,SY324: $i] :
( ( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SY323 @ SY324 ) )
| ( SV99 = SY324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(532,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(533,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(534,plain,
! [SV59: $i] :
( ( ~ ! [SY291: $i,SY292: $i] :
( ~ ( in @ SV59 @ SY292 )
| ~ ( in @ SY291 @ SY292 )
| ( subset @ ( unordered_pair @ SV59 @ SY291 ) @ SY292 ) )
| ~ ~ ( ~ ! [SY293: $i,SY294: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY293 ) @ SY294 )
| ( in @ SV59 @ SY294 ) )
| ~ ! [SY295: $i,SY296: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY295 ) @ SY296 )
| ( in @ SY295 @ SY296 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(535,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(536,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(537,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK22_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(538,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(539,plain,
! [SV60: $i] :
( ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY297 )
| ~ ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY298 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY298 ) )
| ~ ( ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY297 )
| ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY298 ) ) ) )
| ( SY298
= ( set_intersection2 @ SV60 @ SY297 ) ) )
| ~ ! [SY299: $i,SY300: $i] :
( ( SY300
!= ( set_intersection2 @ SV60 @ SY299 ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV60 )
| ~ ( in @ SY301 @ SY299 )
| ( in @ SY301 @ SY300 ) )
| ~ ~ ( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SY300 )
| ( in @ SY302 @ SV60 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY300 )
| ( in @ SX3 @ SY299 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(540,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(541,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(542,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(543,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)],[456]) ).
thf(544,plain,
! [SV61: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV61 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV2 ) @ SV61 )
= SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(545,plain,
! [SV62: $i,SV3: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV3 ) @ SV62 ) )
= $true )
| ( ( ~ ( in @ SV3 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(546,plain,
! [SV63: $i,SV4: $i] :
( ( ( in @ SV4 @ SV63 )
= $true )
| ( ( disjoint @ ( singleton @ SV4 ) @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(547,plain,
! [SV64: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ SV64 ) )
= $true )
| ( ( ! [SY304: $i] :
( ( in @ SY304 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV64 @ ( singleton @ SY304 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(548,plain,
! [SV65: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV65 ) )
= $true )
| ( ( subset @ SV6 @ ( union @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(549,plain,
! [SV66: $i,SV100: $i,SV7: $i] :
( ( ! [SY325: $i] :
( ( SV7 = SY325 )
| ( SV7 = SV100 )
| ( ( unordered_pair @ SV7 @ SV66 )
!= ( unordered_pair @ SV100 @ SY325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(550,plain,
! [SV67: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV67 ) )
= $true )
| ( ( ( set_union2 @ SV8 @ SV67 )
= SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(551,plain,
! [SV101: $i,SV69: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV69 )
| ~ ( subset @ SV10 @ SV101 )
| ( subset @ SV10 @ ( set_intersection2 @ SV69 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(552,plain,
! [SV102: $i,SV70: $i,SV11: $i] :
( ( ~ ( subset @ SV11 @ SV70 )
| ~ ( subset @ SV70 @ SV102 )
| ( subset @ SV11 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(553,plain,
! [SV71: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV71 ) )
= $true )
| ( ( ! [SY309: $i] : ( subset @ ( set_intersection2 @ SV12 @ SY309 ) @ ( set_intersection2 @ SV71 @ SY309 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(554,plain,
! [SV72: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV72 ) )
= $true )
| ( ( ( set_intersection2 @ SV13 @ SV72 )
= SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(555,plain,
! [SV73: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV73 ) )
= $true )
| ( ( ! [SY310: $i] : ( subset @ ( set_difference @ SV15 @ SY310 ) @ ( set_difference @ SV73 @ SY310 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(556,plain,
! [SV18: $i] :
( ( ( subset @ SV18 @ empty_set )
= $false )
| ( ( SV18 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(557,plain,
! [SV77: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV77 ) )
= $true )
| ( ( SV77
= ( set_union2 @ SV20 @ ( set_difference @ SV77 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(558,plain,
! [SV78: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ SV78 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV21 ) @ SV78 )
= SV78 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(559,plain,
! [SV23: $i,SV80: $i] :
( ( ( ~ ( proper_subset @ SV80 @ SV23 ) )
= $true )
| ( ( ~ ( subset @ SV23 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(560,plain,
! [SV24: $i,SV103: $i,SV81: $i] :
( ( ~ ( disjoint @ SV81 @ SV103 )
| ~ ( subset @ SV24 @ SV81 )
| ( disjoint @ SV24 @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(561,plain,
! [SV82: $i,SV26: $i] :
( ( ( ~ ( subset @ ( singleton @ SV26 ) @ ( singleton @ SV82 ) ) )
= $true )
| ( ( SV26 = SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(562,plain,
! [SV104: $i,SV84: $i,SV28: $i] :
( ( ~ ( subset @ SV28 @ SV84 )
| ~ ( subset @ SV104 @ SV84 )
| ( subset @ ( set_union2 @ SV28 @ SV104 ) @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(563,plain,
! [SV85: $i,SV29: $i] :
( ( ( ! [SY313: $i] :
( ( singleton @ SV29 )
!= ( unordered_pair @ SV85 @ SY313 ) ) )
= $true )
| ( ( SV29 = SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(564,plain,
! [SV105: $i,SV86: $i,SV30: $i] :
( ( ( ( singleton @ SV30 )
!= ( unordered_pair @ SV86 @ SV105 ) )
| ( SV86 = SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(565,plain,
! [SV87: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ SV87 ) )
= $true )
| ( ( ~ ( in @ SV87 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(566,plain,
! [SV88: $i,SV32: $i] :
( ( ( ~ ( proper_subset @ SV32 @ SV88 ) )
= $true )
| ( ( ~ ( proper_subset @ SV88 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(567,plain,
! [SV93: $i,SV37: $i] :
( ( empty @ ( ordered_pair @ SV37 @ SV93 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(568,plain,
! [SV106: $i,SV38: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV38 @ SV106 ) ) )
= $true )
| ( ( empty @ SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(569,plain,
! [SV39: $i,SV107: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV107 @ SV39 ) ) )
= $true )
| ( ( empty @ SV39 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(570,plain,
! [SV94: $i,SV44: $i] :
( ( ( ~ ( disjoint @ SV44 @ SV94 ) )
= $true )
| ( ( disjoint @ SV94 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(571,plain,
! [SV49: $i] :
( ( ( empty @ SV49 )
= $false )
| ( ( SV49 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(572,plain,
! [SV50: $i,SV95: $i] :
( ( ( ~ ( empty @ SV95 ) )
= $true )
| ( ( ~ ( in @ SV50 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(573,plain,
! [SV96: $i,SV51: $i] :
( ( ( ( SV51 = SV96 )
| ~ ( empty @ SV51 ) )
= $true )
| ( ( ~ ( empty @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(574,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(575,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)],[500]) ).
thf(576,plain,
! [SV97: $i,SV52: $i] :
( ( ~ ! [SY315: $i,SY316: $i] :
( ~ ( in @ SV52 @ SY315 )
| ~ ( in @ SV97 @ SY316 )
| ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY315 @ SY316 ) ) )
| ~ ~ ( ~ ! [SY317: $i] :
( ! [SY318: $i] :
~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY317 @ SY318 ) )
| ( in @ SV52 @ SY317 ) )
| ~ ! [SY319: $i,SY320: $i] :
( ~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY319 @ SY320 ) )
| ( in @ SV97 @ SY320 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(577,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(578,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)],[503]) ).
thf(579,plain,
! [SV53: $i] :
( ( ~ ! [SY254: $i,SY255: $i] :
( ~ ( ~ ( ! [SY256: $i,SY257: $i] :
( ~ ( in @ SY256 @ SV53 )
| ~ ( in @ SY257 @ SY254 )
| ( ( sK14_D @ SY255 @ SY254 @ SV53 )
!= ( ordered_pair @ SY256 @ SY257 ) ) )
| ~ ( in @ ( sK14_D @ SY255 @ SY254 @ SV53 ) @ SY255 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SY255 @ SY254 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SY255 @ SY254 @ SV53 ) @ SY254 ) )
| ( ( sK14_D @ SY255 @ SY254 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SY255 @ SY254 @ SV53 ) @ ( sK16_SY197 @ SY255 @ SY254 @ SV53 ) ) ) )
| ( in @ ( sK14_D @ SY255 @ SY254 @ SV53 ) @ SY255 ) ) )
| ( SY255
= ( cartesian_product2 @ SV53 @ SY254 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(580,plain,
! [SV53: $i] :
( ( ~ ! [SY258: $i,SY259: $i] :
( ( SY259
!= ( cartesian_product2 @ SV53 @ SY258 ) )
| ~ ( ~ ! [SY260: $i] :
( ! [SY261: $i,SY262: $i] :
( ~ ( in @ SY261 @ SV53 )
| ~ ( in @ SY262 @ SY258 )
| ( SY260
!= ( ordered_pair @ SY261 @ SY262 ) ) )
| ( in @ SY260 @ SY259 ) )
| ~ ! [SY263: $i] :
( ~ ( in @ SY263 @ SY259 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY263 @ SY259 @ SY258 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SY263 @ SY259 @ SY258 @ SV53 ) @ SY258 ) )
| ( SY263
!= ( ordered_pair @ ( sK12_E @ SY263 @ SY259 @ SY258 @ SV53 ) @ ( sK13_SY192 @ SY263 @ SY259 @ SY258 @ SV53 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(581,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(582,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(583,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(584,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(585,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(586,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(587,plain,
! [SV54: $i] :
( ( ~ ! [SY264: $i,SY265: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY265 @ SY264 @ SV54 ) @ SY265 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
!= SV54 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY265 @ SY264 @ SV54 ) @ SY265 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
!= SY264 ) ) )
| ~ ( ( in @ ( sK18_D @ SY265 @ SY264 @ SV54 ) @ SY265 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
= SV54 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
= SY264 ) ) )
| ( SY265
= ( unordered_pair @ SV54 @ SY264 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(588,plain,
! [SV54: $i] :
( ( ~ ! [SY266: $i,SY267: $i] :
( ( SY267
!= ( unordered_pair @ SV54 @ SY266 ) )
| ~ ( ~ ! [SY268: $i] :
( ~ ( in @ SY268 @ SY267 )
| ( SY268 = SV54 )
| ( SY268 = SY266 ) )
| ~ ~ ( ~ ! [SY269: $i] :
( ( SY269 != SV54 )
| ( in @ SY269 @ SY267 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY266 )
| ( in @ SX3 @ SY267 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[511]) ).
thf(589,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(590,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(591,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK20_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(592,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(593,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(594,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(595,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK21_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK21_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK21_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(596,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)],[519]) ).
thf(597,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(598,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)],[521]) ).
thf(599,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK23_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(600,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(601,plain,
! [SV55: $i,SV98: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
| ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 ) )
| ~ ( ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
| ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 ) ) ) )
= $true )
| ( ( SV55 = SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(602,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK19_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK19_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK19_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(603,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)],[526]) ).
thf(604,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ ( sK9_SY191 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_SY191 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(605,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 @ ( sK7_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(606,plain,
! [SV56: $i] :
( ( ~ ! [SY272: $i,SY273: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY273 )
| ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY273 )
| ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY272 ) ) )
| ~ ( ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY273 )
| ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY272 ) ) )
| ( SY273
= ( set_union2 @ SV56 @ SY272 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(607,plain,
! [SV56: $i] :
( ( ~ ! [SY274: $i,SY275: $i] :
( ( SY275
!= ( set_union2 @ SV56 @ SY274 ) )
| ~ ( ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SY275 )
| ( in @ SY276 @ SV56 )
| ( in @ SY276 @ SY274 ) )
| ~ ~ ( ~ ! [SY277: $i] :
( ~ ( in @ SY277 @ SV56 )
| ( in @ SY277 @ SY275 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY274 )
| ( in @ SX3 @ SY275 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(608,plain,
! [SV57: $i] :
( ( ~ ! [SY279: $i,SY280: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY279 )
| ~ ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY280 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY280 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY279 )
| ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY280 ) ) ) )
| ( SY280
= ( set_difference @ SV57 @ SY279 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(609,plain,
! [SV57: $i] :
( ( ~ ! [SY281: $i,SY282: $i] :
( ( SY282
!= ( set_difference @ SV57 @ SY281 ) )
| ~ ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SV57 )
| ( in @ SY283 @ SY281 )
| ( in @ SY283 @ SY282 ) )
| ~ ~ ( ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ SY282 )
| ( in @ SY284 @ SV57 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY282 )
| ~ ( in @ SX3 @ SY281 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[530]) ).
thf(610,plain,
! [SV99: $i,SV58: $i] :
( ( ~ ! [SY321: $i] :
( ! [SY322: $i] :
( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SY321 @ SY322 ) )
| ( SV58 = SY321 ) )
| ~ ! [SY323: $i,SY324: $i] :
( ( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SY323 @ SY324 ) )
| ( SV99 = SY324 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(611,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(612,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(613,plain,
! [SV59: $i] :
( ( ~ ! [SY291: $i,SY292: $i] :
( ~ ( in @ SV59 @ SY292 )
| ~ ( in @ SY291 @ SY292 )
| ( subset @ ( unordered_pair @ SV59 @ SY291 ) @ SY292 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(614,plain,
! [SV59: $i] :
( ( ~ ~ ( ~ ! [SY293: $i,SY294: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY293 ) @ SY294 )
| ( in @ SV59 @ SY294 ) )
| ~ ! [SY295: $i,SY296: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY295 ) @ SY296 )
| ( in @ SY295 @ SY296 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(615,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(616,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(617,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK22_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(618,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(619,plain,
! [SV60: $i] :
( ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY297 )
| ~ ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY298 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY298 ) )
| ~ ( ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY297 )
| ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY298 ) ) ) )
| ( SY298
= ( set_intersection2 @ SV60 @ SY297 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(620,plain,
! [SV60: $i] :
( ( ~ ! [SY299: $i,SY300: $i] :
( ( SY300
!= ( set_intersection2 @ SV60 @ SY299 ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV60 )
| ~ ( in @ SY301 @ SY299 )
| ( in @ SY301 @ SY300 ) )
| ~ ~ ( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SY300 )
| ( in @ SY302 @ SV60 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY300 )
| ( in @ SX3 @ SY299 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[539]) ).
thf(621,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(622,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(623,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(624,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)],[543]) ).
thf(625,plain,
! [SV61: $i,SV2: $i] :
( ( ( in @ SV2 @ SV61 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV2 ) @ SV61 )
= SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(626,plain,
! [SV62: $i,SV3: $i] :
( ( ( disjoint @ ( singleton @ SV3 ) @ SV62 )
= $false )
| ( ( ~ ( in @ SV3 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(627,plain,
! [SV64: $i,SV5: $i] :
( ( ( subset @ SV5 @ SV64 )
= $false )
| ( ( ! [SY304: $i] :
( ( in @ SY304 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV64 @ ( singleton @ SY304 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(628,plain,
! [SV65: $i,SV6: $i] :
( ( ( in @ SV6 @ SV65 )
= $false )
| ( ( subset @ SV6 @ ( union @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(629,plain,
! [SV66: $i,SV100: $i,SV108: $i,SV7: $i] :
( ( ( SV7 = SV108 )
| ( SV7 = SV100 )
| ( ( unordered_pair @ SV7 @ SV66 )
!= ( unordered_pair @ SV100 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(630,plain,
! [SV67: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV67 )
= $false )
| ( ( ( set_union2 @ SV8 @ SV67 )
= SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(631,plain,
! [SV101: $i,SV69: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV69 )
| ~ ( subset @ SV10 @ SV101 ) )
= $true )
| ( ( subset @ SV10 @ ( set_intersection2 @ SV69 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(632,plain,
! [SV102: $i,SV70: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV70 )
| ~ ( subset @ SV70 @ SV102 ) )
= $true )
| ( ( subset @ SV11 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(633,plain,
! [SV71: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV71 )
= $false )
| ( ( ! [SY309: $i] : ( subset @ ( set_intersection2 @ SV12 @ SY309 ) @ ( set_intersection2 @ SV71 @ SY309 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(634,plain,
! [SV72: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV72 )
= $false )
| ( ( ( set_intersection2 @ SV13 @ SV72 )
= SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(635,plain,
! [SV73: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV73 )
= $false )
| ( ( ! [SY310: $i] : ( subset @ ( set_difference @ SV15 @ SY310 ) @ ( set_difference @ SV73 @ SY310 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(636,plain,
! [SV77: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV77 )
= $false )
| ( ( SV77
= ( set_union2 @ SV20 @ ( set_difference @ SV77 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(637,plain,
! [SV78: $i,SV21: $i] :
( ( ( in @ SV21 @ SV78 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV21 ) @ SV78 )
= SV78 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(638,plain,
! [SV23: $i,SV80: $i] :
( ( ( proper_subset @ SV80 @ SV23 )
= $false )
| ( ( ~ ( subset @ SV23 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(639,plain,
! [SV24: $i,SV103: $i,SV81: $i] :
( ( ( ~ ( disjoint @ SV81 @ SV103 )
| ~ ( subset @ SV24 @ SV81 ) )
= $true )
| ( ( disjoint @ SV24 @ SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(640,plain,
! [SV82: $i,SV26: $i] :
( ( ( subset @ ( singleton @ SV26 ) @ ( singleton @ SV82 ) )
= $false )
| ( ( SV26 = SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(641,plain,
! [SV104: $i,SV84: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV84 )
| ~ ( subset @ SV104 @ SV84 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV28 @ SV104 ) @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(642,plain,
! [SV109: $i,SV85: $i,SV29: $i] :
( ( ( ( ( singleton @ SV29 )
!= ( unordered_pair @ SV85 @ SV109 ) ) )
= $true )
| ( ( SV29 = SV85 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(643,plain,
! [SV105: $i,SV86: $i,SV30: $i] :
( ( ( ( ( singleton @ SV30 )
!= ( unordered_pair @ SV86 @ SV105 ) ) )
= $true )
| ( ( SV86 = SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(644,plain,
! [SV87: $i,SV31: $i] :
( ( ( in @ SV31 @ SV87 )
= $false )
| ( ( ~ ( in @ SV87 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(645,plain,
! [SV88: $i,SV32: $i] :
( ( ( proper_subset @ SV32 @ SV88 )
= $false )
| ( ( ~ ( proper_subset @ SV88 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(646,plain,
! [SV106: $i,SV38: $i] :
( ( ( empty @ ( set_union2 @ SV38 @ SV106 ) )
= $false )
| ( ( empty @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(647,plain,
! [SV39: $i,SV107: $i] :
( ( ( empty @ ( set_union2 @ SV107 @ SV39 ) )
= $false )
| ( ( empty @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(648,plain,
! [SV94: $i,SV44: $i] :
( ( ( disjoint @ SV44 @ SV94 )
= $false )
| ( ( disjoint @ SV94 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(649,plain,
! [SV50: $i,SV95: $i] :
( ( ( empty @ SV95 )
= $false )
| ( ( ~ ( in @ SV50 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(650,plain,
! [SV96: $i,SV51: $i] :
( ( ( SV51 = SV96 )
= $true )
| ( ( ~ ( empty @ SV51 ) )
= $true )
| ( ( ~ ( empty @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(651,plain,
! [SV110: $i] :
( ( ! [SY326: $i] :
( ~ ( subset @ SV110 @ ( singleton @ SY326 ) )
| ( SV110 = empty_set )
| ( SV110
= ( singleton @ SY326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(652,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)],[575]) ).
thf(653,plain,
! [SV97: $i,SV52: $i] :
( ( ~ ! [SY315: $i,SY316: $i] :
( ~ ( in @ SV52 @ SY315 )
| ~ ( in @ SV97 @ SY316 )
| ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY315 @ SY316 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[576]) ).
thf(654,plain,
! [SV97: $i,SV52: $i] :
( ( ~ ~ ( ~ ! [SY317: $i] :
( ! [SY318: $i] :
~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY317 @ SY318 ) )
| ( in @ SV52 @ SY317 ) )
| ~ ! [SY319: $i,SY320: $i] :
( ~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY319 @ SY320 ) )
| ( in @ SV97 @ SY320 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[576]) ).
thf(655,plain,
! [SV111: $i] :
( ( ! [SY327: $i] :
( ~ ( subset @ SV111 @ ( singleton @ SY327 ) )
| ( SV111 = empty_set )
| ( SV111
= ( singleton @ SY327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(656,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)],[578]) ).
thf(657,plain,
! [SV53: $i] :
( ( ! [SY254: $i,SY255: $i] :
( ~ ( ~ ( ! [SY256: $i,SY257: $i] :
( ~ ( in @ SY256 @ SV53 )
| ~ ( in @ SY257 @ SY254 )
| ( ( sK14_D @ SY255 @ SY254 @ SV53 )
!= ( ordered_pair @ SY256 @ SY257 ) ) )
| ~ ( in @ ( sK14_D @ SY255 @ SY254 @ SV53 ) @ SY255 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SY255 @ SY254 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SY255 @ SY254 @ SV53 ) @ SY254 ) )
| ( ( sK14_D @ SY255 @ SY254 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SY255 @ SY254 @ SV53 ) @ ( sK16_SY197 @ SY255 @ SY254 @ SV53 ) ) ) )
| ( in @ ( sK14_D @ SY255 @ SY254 @ SV53 ) @ SY255 ) ) )
| ( SY255
= ( cartesian_product2 @ SV53 @ SY254 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(658,plain,
! [SV53: $i] :
( ( ! [SY258: $i,SY259: $i] :
( ( SY259
!= ( cartesian_product2 @ SV53 @ SY258 ) )
| ~ ( ~ ! [SY260: $i] :
( ! [SY261: $i,SY262: $i] :
( ~ ( in @ SY261 @ SV53 )
| ~ ( in @ SY262 @ SY258 )
| ( SY260
!= ( ordered_pair @ SY261 @ SY262 ) ) )
| ( in @ SY260 @ SY259 ) )
| ~ ! [SY263: $i] :
( ~ ( in @ SY263 @ SY259 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY263 @ SY259 @ SY258 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SY263 @ SY259 @ SY258 @ SV53 ) @ SY258 ) )
| ( SY263
!= ( ordered_pair @ ( sK12_E @ SY263 @ SY259 @ SY258 @ SV53 ) @ ( sK13_SY192 @ SY263 @ SY259 @ SY258 @ SV53 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(659,plain,
! [SV112: $i] :
( ( ! [SY328: $i] :
( ~ ( in @ SV112 @ SY328 )
| ( subset @ ( singleton @ SV112 ) @ SY328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(660,plain,
! [SV113: $i] :
( ( ! [SY329: $i] :
( ~ ( subset @ ( singleton @ SV113 ) @ SY329 )
| ( in @ SV113 @ SY329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(661,plain,
! [SV114: $i] :
( ( ! [SY330: $i] :
( ( ( set_difference @ SV114 @ SY330 )
!= empty_set )
| ( subset @ SV114 @ SY330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(662,plain,
! [SV115: $i] :
( ( ! [SY331: $i] :
( ~ ( subset @ SV115 @ SY331 )
| ( ( set_difference @ SV115 @ SY331 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(663,plain,
! [SV116: $i] :
( ( ! [SY332: $i] :
( ~ ( ~ ( in @ ( sK11_C @ SY332 @ SV116 ) @ SV116 )
| ~ ~ ( in @ ( sK11_C @ SY332 @ SV116 ) @ SY332 ) )
| ( subset @ SV116 @ SY332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(664,plain,
! [SV117: $i] :
( ( ! [SY333: $i] :
( ~ ( subset @ SV117 @ SY333 )
| ! [SY334: $i] :
( ~ ( in @ SY334 @ SV117 )
| ( in @ SY334 @ SY333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(665,plain,
! [SV54: $i] :
( ( ! [SY264: $i,SY265: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY265 @ SY264 @ SV54 ) @ SY265 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
!= SV54 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY265 @ SY264 @ SV54 ) @ SY265 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
!= SY264 ) ) )
| ~ ( ( in @ ( sK18_D @ SY265 @ SY264 @ SV54 ) @ SY265 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
= SV54 )
| ( ( sK18_D @ SY265 @ SY264 @ SV54 )
= SY264 ) ) )
| ( SY265
= ( unordered_pair @ SV54 @ SY264 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(666,plain,
! [SV54: $i] :
( ( ! [SY266: $i,SY267: $i] :
( ( SY267
!= ( unordered_pair @ SV54 @ SY266 ) )
| ~ ( ~ ! [SY268: $i] :
( ~ ( in @ SY268 @ SY267 )
| ( SY268 = SV54 )
| ( SY268 = SY266 ) )
| ~ ~ ( ~ ! [SY269: $i] :
( ( SY269 != SV54 )
| ( in @ SY269 @ SY267 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY266 )
| ( in @ SX3 @ SY267 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(667,plain,
! [SV118: $i] :
( ( ! [SY335: $i] :
( ( ( set_difference @ SV118 @ SY335 )
!= empty_set )
| ( subset @ SV118 @ SY335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(668,plain,
! [SV119: $i] :
( ( ! [SY336: $i] :
( ~ ( subset @ SV119 @ SY336 )
| ( ( set_difference @ SV119 @ SY336 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(669,plain,
! [SV120: $i] :
( ( ( in @ ( sK20_B @ SV120 ) @ SV120 )
| ( SV120 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(670,plain,
! [SV121: $i] :
( ( ( SV121 != empty_set )
| ! [SY337: $i] :
~ ( in @ SY337 @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(671,plain,
! [SV122: $i] :
( ( ! [SY338: $i] :
( ( ( set_difference @ SV122 @ SY338 )
!= SV122 )
| ( disjoint @ SV122 @ SY338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(672,plain,
! [SV123: $i] :
( ( ! [SY339: $i] :
( ~ ( disjoint @ SV123 @ SY339 )
| ( ( set_difference @ SV123 @ SY339 )
= SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(673,plain,
! [SV124: $i] :
( ( ! [SY340: $i] :
( ~ ( ~ ( ( ( sK21_C @ SY340 @ SV124 )
!= SV124 )
| ~ ( in @ ( sK21_C @ SY340 @ SV124 ) @ SY340 ) )
| ~ ( ( ( sK21_C @ SY340 @ SV124 )
= SV124 )
| ( in @ ( sK21_C @ SY340 @ SV124 ) @ SY340 ) ) )
| ( SY340
= ( singleton @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(674,plain,
! [SV125: $i] :
( ( ! [SY341: $i] :
( ( SY341
!= ( singleton @ SV125 ) )
| ~ ( ~ ! [SY342: $i] :
( ( SY342 != SV125 )
| ( in @ SY342 @ SY341 ) )
| ~ ! [SY343: $i] :
( ~ ( in @ SY343 @ SY341 )
| ( SY343 = SV125 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(675,plain,
! [SV126: $i] :
( ( ! [SY344: $i] :
( ( SV126 = SY344 )
| ~ ( subset @ SV126 @ SY344 )
| ( proper_subset @ SV126 @ SY344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(676,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)],[598]) ).
thf(677,plain,
! [SV127: $i] :
( ( ! [SY345: $i] :
( ( disjoint @ SV127 @ SY345 )
| ~ ( ~ ( in @ ( sK23_C @ SY345 @ SV127 ) @ SV127 )
| ~ ( in @ ( sK23_C @ SY345 @ SV127 ) @ SY345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(678,plain,
! [SV128: $i] :
( ( ! [SY346: $i] :
( ! [SY347: $i] :
( ~ ( in @ SY347 @ SV128 )
| ~ ( in @ SY347 @ SY346 ) )
| ~ ( disjoint @ SV128 @ SY346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(679,plain,
! [SV55: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
| ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 ) )
| ~ ( ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
| ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 ) ) )
= $false )
| ( ( SV55 = SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(680,plain,
! [SV129: $i] :
( ( ! [SY348: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_C @ SY348 @ SV129 ) @ SY348 )
| ~ ( subset @ ( sK19_C @ SY348 @ SV129 ) @ SV129 ) )
| ~ ( ( in @ ( sK19_C @ SY348 @ SV129 ) @ SY348 )
| ( subset @ ( sK19_C @ SY348 @ SV129 ) @ SV129 ) ) )
| ( SY348
= ( powerset @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(681,plain,
! [SV130: $i] :
( ( ! [SY349: $i] :
( ( SY349
!= ( powerset @ SV130 ) )
| ~ ( ~ ! [SY350: $i] :
( ~ ( in @ SY350 @ SY349 )
| ( subset @ SY350 @ SV130 ) )
| ~ ! [SY351: $i] :
( ~ ( subset @ SY351 @ SV130 )
| ( in @ SY351 @ SY349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(682,plain,
! [SV131: $i] :
( ( ! [SY352: $i] :
( ~ ( ~ ( ! [SY353: $i] :
( ~ ( in @ ( sK8_C @ SY352 @ SV131 ) @ SY353 )
| ~ ( in @ SY353 @ SV131 ) )
| ~ ( in @ ( sK8_C @ SY352 @ SV131 ) @ SY352 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SY352 @ SV131 ) @ ( sK9_SY191 @ SY352 @ SV131 ) )
| ~ ( in @ ( sK9_SY191 @ SY352 @ SV131 ) @ SV131 ) )
| ( in @ ( sK8_C @ SY352 @ SV131 ) @ SY352 ) ) )
| ( SY352
= ( union @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(683,plain,
! [SV132: $i] :
( ( ! [SY354: $i] :
( ( SY354
!= ( union @ SV132 ) )
| ~ ( ~ ! [SY355: $i] :
( ! [SY356: $i] :
( ~ ( in @ SY355 @ SY356 )
| ~ ( in @ SY356 @ SV132 ) )
| ( in @ SY355 @ SY354 ) )
| ~ ! [SY357: $i] :
( ~ ( in @ SY357 @ SY354 )
| ~ ( ~ ( in @ SY357 @ ( sK7_D @ SY357 @ SY354 @ SV132 ) )
| ~ ( in @ ( sK7_D @ SY357 @ SY354 @ SV132 ) @ SV132 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(684,plain,
! [SV56: $i] :
( ( ! [SY272: $i,SY273: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY273 )
| ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY273 )
| ~ ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY272 ) ) )
| ~ ( ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY273 )
| ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SY273 @ SY272 @ SV56 ) @ SY272 ) ) )
| ( SY273
= ( set_union2 @ SV56 @ SY272 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(685,plain,
! [SV56: $i] :
( ( ! [SY274: $i,SY275: $i] :
( ( SY275
!= ( set_union2 @ SV56 @ SY274 ) )
| ~ ( ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SY275 )
| ( in @ SY276 @ SV56 )
| ( in @ SY276 @ SY274 ) )
| ~ ~ ( ~ ! [SY277: $i] :
( ~ ( in @ SY277 @ SV56 )
| ( in @ SY277 @ SY275 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY274 )
| ( in @ SX3 @ SY275 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(686,plain,
! [SV57: $i] :
( ( ! [SY279: $i,SY280: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY279 )
| ~ ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY280 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY280 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY279 )
| ( in @ ( sK6_D @ SY280 @ SY279 @ SV57 ) @ SY280 ) ) ) )
| ( SY280
= ( set_difference @ SV57 @ SY279 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(687,plain,
! [SV57: $i] :
( ( ! [SY281: $i,SY282: $i] :
( ( SY282
!= ( set_difference @ SV57 @ SY281 ) )
| ~ ( ~ ! [SY283: $i] :
( ~ ( in @ SY283 @ SV57 )
| ( in @ SY283 @ SY281 )
| ( in @ SY283 @ SY282 ) )
| ~ ~ ( ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ SY282 )
| ( in @ SY284 @ SV57 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY282 )
| ~ ( in @ SX3 @ SY281 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(688,plain,
! [SV99: $i,SV58: $i] :
( ( ~ ! [SY321: $i] :
( ! [SY322: $i] :
( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SY321 @ SY322 ) )
| ( SV58 = SY321 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(689,plain,
! [SV99: $i,SV58: $i] :
( ( ~ ! [SY323: $i,SY324: $i] :
( ( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SY323 @ SY324 ) )
| ( SV99 = SY324 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[610]) ).
thf(690,plain,
! [SV133: $i] :
( ( ! [SY358: $i] :
( ( ( set_difference @ SV133 @ ( singleton @ SY358 ) )
!= SV133 )
| ~ ( in @ SY358 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(691,plain,
! [SV134: $i] :
( ( ! [SY359: $i] :
( ( in @ SY359 @ SV134 )
| ( ( set_difference @ SV134 @ ( singleton @ SY359 ) )
= SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(692,plain,
! [SV59: $i] :
( ( ! [SY291: $i,SY292: $i] :
( ~ ( in @ SV59 @ SY292 )
| ~ ( in @ SY291 @ SY292 )
| ( subset @ ( unordered_pair @ SV59 @ SY291 ) @ SY292 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[613]) ).
thf(693,plain,
! [SV59: $i] :
( ( ~ ( ~ ! [SY293: $i,SY294: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY293 ) @ SY294 )
| ( in @ SV59 @ SY294 ) )
| ~ ! [SY295: $i,SY296: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY295 ) @ SY296 )
| ( in @ SY295 @ SY296 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(694,plain,
! [SV135: $i] :
( ( ! [SY360: $i] :
( ( ( set_intersection2 @ SV135 @ SY360 )
!= empty_set )
| ( disjoint @ SV135 @ SY360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(695,plain,
! [SV136: $i] :
( ( ! [SY361: $i] :
( ~ ( disjoint @ SV136 @ SY361 )
| ( ( set_intersection2 @ SV136 @ SY361 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(696,plain,
! [SV137: $i] :
( ( ! [SY362: $i] :
( ( disjoint @ SV137 @ SY362 )
| ( in @ ( sK22_C @ SY362 @ SV137 ) @ ( set_intersection2 @ SV137 @ SY362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(697,plain,
! [SV138: $i] :
( ( ! [SY363: $i] :
( ! [SY364: $i] :
~ ( in @ SY364 @ ( set_intersection2 @ SV138 @ SY363 ) )
| ~ ( disjoint @ SV138 @ SY363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(698,plain,
! [SV60: $i] :
( ( ! [SY297: $i,SY298: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY297 )
| ~ ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY298 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY298 ) )
| ~ ( ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY297 )
| ( in @ ( sK10_D @ SY298 @ SY297 @ SV60 ) @ SY298 ) ) ) )
| ( SY298
= ( set_intersection2 @ SV60 @ SY297 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[619]) ).
thf(699,plain,
! [SV60: $i] :
( ( ! [SY299: $i,SY300: $i] :
( ( SY300
!= ( set_intersection2 @ SV60 @ SY299 ) )
| ~ ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV60 )
| ~ ( in @ SY301 @ SY299 )
| ( in @ SY301 @ SY300 ) )
| ~ ~ ( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SY300 )
| ( in @ SY302 @ SV60 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY300 )
| ( in @ SX3 @ SY299 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[620]) ).
thf(700,plain,
! [SV139: $i] :
( ( ! [SY365: $i] :
( ~ ( in @ SV139 @ SY365 )
| ( subset @ ( singleton @ SV139 ) @ SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(701,plain,
! [SV140: $i] :
( ( ! [SY366: $i] :
( ~ ( subset @ ( singleton @ SV140 ) @ SY366 )
| ( in @ SV140 @ SY366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(702,plain,
! [SV141: $i] :
( ( ! [SY367: $i] :
( ~ ( subset @ SV141 @ SY367 )
| ~ ( subset @ SY367 @ SV141 )
| ( SV141 = SY367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(703,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)],[624]) ).
thf(704,plain,
! [SV62: $i,SV3: $i] :
( ( ( in @ SV3 @ SV62 )
= $false )
| ( ( disjoint @ ( singleton @ SV3 ) @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(705,plain,
! [SV64: $i,SV5: $i,SV142: $i] :
( ( ( ( in @ SV142 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV64 @ ( singleton @ SV142 ) ) ) )
= $true )
| ( ( subset @ SV5 @ SV64 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(706,plain,
! [SV66: $i,SV100: $i,SV108: $i,SV7: $i] :
( ( ( SV7 = SV108 )
= $true )
| ( ( ( SV7 = SV100 )
| ( ( unordered_pair @ SV7 @ SV66 )
!= ( unordered_pair @ SV100 @ SV108 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(707,plain,
! [SV101: $i,SV69: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV69 ) )
= $true )
| ( ( ~ ( subset @ SV10 @ SV101 ) )
= $true )
| ( ( subset @ SV10 @ ( set_intersection2 @ SV69 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(708,plain,
! [SV102: $i,SV70: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV70 ) )
= $true )
| ( ( ~ ( subset @ SV70 @ SV102 ) )
= $true )
| ( ( subset @ SV11 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(709,plain,
! [SV71: $i,SV143: $i,SV12: $i] :
( ( ( subset @ ( set_intersection2 @ SV12 @ SV143 ) @ ( set_intersection2 @ SV71 @ SV143 ) )
= $true )
| ( ( subset @ SV12 @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(710,plain,
! [SV73: $i,SV144: $i,SV15: $i] :
( ( ( subset @ ( set_difference @ SV15 @ SV144 ) @ ( set_difference @ SV73 @ SV144 ) )
= $true )
| ( ( subset @ SV15 @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(711,plain,
! [SV80: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV80 )
= $false )
| ( ( proper_subset @ SV80 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(712,plain,
! [SV24: $i,SV103: $i,SV81: $i] :
( ( ( ~ ( disjoint @ SV81 @ SV103 ) )
= $true )
| ( ( ~ ( subset @ SV24 @ SV81 ) )
= $true )
| ( ( disjoint @ SV24 @ SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(713,plain,
! [SV104: $i,SV84: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV84 ) )
= $true )
| ( ( ~ ( subset @ SV104 @ SV84 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV28 @ SV104 ) @ SV84 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(714,plain,
! [SV109: $i,SV85: $i,SV29: $i] :
( ( ( ( singleton @ SV29 )
= ( unordered_pair @ SV85 @ SV109 ) )
= $false )
| ( ( SV29 = SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(715,plain,
! [SV105: $i,SV86: $i,SV30: $i] :
( ( ( ( singleton @ SV30 )
= ( unordered_pair @ SV86 @ SV105 ) )
= $false )
| ( ( SV86 = SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(716,plain,
! [SV31: $i,SV87: $i] :
( ( ( in @ SV87 @ SV31 )
= $false )
| ( ( in @ SV31 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(717,plain,
! [SV32: $i,SV88: $i] :
( ( ( proper_subset @ SV88 @ SV32 )
= $false )
| ( ( proper_subset @ SV32 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(718,plain,
! [SV95: $i,SV50: $i] :
( ( ( in @ SV50 @ SV95 )
= $false )
| ( ( empty @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(719,plain,
! [SV96: $i,SV51: $i] :
( ( ( empty @ SV51 )
= $false )
| ( ( SV51 = SV96 )
= $true )
| ( ( ~ ( empty @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(720,plain,
! [SV145: $i,SV110: $i] :
( ( ~ ( subset @ SV110 @ ( singleton @ SV145 ) )
| ( SV110 = empty_set )
| ( SV110
= ( singleton @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(721,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(722,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(723,plain,
! [SV97: $i,SV52: $i] :
( ( ! [SY315: $i,SY316: $i] :
( ~ ( in @ SV52 @ SY315 )
| ~ ( in @ SV97 @ SY316 )
| ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY315 @ SY316 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[653]) ).
thf(724,plain,
! [SV97: $i,SV52: $i] :
( ( ~ ( ~ ! [SY317: $i] :
( ! [SY318: $i] :
~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY317 @ SY318 ) )
| ( in @ SV52 @ SY317 ) )
| ~ ! [SY319: $i,SY320: $i] :
( ~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY319 @ SY320 ) )
| ( in @ SV97 @ SY320 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(725,plain,
! [SV146: $i,SV111: $i] :
( ( ~ ( subset @ SV111 @ ( singleton @ SV146 ) )
| ( SV111 = empty_set )
| ( SV111
= ( singleton @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(726,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(727,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[656]) ).
thf(728,plain,
! [SV147: $i,SV53: $i] :
( ( ! [SY368: $i] :
( ~ ( ~ ( ! [SY369: $i,SY370: $i] :
( ~ ( in @ SY369 @ SV53 )
| ~ ( in @ SY370 @ SV147 )
| ( ( sK14_D @ SY368 @ SV147 @ SV53 )
!= ( ordered_pair @ SY369 @ SY370 ) ) )
| ~ ( in @ ( sK14_D @ SY368 @ SV147 @ SV53 ) @ SY368 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SY368 @ SV147 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SY368 @ SV147 @ SV53 ) @ SV147 ) )
| ( ( sK14_D @ SY368 @ SV147 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SY368 @ SV147 @ SV53 ) @ ( sK16_SY197 @ SY368 @ SV147 @ SV53 ) ) ) )
| ( in @ ( sK14_D @ SY368 @ SV147 @ SV53 ) @ SY368 ) ) )
| ( SY368
= ( cartesian_product2 @ SV53 @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(729,plain,
! [SV148: $i,SV53: $i] :
( ( ! [SY371: $i] :
( ( SY371
!= ( cartesian_product2 @ SV53 @ SV148 ) )
| ~ ( ~ ! [SY372: $i] :
( ! [SY373: $i,SY374: $i] :
( ~ ( in @ SY373 @ SV53 )
| ~ ( in @ SY374 @ SV148 )
| ( SY372
!= ( ordered_pair @ SY373 @ SY374 ) ) )
| ( in @ SY372 @ SY371 ) )
| ~ ! [SY375: $i] :
( ~ ( in @ SY375 @ SY371 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY375 @ SY371 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SY375 @ SY371 @ SV148 @ SV53 ) @ SV148 ) )
| ( SY375
!= ( ordered_pair @ ( sK12_E @ SY375 @ SY371 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SY375 @ SY371 @ SV148 @ SV53 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(730,plain,
! [SV149: $i,SV112: $i] :
( ( ~ ( in @ SV112 @ SV149 )
| ( subset @ ( singleton @ SV112 ) @ SV149 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(731,plain,
! [SV150: $i,SV113: $i] :
( ( ~ ( subset @ ( singleton @ SV113 ) @ SV150 )
| ( in @ SV113 @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(732,plain,
! [SV151: $i,SV114: $i] :
( ( ( ( set_difference @ SV114 @ SV151 )
!= empty_set )
| ( subset @ SV114 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(733,plain,
! [SV152: $i,SV115: $i] :
( ( ~ ( subset @ SV115 @ SV152 )
| ( ( set_difference @ SV115 @ SV152 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(734,plain,
! [SV116: $i,SV153: $i] :
( ( ~ ( ~ ( in @ ( sK11_C @ SV153 @ SV116 ) @ SV116 )
| ~ ~ ( in @ ( sK11_C @ SV153 @ SV116 ) @ SV153 ) )
| ( subset @ SV116 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(735,plain,
! [SV154: $i,SV117: $i] :
( ( ~ ( subset @ SV117 @ SV154 )
| ! [SY376: $i] :
( ~ ( in @ SY376 @ SV117 )
| ( in @ SY376 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(736,plain,
! [SV54: $i,SV155: $i] :
( ( ! [SY377: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY377 @ SV155 @ SV54 ) @ SY377 )
| ( ( sK18_D @ SY377 @ SV155 @ SV54 )
!= SV54 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY377 @ SV155 @ SV54 ) @ SY377 )
| ( ( sK18_D @ SY377 @ SV155 @ SV54 )
!= SV155 ) ) )
| ~ ( ( in @ ( sK18_D @ SY377 @ SV155 @ SV54 ) @ SY377 )
| ( ( sK18_D @ SY377 @ SV155 @ SV54 )
= SV54 )
| ( ( sK18_D @ SY377 @ SV155 @ SV54 )
= SV155 ) ) )
| ( SY377
= ( unordered_pair @ SV54 @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(737,plain,
! [SV156: $i,SV54: $i] :
( ( ! [SY378: $i] :
( ( SY378
!= ( unordered_pair @ SV54 @ SV156 ) )
| ~ ( ~ ! [SY379: $i] :
( ~ ( in @ SY379 @ SY378 )
| ( SY379 = SV54 )
| ( SY379 = SV156 ) )
| ~ ~ ( ~ ! [SY269: $i] :
( ( SY269 != SV54 )
| ( in @ SY269 @ SY378 ) )
| ~ ! [SY381: $i] :
( ( SY381 != SV156 )
| ( in @ SY381 @ SY378 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(738,plain,
! [SV157: $i,SV118: $i] :
( ( ( ( set_difference @ SV118 @ SV157 )
!= empty_set )
| ( subset @ SV118 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(739,plain,
! [SV158: $i,SV119: $i] :
( ( ~ ( subset @ SV119 @ SV158 )
| ( ( set_difference @ SV119 @ SV158 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(740,plain,
! [SV120: $i] :
( ( ( in @ ( sK20_B @ SV120 ) @ SV120 )
= $true )
| ( ( SV120 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(741,plain,
! [SV121: $i] :
( ( ( ( SV121 != empty_set ) )
= $true )
| ( ( ! [SY337: $i] :
~ ( in @ SY337 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(742,plain,
! [SV159: $i,SV122: $i] :
( ( ( ( set_difference @ SV122 @ SV159 )
!= SV122 )
| ( disjoint @ SV122 @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(743,plain,
! [SV160: $i,SV123: $i] :
( ( ~ ( disjoint @ SV123 @ SV160 )
| ( ( set_difference @ SV123 @ SV160 )
= SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(744,plain,
! [SV124: $i,SV161: $i] :
( ( ~ ( ~ ( ( ( sK21_C @ SV161 @ SV124 )
!= SV124 )
| ~ ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 ) )
| ~ ( ( ( sK21_C @ SV161 @ SV124 )
= SV124 )
| ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 ) ) )
| ( SV161
= ( singleton @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(745,plain,
! [SV125: $i,SV162: $i] :
( ( ( SV162
!= ( singleton @ SV125 ) )
| ~ ( ~ ! [SY382: $i] :
( ( SY382 != SV125 )
| ( in @ SY382 @ SV162 ) )
| ~ ! [SY383: $i] :
( ~ ( in @ SY383 @ SV162 )
| ( SY383 = SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(746,plain,
! [SV163: $i,SV126: $i] :
( ( ( SV126 = SV163 )
| ~ ( subset @ SV126 @ SV163 )
| ( proper_subset @ SV126 @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(747,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(748,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(749,plain,
! [SV164: $i,SV127: $i] :
( ( ( disjoint @ SV127 @ SV164 )
| ~ ( ~ ( in @ ( sK23_C @ SV164 @ SV127 ) @ SV127 )
| ~ ( in @ ( sK23_C @ SV164 @ SV127 ) @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(750,plain,
! [SV165: $i,SV128: $i] :
( ( ! [SY384: $i] :
( ~ ( in @ SY384 @ SV128 )
| ~ ( in @ SY384 @ SV165 ) )
| ~ ( disjoint @ SV128 @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(751,plain,
! [SV55: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
| ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 ) ) )
= $false )
| ( ( SV55 = SV98 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(752,plain,
! [SV55: $i,SV98: $i] :
( ( ( ~ ( ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
| ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 ) ) )
= $false )
| ( ( SV55 = SV98 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[679]) ).
thf(753,plain,
! [SV129: $i,SV166: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
| ~ ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 ) )
| ~ ( ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
| ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 ) ) )
| ( SV166
= ( powerset @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(754,plain,
! [SV130: $i,SV167: $i] :
( ( ( SV167
!= ( powerset @ SV130 ) )
| ~ ( ~ ! [SY385: $i] :
( ~ ( in @ SY385 @ SV167 )
| ( subset @ SY385 @ SV130 ) )
| ~ ! [SY386: $i] :
( ~ ( subset @ SY386 @ SV130 )
| ( in @ SY386 @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(755,plain,
! [SV131: $i,SV168: $i] :
( ( ~ ( ~ ( ! [SY387: $i] :
( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SY387 )
| ~ ( in @ SY387 @ SV131 ) )
| ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ ( sK9_SY191 @ SV168 @ SV131 ) )
| ~ ( in @ ( sK9_SY191 @ SV168 @ SV131 ) @ SV131 ) )
| ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) ) )
| ( SV168
= ( union @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(756,plain,
! [SV132: $i,SV169: $i] :
( ( ( SV169
!= ( union @ SV132 ) )
| ~ ( ~ ! [SY388: $i] :
( ! [SY356: $i] :
( ~ ( in @ SY388 @ SY356 )
| ~ ( in @ SY356 @ SV132 ) )
| ( in @ SY388 @ SV169 ) )
| ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV169 )
| ~ ( ~ ( in @ SY390 @ ( sK7_D @ SY390 @ SV169 @ SV132 ) )
| ~ ( in @ ( sK7_D @ SY390 @ SV169 @ SV132 ) @ SV132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(757,plain,
! [SV56: $i,SV170: $i] :
( ( ! [SY391: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY391 @ SV170 @ SV56 ) @ SY391 )
| ~ ( in @ ( sK17_D @ SY391 @ SV170 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY391 @ SV170 @ SV56 ) @ SY391 )
| ~ ( in @ ( sK17_D @ SY391 @ SV170 @ SV56 ) @ SV170 ) ) )
| ~ ( ( in @ ( sK17_D @ SY391 @ SV170 @ SV56 ) @ SY391 )
| ( in @ ( sK17_D @ SY391 @ SV170 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SY391 @ SV170 @ SV56 ) @ SV170 ) ) )
| ( SY391
= ( set_union2 @ SV56 @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(758,plain,
! [SV171: $i,SV56: $i] :
( ( ! [SY392: $i] :
( ( SY392
!= ( set_union2 @ SV56 @ SV171 ) )
| ~ ( ~ ! [SY393: $i] :
( ~ ( in @ SY393 @ SY392 )
| ( in @ SY393 @ SV56 )
| ( in @ SY393 @ SV171 ) )
| ~ ~ ( ~ ! [SY277: $i] :
( ~ ( in @ SY277 @ SV56 )
| ( in @ SY277 @ SY392 ) )
| ~ ! [SY395: $i] :
( ~ ( in @ SY395 @ SV171 )
| ( in @ SY395 @ SY392 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(759,plain,
! [SV57: $i,SV172: $i] :
( ( ! [SY396: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY396 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SY396 @ SV172 @ SV57 ) @ SV172 )
| ~ ( in @ ( sK6_D @ SY396 @ SV172 @ SV57 ) @ SY396 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY396 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SY396 @ SV172 @ SV57 ) @ SY396 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY396 @ SV172 @ SV57 ) @ SV172 )
| ( in @ ( sK6_D @ SY396 @ SV172 @ SV57 ) @ SY396 ) ) ) )
| ( SY396
= ( set_difference @ SV57 @ SV172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(760,plain,
! [SV173: $i,SV57: $i] :
( ( ! [SY397: $i] :
( ( SY397
!= ( set_difference @ SV57 @ SV173 ) )
| ~ ( ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SV57 )
| ( in @ SY398 @ SV173 )
| ( in @ SY398 @ SY397 ) )
| ~ ~ ( ~ ! [SY284: $i] :
( ~ ( in @ SY284 @ SY397 )
| ( in @ SY284 @ SV57 ) )
| ~ ! [SY400: $i] :
( ~ ( in @ SY400 @ SY397 )
| ~ ( in @ SY400 @ SV173 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(761,plain,
! [SV99: $i,SV58: $i] :
( ( ! [SY321: $i] :
( ! [SY322: $i] :
( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SY321 @ SY322 ) )
| ( SV58 = SY321 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(762,plain,
! [SV99: $i,SV58: $i] :
( ( ! [SY323: $i,SY324: $i] :
( ( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SY323 @ SY324 ) )
| ( SV99 = SY324 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[689]) ).
thf(763,plain,
! [SV174: $i,SV133: $i] :
( ( ( ( set_difference @ SV133 @ ( singleton @ SV174 ) )
!= SV133 )
| ~ ( in @ SV174 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(764,plain,
! [SV134: $i,SV175: $i] :
( ( ( in @ SV175 @ SV134 )
| ( ( set_difference @ SV134 @ ( singleton @ SV175 ) )
= SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(765,plain,
! [SV176: $i,SV59: $i] :
( ( ! [SY401: $i] :
( ~ ( in @ SV59 @ SY401 )
| ~ ( in @ SV176 @ SY401 )
| ( subset @ ( unordered_pair @ SV59 @ SV176 ) @ SY401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(766,plain,
! [SV59: $i] :
( ( ~ ! [SY293: $i,SY294: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY293 ) @ SY294 )
| ( in @ SV59 @ SY294 ) )
| ~ ! [SY295: $i,SY296: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY295 ) @ SY296 )
| ( in @ SY295 @ SY296 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(767,plain,
! [SV177: $i,SV135: $i] :
( ( ( ( set_intersection2 @ SV135 @ SV177 )
!= empty_set )
| ( disjoint @ SV135 @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(768,plain,
! [SV178: $i,SV136: $i] :
( ( ~ ( disjoint @ SV136 @ SV178 )
| ( ( set_intersection2 @ SV136 @ SV178 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(769,plain,
! [SV179: $i,SV137: $i] :
( ( ( disjoint @ SV137 @ SV179 )
| ( in @ ( sK22_C @ SV179 @ SV137 ) @ ( set_intersection2 @ SV137 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(770,plain,
! [SV180: $i,SV138: $i] :
( ( ! [SY402: $i] :
~ ( in @ SY402 @ ( set_intersection2 @ SV138 @ SV180 ) )
| ~ ( disjoint @ SV138 @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(771,plain,
! [SV60: $i,SV181: $i] :
( ( ! [SY403: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY403 @ SV181 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK10_D @ SY403 @ SV181 @ SV60 ) @ SV181 )
| ~ ( in @ ( sK10_D @ SY403 @ SV181 @ SV60 ) @ SY403 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY403 @ SV181 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SY403 @ SV181 @ SV60 ) @ SY403 ) )
| ~ ( ( in @ ( sK10_D @ SY403 @ SV181 @ SV60 ) @ SV181 )
| ( in @ ( sK10_D @ SY403 @ SV181 @ SV60 ) @ SY403 ) ) ) )
| ( SY403
= ( set_intersection2 @ SV60 @ SV181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(772,plain,
! [SV182: $i,SV60: $i] :
( ( ! [SY404: $i] :
( ( SY404
!= ( set_intersection2 @ SV60 @ SV182 ) )
| ~ ( ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SV60 )
| ~ ( in @ SY405 @ SV182 )
| ( in @ SY405 @ SY404 ) )
| ~ ~ ( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SY404 )
| ( in @ SY302 @ SV60 ) )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SY404 )
| ( in @ SY407 @ SV182 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(773,plain,
! [SV183: $i,SV139: $i] :
( ( ~ ( in @ SV139 @ SV183 )
| ( subset @ ( singleton @ SV139 ) @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(774,plain,
! [SV184: $i,SV140: $i] :
( ( ~ ( subset @ ( singleton @ SV140 ) @ SV184 )
| ( in @ SV140 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(775,plain,
! [SV185: $i,SV141: $i] :
( ( ~ ( subset @ SV141 @ SV185 )
| ~ ( subset @ SV185 @ SV141 )
| ( SV141 = SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(776,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(777,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[703]) ).
thf(778,plain,
! [SV64: $i,SV5: $i,SV142: $i] :
( ( ( in @ SV142 @ SV5 )
= $true )
| ( ( subset @ SV5 @ ( set_difference @ SV64 @ ( singleton @ SV142 ) ) )
= $true )
| ( ( subset @ SV5 @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(779,plain,
! [SV108: $i,SV66: $i,SV100: $i,SV7: $i] :
( ( ( SV7 = SV100 )
= $true )
| ( ( ( ( unordered_pair @ SV7 @ SV66 )
!= ( unordered_pair @ SV100 @ SV108 ) ) )
= $true )
| ( ( SV7 = SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(780,plain,
! [SV101: $i,SV69: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV69 )
= $false )
| ( ( ~ ( subset @ SV10 @ SV101 ) )
= $true )
| ( ( subset @ SV10 @ ( set_intersection2 @ SV69 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(781,plain,
! [SV102: $i,SV70: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV70 )
= $false )
| ( ( ~ ( subset @ SV70 @ SV102 ) )
= $true )
| ( ( subset @ SV11 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(782,plain,
! [SV24: $i,SV103: $i,SV81: $i] :
( ( ( disjoint @ SV81 @ SV103 )
= $false )
| ( ( ~ ( subset @ SV24 @ SV81 ) )
= $true )
| ( ( disjoint @ SV24 @ SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(783,plain,
! [SV104: $i,SV84: $i,SV28: $i] :
( ( ( subset @ SV28 @ SV84 )
= $false )
| ( ( ~ ( subset @ SV104 @ SV84 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV28 @ SV104 ) @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(784,plain,
! [SV51: $i,SV96: $i] :
( ( ( empty @ SV96 )
= $false )
| ( ( SV51 = SV96 )
= $true )
| ( ( empty @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(785,plain,
! [SV145: $i,SV110: $i] :
( ( ( ~ ( subset @ SV110 @ ( singleton @ SV145 ) ) )
= $true )
| ( ( ( SV110 = empty_set )
| ( SV110
= ( singleton @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(786,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[721]) ).
thf(787,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[722]) ).
thf(788,plain,
! [SV97: $i,SV186: $i,SV52: $i] :
( ( ! [SY408: $i] :
( ~ ( in @ SV52 @ SV186 )
| ~ ( in @ SV97 @ SY408 )
| ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV186 @ SY408 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(789,plain,
! [SV97: $i,SV52: $i] :
( ( ~ ! [SY317: $i] :
( ! [SY318: $i] :
~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY317 @ SY318 ) )
| ( in @ SV52 @ SY317 ) )
| ~ ! [SY319: $i,SY320: $i] :
( ~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY319 @ SY320 ) )
| ( in @ SV97 @ SY320 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(790,plain,
! [SV146: $i,SV111: $i] :
( ( ( ~ ( subset @ SV111 @ ( singleton @ SV146 ) ) )
= $true )
| ( ( ( SV111 = empty_set )
| ( SV111
= ( singleton @ SV146 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(791,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[726]) ).
thf(792,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[727]) ).
thf(793,plain,
! [SV187: $i,SV147: $i,SV53: $i] :
( ( ~ ( ~ ( ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ SV53 )
| ~ ( in @ SY410 @ SV147 )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ SY409 @ SY410 ) ) )
| ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) @ SV147 ) )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) ) ) )
| ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) ) )
| ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(794,plain,
! [SV148: $i,SV53: $i,SV188: $i] :
( ( ( SV188
!= ( cartesian_product2 @ SV53 @ SV148 ) )
| ~ ( ~ ! [SY411: $i] :
( ! [SY373: $i,SY374: $i] :
( ~ ( in @ SY373 @ SV53 )
| ~ ( in @ SY374 @ SV148 )
| ( SY411
!= ( ordered_pair @ SY373 @ SY374 ) ) )
| ( in @ SY411 @ SV188 ) )
| ~ ! [SY414: $i] :
( ~ ( in @ SY414 @ SV188 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY414 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SY414 @ SV188 @ SV148 @ SV53 ) @ SV148 ) )
| ( SY414
!= ( ordered_pair @ ( sK12_E @ SY414 @ SV188 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SY414 @ SV188 @ SV148 @ SV53 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(795,plain,
! [SV149: $i,SV112: $i] :
( ( ( ~ ( in @ SV112 @ SV149 ) )
= $true )
| ( ( subset @ ( singleton @ SV112 ) @ SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(796,plain,
! [SV150: $i,SV113: $i] :
( ( ( ~ ( subset @ ( singleton @ SV113 ) @ SV150 ) )
= $true )
| ( ( in @ SV113 @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[731]) ).
thf(797,plain,
! [SV151: $i,SV114: $i] :
( ( ( ( ( set_difference @ SV114 @ SV151 )
!= empty_set ) )
= $true )
| ( ( subset @ SV114 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(798,plain,
! [SV152: $i,SV115: $i] :
( ( ( ~ ( subset @ SV115 @ SV152 ) )
= $true )
| ( ( ( set_difference @ SV115 @ SV152 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(799,plain,
! [SV116: $i,SV153: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_C @ SV153 @ SV116 ) @ SV116 )
| ~ ~ ( in @ ( sK11_C @ SV153 @ SV116 ) @ SV153 ) ) )
= $true )
| ( ( subset @ SV116 @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(800,plain,
! [SV154: $i,SV117: $i] :
( ( ( ~ ( subset @ SV117 @ SV154 ) )
= $true )
| ( ( ! [SY376: $i] :
( ~ ( in @ SY376 @ SV117 )
| ( in @ SY376 @ SV154 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(801,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV54 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV155 ) ) )
| ~ ( ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV54 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV155 ) ) )
| ( SV189
= ( unordered_pair @ SV54 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(802,plain,
! [SV156: $i,SV54: $i,SV190: $i] :
( ( ( SV190
!= ( unordered_pair @ SV54 @ SV156 ) )
| ~ ( ~ ! [SY415: $i] :
( ~ ( in @ SY415 @ SV190 )
| ( SY415 = SV54 )
| ( SY415 = SV156 ) )
| ~ ~ ( ~ ! [SY416: $i] :
( ( SY416 != SV54 )
| ( in @ SY416 @ SV190 ) )
| ~ ! [SY417: $i] :
( ( SY417 != SV156 )
| ( in @ SY417 @ SV190 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(803,plain,
! [SV157: $i,SV118: $i] :
( ( ( ( ( set_difference @ SV118 @ SV157 )
!= empty_set ) )
= $true )
| ( ( subset @ SV118 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(804,plain,
! [SV158: $i,SV119: $i] :
( ( ( ~ ( subset @ SV119 @ SV158 ) )
= $true )
| ( ( ( set_difference @ SV119 @ SV158 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[739]) ).
thf(805,plain,
! [SV121: $i] :
( ( ( SV121 = empty_set )
= $false )
| ( ( ! [SY337: $i] :
~ ( in @ SY337 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(806,plain,
! [SV159: $i,SV122: $i] :
( ( ( ( ( set_difference @ SV122 @ SV159 )
!= SV122 ) )
= $true )
| ( ( disjoint @ SV122 @ SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(807,plain,
! [SV160: $i,SV123: $i] :
( ( ( ~ ( disjoint @ SV123 @ SV160 ) )
= $true )
| ( ( ( set_difference @ SV123 @ SV160 )
= SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(808,plain,
! [SV124: $i,SV161: $i] :
( ( ( ~ ( ~ ( ( ( sK21_C @ SV161 @ SV124 )
!= SV124 )
| ~ ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 ) )
| ~ ( ( ( sK21_C @ SV161 @ SV124 )
= SV124 )
| ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 ) ) ) )
= $true )
| ( ( SV161
= ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(809,plain,
! [SV125: $i,SV162: $i] :
( ( ( ( SV162
!= ( singleton @ SV125 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY382: $i] :
( ( SY382 != SV125 )
| ( in @ SY382 @ SV162 ) )
| ~ ! [SY383: $i] :
( ~ ( in @ SY383 @ SV162 )
| ( SY383 = SV125 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(810,plain,
! [SV163: $i,SV126: $i] :
( ( ( ( SV126 = SV163 )
| ~ ( subset @ SV126 @ SV163 ) )
= $true )
| ( ( proper_subset @ SV126 @ SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(811,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[747]) ).
thf(812,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[748]) ).
thf(813,plain,
! [SV164: $i,SV127: $i] :
( ( ( disjoint @ SV127 @ SV164 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK23_C @ SV164 @ SV127 ) @ SV127 )
| ~ ( in @ ( sK23_C @ SV164 @ SV127 ) @ SV164 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(814,plain,
! [SV165: $i,SV128: $i] :
( ( ( ! [SY384: $i] :
( ~ ( in @ SY384 @ SV128 )
| ~ ( in @ SY384 @ SV165 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV128 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(815,plain,
! [SV55: $i,SV98: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
| ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 ) )
= $true )
| ( ( SV55 = SV98 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(816,plain,
! [SV55: $i,SV98: $i] :
( ( ( ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
| ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 ) )
= $true )
| ( ( SV55 = SV98 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(817,plain,
! [SV129: $i,SV166: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
| ~ ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 ) )
| ~ ( ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
| ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 ) ) ) )
= $true )
| ( ( SV166
= ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(818,plain,
! [SV130: $i,SV167: $i] :
( ( ( ( SV167
!= ( powerset @ SV130 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY385: $i] :
( ~ ( in @ SY385 @ SV167 )
| ( subset @ SY385 @ SV130 ) )
| ~ ! [SY386: $i] :
( ~ ( subset @ SY386 @ SV130 )
| ( in @ SY386 @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(819,plain,
! [SV131: $i,SV168: $i] :
( ( ( ~ ( ~ ( ! [SY387: $i] :
( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SY387 )
| ~ ( in @ SY387 @ SV131 ) )
| ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ ( sK9_SY191 @ SV168 @ SV131 ) )
| ~ ( in @ ( sK9_SY191 @ SV168 @ SV131 ) @ SV131 ) )
| ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) ) ) )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(820,plain,
! [SV132: $i,SV169: $i] :
( ( ( ( SV169
!= ( union @ SV132 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY388: $i] :
( ! [SY356: $i] :
( ~ ( in @ SY388 @ SY356 )
| ~ ( in @ SY356 @ SV132 ) )
| ( in @ SY388 @ SV169 ) )
| ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV169 )
| ~ ( ~ ( in @ SY390 @ ( sK7_D @ SY390 @ SV169 @ SV132 ) )
| ~ ( in @ ( sK7_D @ SY390 @ SV169 @ SV132 ) @ SV132 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(821,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) ) )
| ~ ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) ) )
| ( SV191
= ( set_union2 @ SV56 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(822,plain,
! [SV171: $i,SV56: $i,SV192: $i] :
( ( ( SV192
!= ( set_union2 @ SV56 @ SV171 ) )
| ~ ( ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV192 )
| ( in @ SY418 @ SV56 )
| ( in @ SY418 @ SV171 ) )
| ~ ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV56 )
| ( in @ SY419 @ SV192 ) )
| ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV171 )
| ( in @ SY420 @ SV192 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(823,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) ) ) )
| ( SV193
= ( set_difference @ SV57 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(824,plain,
! [SV173: $i,SV57: $i,SV194: $i] :
( ( ( SV194
!= ( set_difference @ SV57 @ SV173 ) )
| ~ ( ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV57 )
| ( in @ SY421 @ SV173 )
| ( in @ SY421 @ SV194 ) )
| ~ ~ ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV194 )
| ( in @ SY422 @ SV57 ) )
| ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV194 )
| ~ ( in @ SY423 @ SV173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(825,plain,
! [SV195: $i,SV99: $i,SV58: $i] :
( ( ! [SY424: $i] :
( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SV195 @ SY424 ) )
| ( SV58 = SV195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(826,plain,
! [SV196: $i,SV99: $i,SV58: $i] :
( ( ! [SY425: $i] :
( ( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SV196 @ SY425 ) )
| ( SV99 = SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(827,plain,
! [SV174: $i,SV133: $i] :
( ( ( ( ( set_difference @ SV133 @ ( singleton @ SV174 ) )
!= SV133 ) )
= $true )
| ( ( ~ ( in @ SV174 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(828,plain,
! [SV134: $i,SV175: $i] :
( ( ( in @ SV175 @ SV134 )
= $true )
| ( ( ( set_difference @ SV134 @ ( singleton @ SV175 ) )
= SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(829,plain,
! [SV176: $i,SV197: $i,SV59: $i] :
( ( ~ ( in @ SV59 @ SV197 )
| ~ ( in @ SV176 @ SV197 )
| ( subset @ ( unordered_pair @ SV59 @ SV176 ) @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(830,plain,
! [SV59: $i] :
( ( ~ ! [SY293: $i,SY294: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY293 ) @ SY294 )
| ( in @ SV59 @ SY294 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[766]) ).
thf(831,plain,
! [SV59: $i] :
( ( ~ ! [SY295: $i,SY296: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY295 ) @ SY296 )
| ( in @ SY295 @ SY296 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[766]) ).
thf(832,plain,
! [SV177: $i,SV135: $i] :
( ( ( ( ( set_intersection2 @ SV135 @ SV177 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV135 @ SV177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(833,plain,
! [SV178: $i,SV136: $i] :
( ( ( ~ ( disjoint @ SV136 @ SV178 ) )
= $true )
| ( ( ( set_intersection2 @ SV136 @ SV178 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(834,plain,
! [SV179: $i,SV137: $i] :
( ( ( disjoint @ SV137 @ SV179 )
= $true )
| ( ( in @ ( sK22_C @ SV179 @ SV137 ) @ ( set_intersection2 @ SV137 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(835,plain,
! [SV180: $i,SV138: $i] :
( ( ( ! [SY402: $i] :
~ ( in @ SY402 @ ( set_intersection2 @ SV138 @ SV180 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV138 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(836,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
| ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) ) ) )
| ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(837,plain,
! [SV182: $i,SV60: $i,SV199: $i] :
( ( ( SV199
!= ( set_intersection2 @ SV60 @ SV182 ) )
| ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV60 )
| ~ ( in @ SY426 @ SV182 )
| ( in @ SY426 @ SV199 ) )
| ~ ~ ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV199 )
| ( in @ SY427 @ SV60 ) )
| ~ ! [SY428: $i] :
( ~ ( in @ SY428 @ SV199 )
| ( in @ SY428 @ SV182 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(838,plain,
! [SV183: $i,SV139: $i] :
( ( ( ~ ( in @ SV139 @ SV183 ) )
= $true )
| ( ( subset @ ( singleton @ SV139 ) @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(839,plain,
! [SV184: $i,SV140: $i] :
( ( ( ~ ( subset @ ( singleton @ SV140 ) @ SV184 ) )
= $true )
| ( ( in @ SV140 @ SV184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(840,plain,
! [SV185: $i,SV141: $i] :
( ( ( ~ ( subset @ SV141 @ SV185 )
| ~ ( subset @ SV185 @ SV141 ) )
= $true )
| ( ( SV141 = SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(841,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[776]) ).
thf(842,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[777]) ).
thf(843,plain,
! [SV108: $i,SV100: $i,SV66: $i,SV7: $i] :
( ( ( ( unordered_pair @ SV7 @ SV66 )
= ( unordered_pair @ SV100 @ SV108 ) )
= $false )
| ( ( SV7 = SV100 )
= $true )
| ( ( SV7 = SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(844,plain,
! [SV69: $i,SV101: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV101 )
= $false )
| ( ( subset @ SV10 @ SV69 )
= $false )
| ( ( subset @ SV10 @ ( set_intersection2 @ SV69 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(845,plain,
! [SV11: $i,SV102: $i,SV70: $i] :
( ( ( subset @ SV70 @ SV102 )
= $false )
| ( ( subset @ SV11 @ SV70 )
= $false )
| ( ( subset @ SV11 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(846,plain,
! [SV103: $i,SV81: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV81 )
= $false )
| ( ( disjoint @ SV81 @ SV103 )
= $false )
| ( ( disjoint @ SV24 @ SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(847,plain,
! [SV28: $i,SV84: $i,SV104: $i] :
( ( ( subset @ SV104 @ SV84 )
= $false )
| ( ( subset @ SV28 @ SV84 )
= $false )
| ( ( subset @ ( set_union2 @ SV28 @ SV104 ) @ SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(848,plain,
! [SV145: $i,SV110: $i] :
( ( ( subset @ SV110 @ ( singleton @ SV145 ) )
= $false )
| ( ( ( SV110 = empty_set )
| ( SV110
= ( singleton @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(849,plain,
! [SV200: $i] :
( ( ( SV200 != empty_set )
| ! [SY429: $i] : ( subset @ SV200 @ ( singleton @ SY429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(850,plain,
! [SV201: $i] :
( ( ! [SY430: $i] :
( ( SV201
!= ( singleton @ SY430 ) )
| ( subset @ SV201 @ ( singleton @ SY430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(851,plain,
! [SV202: $i,SV97: $i,SV186: $i,SV52: $i] :
( ( ~ ( in @ SV52 @ SV186 )
| ~ ( in @ SV97 @ SV202 )
| ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV186 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(852,plain,
! [SV97: $i,SV52: $i] :
( ( ~ ! [SY317: $i] :
( ! [SY318: $i] :
~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY317 @ SY318 ) )
| ( in @ SV52 @ SY317 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(853,plain,
! [SV97: $i,SV52: $i] :
( ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY319 @ SY320 ) )
| ( in @ SV97 @ SY320 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[789]) ).
thf(854,plain,
! [SV146: $i,SV111: $i] :
( ( ( subset @ SV111 @ ( singleton @ SV146 ) )
= $false )
| ( ( ( SV111 = empty_set )
| ( SV111
= ( singleton @ SV146 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(855,plain,
! [SV203: $i] :
( ( ( SV203 != empty_set )
| ! [SY431: $i] : ( subset @ SV203 @ ( singleton @ SY431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(856,plain,
! [SV204: $i] :
( ( ! [SY432: $i] :
( ( SV204
!= ( singleton @ SY432 ) )
| ( subset @ SV204 @ ( singleton @ SY432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(857,plain,
! [SV187: $i,SV147: $i,SV53: $i] :
( ( ( ~ ( ~ ( ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ SV53 )
| ~ ( in @ SY410 @ SV147 )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ SY409 @ SY410 ) ) )
| ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) @ SV147 ) )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) ) ) )
| ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) ) ) )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(858,plain,
! [SV148: $i,SV53: $i,SV188: $i] :
( ( ( ( SV188
!= ( cartesian_product2 @ SV53 @ SV148 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY411: $i] :
( ! [SY373: $i,SY374: $i] :
( ~ ( in @ SY373 @ SV53 )
| ~ ( in @ SY374 @ SV148 )
| ( SY411
!= ( ordered_pair @ SY373 @ SY374 ) ) )
| ( in @ SY411 @ SV188 ) )
| ~ ! [SY414: $i] :
( ~ ( in @ SY414 @ SV188 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY414 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SY414 @ SV188 @ SV148 @ SV53 ) @ SV148 ) )
| ( SY414
!= ( ordered_pair @ ( sK12_E @ SY414 @ SV188 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SY414 @ SV188 @ SV148 @ SV53 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(859,plain,
! [SV149: $i,SV112: $i] :
( ( ( in @ SV112 @ SV149 )
= $false )
| ( ( subset @ ( singleton @ SV112 ) @ SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(860,plain,
! [SV150: $i,SV113: $i] :
( ( ( subset @ ( singleton @ SV113 ) @ SV150 )
= $false )
| ( ( in @ SV113 @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(861,plain,
! [SV151: $i,SV114: $i] :
( ( ( ( set_difference @ SV114 @ SV151 )
= empty_set )
= $false )
| ( ( subset @ SV114 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(862,plain,
! [SV152: $i,SV115: $i] :
( ( ( subset @ SV115 @ SV152 )
= $false )
| ( ( ( set_difference @ SV115 @ SV152 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(863,plain,
! [SV116: $i,SV153: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV153 @ SV116 ) @ SV116 )
| ~ ~ ( in @ ( sK11_C @ SV153 @ SV116 ) @ SV153 ) )
= $false )
| ( ( subset @ SV116 @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(864,plain,
! [SV154: $i,SV117: $i] :
( ( ( subset @ SV117 @ SV154 )
= $false )
| ( ( ! [SY376: $i] :
( ~ ( in @ SY376 @ SV117 )
| ( in @ SY376 @ SV154 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(865,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV54 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV155 ) ) )
| ~ ( ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV54 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV155 ) ) ) )
= $true )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(866,plain,
! [SV156: $i,SV54: $i,SV190: $i] :
( ( ( ( SV190
!= ( unordered_pair @ SV54 @ SV156 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY415: $i] :
( ~ ( in @ SY415 @ SV190 )
| ( SY415 = SV54 )
| ( SY415 = SV156 ) )
| ~ ~ ( ~ ! [SY416: $i] :
( ( SY416 != SV54 )
| ( in @ SY416 @ SV190 ) )
| ~ ! [SY417: $i] :
( ( SY417 != SV156 )
| ( in @ SY417 @ SV190 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(867,plain,
! [SV157: $i,SV118: $i] :
( ( ( ( set_difference @ SV118 @ SV157 )
= empty_set )
= $false )
| ( ( subset @ SV118 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(868,plain,
! [SV158: $i,SV119: $i] :
( ( ( subset @ SV119 @ SV158 )
= $false )
| ( ( ( set_difference @ SV119 @ SV158 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(869,plain,
! [SV121: $i,SV205: $i] :
( ( ( ~ ( in @ SV205 @ SV121 ) )
= $true )
| ( ( SV121 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(870,plain,
! [SV159: $i,SV122: $i] :
( ( ( ( set_difference @ SV122 @ SV159 )
= SV122 )
= $false )
| ( ( disjoint @ SV122 @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(871,plain,
! [SV160: $i,SV123: $i] :
( ( ( disjoint @ SV123 @ SV160 )
= $false )
| ( ( ( set_difference @ SV123 @ SV160 )
= SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(872,plain,
! [SV124: $i,SV161: $i] :
( ( ( ~ ( ( ( sK21_C @ SV161 @ SV124 )
!= SV124 )
| ~ ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 ) )
| ~ ( ( ( sK21_C @ SV161 @ SV124 )
= SV124 )
| ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 ) ) )
= $false )
| ( ( SV161
= ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(873,plain,
! [SV125: $i,SV162: $i] :
( ( ( SV162
= ( singleton @ SV125 ) )
= $false )
| ( ( ~ ( ~ ! [SY382: $i] :
( ( SY382 != SV125 )
| ( in @ SY382 @ SV162 ) )
| ~ ! [SY383: $i] :
( ~ ( in @ SY383 @ SV162 )
| ( SY383 = SV125 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(874,plain,
! [SV163: $i,SV126: $i] :
( ( ( SV126 = SV163 )
= $true )
| ( ( ~ ( subset @ SV126 @ SV163 ) )
= $true )
| ( ( proper_subset @ SV126 @ SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(875,plain,
! [SV206: $i] :
( ( ! [SY433: $i] :
( ~ ( proper_subset @ SV206 @ SY433 )
| ( SV206 != SY433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(876,plain,
! [SV207: $i] :
( ( ! [SY434: $i] :
( ~ ( proper_subset @ SV207 @ SY434 )
| ( subset @ SV207 @ SY434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(877,plain,
! [SV127: $i,SV164: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV164 @ SV127 ) @ SV127 )
| ~ ( in @ ( sK23_C @ SV164 @ SV127 ) @ SV164 ) )
= $false )
| ( ( disjoint @ SV127 @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(878,plain,
! [SV165: $i,SV128: $i,SV208: $i] :
( ( ( ~ ( in @ SV208 @ SV128 )
| ~ ( in @ SV208 @ SV165 ) )
= $true )
| ( ( ~ ( disjoint @ SV128 @ SV165 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(879,plain,
! [SV55: $i,SV98: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 ) )
= $true )
| ( ( ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 ) )
= $true )
| ( ( SV55 = SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(880,plain,
! [SV55: $i,SV98: $i] :
( ( ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
= $true )
| ( ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 )
= $true )
| ( ( SV55 = SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(881,plain,
! [SV129: $i,SV166: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
| ~ ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 ) )
| ~ ( ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
| ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 ) ) )
= $false )
| ( ( SV166
= ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(882,plain,
! [SV130: $i,SV167: $i] :
( ( ( SV167
= ( powerset @ SV130 ) )
= $false )
| ( ( ~ ( ~ ! [SY385: $i] :
( ~ ( in @ SY385 @ SV167 )
| ( subset @ SY385 @ SV130 ) )
| ~ ! [SY386: $i] :
( ~ ( subset @ SY386 @ SV130 )
| ( in @ SY386 @ SV167 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(883,plain,
! [SV131: $i,SV168: $i] :
( ( ( ~ ( ! [SY387: $i] :
( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SY387 )
| ~ ( in @ SY387 @ SV131 ) )
| ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ ( sK9_SY191 @ SV168 @ SV131 ) )
| ~ ( in @ ( sK9_SY191 @ SV168 @ SV131 ) @ SV131 ) )
| ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) ) )
= $false )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(884,plain,
! [SV132: $i,SV169: $i] :
( ( ( SV169
= ( union @ SV132 ) )
= $false )
| ( ( ~ ( ~ ! [SY388: $i] :
( ! [SY356: $i] :
( ~ ( in @ SY388 @ SY356 )
| ~ ( in @ SY356 @ SV132 ) )
| ( in @ SY388 @ SV169 ) )
| ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV169 )
| ~ ( ~ ( in @ SY390 @ ( sK7_D @ SY390 @ SV169 @ SV132 ) )
| ~ ( in @ ( sK7_D @ SY390 @ SV169 @ SV132 ) @ SV132 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(885,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) ) )
| ~ ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) ) ) )
= $true )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(886,plain,
! [SV171: $i,SV56: $i,SV192: $i] :
( ( ( ( SV192
!= ( set_union2 @ SV56 @ SV171 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV192 )
| ( in @ SY418 @ SV56 )
| ( in @ SY418 @ SV171 ) )
| ~ ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV56 )
| ( in @ SY419 @ SV192 ) )
| ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV171 )
| ( in @ SY420 @ SV192 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(887,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) ) ) ) )
= $true )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(888,plain,
! [SV173: $i,SV57: $i,SV194: $i] :
( ( ( ( SV194
!= ( set_difference @ SV57 @ SV173 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV57 )
| ( in @ SY421 @ SV173 )
| ( in @ SY421 @ SV194 ) )
| ~ ~ ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV194 )
| ( in @ SY422 @ SV57 ) )
| ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV194 )
| ~ ( in @ SY423 @ SV173 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(889,plain,
! [SV195: $i,SV99: $i,SV58: $i] :
( ( ( ! [SY424: $i] :
( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SV195 @ SY424 ) ) )
= $true )
| ( ( SV58 = SV195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(890,plain,
! [SV209: $i,SV196: $i,SV99: $i,SV58: $i] :
( ( ( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SV196 @ SV209 ) )
| ( SV99 = SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(891,plain,
! [SV174: $i,SV133: $i] :
( ( ( ( set_difference @ SV133 @ ( singleton @ SV174 ) )
= SV133 )
= $false )
| ( ( ~ ( in @ SV174 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(892,plain,
! [SV176: $i,SV197: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV197 )
| ~ ( in @ SV176 @ SV197 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV59 @ SV176 ) @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(893,plain,
! [SV59: $i] :
( ( ! [SY293: $i,SY294: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY293 ) @ SY294 )
| ( in @ SV59 @ SY294 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(894,plain,
! [SV59: $i] :
( ( ! [SY295: $i,SY296: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SY295 ) @ SY296 )
| ( in @ SY295 @ SY296 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(895,plain,
! [SV177: $i,SV135: $i] :
( ( ( ( set_intersection2 @ SV135 @ SV177 )
= empty_set )
= $false )
| ( ( disjoint @ SV135 @ SV177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(896,plain,
! [SV178: $i,SV136: $i] :
( ( ( disjoint @ SV136 @ SV178 )
= $false )
| ( ( ( set_intersection2 @ SV136 @ SV178 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(897,plain,
! [SV180: $i,SV138: $i,SV210: $i] :
( ( ( ~ ( in @ SV210 @ ( set_intersection2 @ SV138 @ SV180 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV138 @ SV180 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(898,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
| ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) ) ) ) )
= $true )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(899,plain,
! [SV182: $i,SV60: $i,SV199: $i] :
( ( ( ( SV199
!= ( set_intersection2 @ SV60 @ SV182 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV60 )
| ~ ( in @ SY426 @ SV182 )
| ( in @ SY426 @ SV199 ) )
| ~ ~ ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV199 )
| ( in @ SY427 @ SV60 ) )
| ~ ! [SY428: $i] :
( ~ ( in @ SY428 @ SV199 )
| ( in @ SY428 @ SV182 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[837]) ).
thf(900,plain,
! [SV183: $i,SV139: $i] :
( ( ( in @ SV139 @ SV183 )
= $false )
| ( ( subset @ ( singleton @ SV139 ) @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(901,plain,
! [SV184: $i,SV140: $i] :
( ( ( subset @ ( singleton @ SV140 ) @ SV184 )
= $false )
| ( ( in @ SV140 @ SV184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(902,plain,
! [SV185: $i,SV141: $i] :
( ( ( ~ ( subset @ SV141 @ SV185 ) )
= $true )
| ( ( ~ ( subset @ SV185 @ SV141 ) )
= $true )
| ( ( SV141 = SV185 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(903,plain,
! [SV211: $i] :
( ( ! [SY435: $i] :
( ( SV211 != SY435 )
| ( subset @ SV211 @ SY435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(904,plain,
! [SV212: $i] :
( ( ! [SY436: $i] :
( ( SV212 != SY436 )
| ( subset @ SY436 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(905,plain,
! [SV145: $i,SV110: $i] :
( ( ( SV110 = empty_set )
= $true )
| ( ( SV110
= ( singleton @ SV145 ) )
= $true )
| ( ( subset @ SV110 @ ( singleton @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(906,plain,
! [SV200: $i] :
( ( ( ( SV200 != empty_set ) )
= $true )
| ( ( ! [SY429: $i] : ( subset @ SV200 @ ( singleton @ SY429 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(907,plain,
! [SV213: $i,SV201: $i] :
( ( ( SV201
!= ( singleton @ SV213 ) )
| ( subset @ SV201 @ ( singleton @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(908,plain,
! [SV202: $i,SV97: $i,SV186: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV186 )
| ~ ( in @ SV97 @ SV202 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV186 @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(909,plain,
! [SV97: $i,SV52: $i] :
( ( ! [SY317: $i] :
( ! [SY318: $i] :
~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY317 @ SY318 ) )
| ( in @ SV52 @ SY317 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[852]) ).
thf(910,plain,
! [SV97: $i,SV52: $i] :
( ( ! [SY319: $i,SY320: $i] :
( ~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SY319 @ SY320 ) )
| ( in @ SV97 @ SY320 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(911,plain,
! [SV146: $i,SV111: $i] :
( ( ( SV111 = empty_set )
= $true )
| ( ( SV111
= ( singleton @ SV146 ) )
= $true )
| ( ( subset @ SV111 @ ( singleton @ SV146 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(912,plain,
! [SV203: $i] :
( ( ( ( SV203 != empty_set ) )
= $true )
| ( ( ! [SY431: $i] : ( subset @ SV203 @ ( singleton @ SY431 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(913,plain,
! [SV214: $i,SV204: $i] :
( ( ( SV204
!= ( singleton @ SV214 ) )
| ( subset @ SV204 @ ( singleton @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(914,plain,
! [SV187: $i,SV147: $i,SV53: $i] :
( ( ( ~ ( ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ SV53 )
| ~ ( in @ SY410 @ SV147 )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ SY409 @ SY410 ) ) )
| ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) @ SV147 ) )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) ) ) )
| ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) ) )
= $false )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(915,plain,
! [SV148: $i,SV53: $i,SV188: $i] :
( ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false )
| ( ( ~ ( ~ ! [SY411: $i] :
( ! [SY373: $i,SY374: $i] :
( ~ ( in @ SY373 @ SV53 )
| ~ ( in @ SY374 @ SV148 )
| ( SY411
!= ( ordered_pair @ SY373 @ SY374 ) ) )
| ( in @ SY411 @ SV188 ) )
| ~ ! [SY414: $i] :
( ~ ( in @ SY414 @ SV188 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY414 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SY414 @ SV188 @ SV148 @ SV53 ) @ SV148 ) )
| ( SY414
!= ( ordered_pair @ ( sK12_E @ SY414 @ SV188 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SY414 @ SV188 @ SV148 @ SV53 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(916,plain,
! [SV116: $i,SV153: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV153 @ SV116 ) @ SV116 ) )
= $false )
| ( ( subset @ SV116 @ SV153 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(917,plain,
! [SV116: $i,SV153: $i] :
( ( ( ~ ~ ( in @ ( sK11_C @ SV153 @ SV116 ) @ SV153 ) )
= $false )
| ( ( subset @ SV116 @ SV153 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(918,plain,
! [SV154: $i,SV117: $i,SV215: $i] :
( ( ( ~ ( in @ SV215 @ SV117 )
| ( in @ SV215 @ SV154 ) )
= $true )
| ( ( subset @ SV117 @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(919,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV54 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV155 ) ) )
| ~ ( ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV54 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV155 ) ) )
= $false )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(920,plain,
! [SV156: $i,SV54: $i,SV190: $i] :
( ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false )
| ( ( ~ ( ~ ! [SY415: $i] :
( ~ ( in @ SY415 @ SV190 )
| ( SY415 = SV54 )
| ( SY415 = SV156 ) )
| ~ ~ ( ~ ! [SY416: $i] :
( ( SY416 != SV54 )
| ( in @ SY416 @ SV190 ) )
| ~ ! [SY417: $i] :
( ( SY417 != SV156 )
| ( in @ SY417 @ SV190 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(921,plain,
! [SV121: $i,SV205: $i] :
( ( ( in @ SV205 @ SV121 )
= $false )
| ( ( SV121 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(922,plain,
! [SV124: $i,SV161: $i] :
( ( ( ~ ( ( ( sK21_C @ SV161 @ SV124 )
!= SV124 )
| ~ ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 ) ) )
= $false )
| ( ( SV161
= ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[872]) ).
thf(923,plain,
! [SV124: $i,SV161: $i] :
( ( ( ~ ( ( ( sK21_C @ SV161 @ SV124 )
= SV124 )
| ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 ) ) )
= $false )
| ( ( SV161
= ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[872]) ).
thf(924,plain,
! [SV162: $i,SV125: $i] :
( ( ( ~ ! [SY382: $i] :
( ( SY382 != SV125 )
| ( in @ SY382 @ SV162 ) )
| ~ ! [SY383: $i] :
( ~ ( in @ SY383 @ SV162 )
| ( SY383 = SV125 ) ) )
= $false )
| ( ( SV162
= ( singleton @ SV125 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(925,plain,
! [SV163: $i,SV126: $i] :
( ( ( subset @ SV126 @ SV163 )
= $false )
| ( ( SV126 = SV163 )
= $true )
| ( ( proper_subset @ SV126 @ SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(926,plain,
! [SV216: $i,SV206: $i] :
( ( ~ ( proper_subset @ SV206 @ SV216 )
| ( SV206 != SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(927,plain,
! [SV217: $i,SV207: $i] :
( ( ~ ( proper_subset @ SV207 @ SV217 )
| ( subset @ SV207 @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(928,plain,
! [SV127: $i,SV164: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV164 @ SV127 ) @ SV127 ) )
= $false )
| ( ( disjoint @ SV127 @ SV164 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(929,plain,
! [SV127: $i,SV164: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV164 @ SV127 ) @ SV164 ) )
= $false )
| ( ( disjoint @ SV127 @ SV164 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(930,plain,
! [SV165: $i,SV128: $i,SV208: $i] :
( ( ( ~ ( in @ SV208 @ SV128 ) )
= $true )
| ( ( ~ ( in @ SV208 @ SV165 ) )
= $true )
| ( ( ~ ( disjoint @ SV128 @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(931,plain,
! [SV55: $i,SV98: $i] :
( ( ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
= $false )
| ( ( ~ ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 ) )
= $true )
| ( ( SV55 = SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(932,plain,
! [SV129: $i,SV166: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
| ~ ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 ) ) )
= $false )
| ( ( SV166
= ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(933,plain,
! [SV129: $i,SV166: $i] :
( ( ( ~ ( ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
| ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 ) ) )
= $false )
| ( ( SV166
= ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(934,plain,
! [SV130: $i,SV167: $i] :
( ( ( ~ ! [SY385: $i] :
( ~ ( in @ SY385 @ SV167 )
| ( subset @ SY385 @ SV130 ) )
| ~ ! [SY386: $i] :
( ~ ( subset @ SY386 @ SV130 )
| ( in @ SY386 @ SV167 ) ) )
= $false )
| ( ( SV167
= ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(935,plain,
! [SV131: $i,SV168: $i] :
( ( ( ~ ( ! [SY387: $i] :
( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SY387 )
| ~ ( in @ SY387 @ SV131 ) )
| ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) ) )
= $false )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(936,plain,
! [SV131: $i,SV168: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ ( sK9_SY191 @ SV168 @ SV131 ) )
| ~ ( in @ ( sK9_SY191 @ SV168 @ SV131 ) @ SV131 ) )
| ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) ) )
= $false )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[883]) ).
thf(937,plain,
! [SV169: $i,SV132: $i] :
( ( ( ~ ! [SY388: $i] :
( ! [SY356: $i] :
( ~ ( in @ SY388 @ SY356 )
| ~ ( in @ SY356 @ SV132 ) )
| ( in @ SY388 @ SV169 ) )
| ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV169 )
| ~ ( ~ ( in @ SY390 @ ( sK7_D @ SY390 @ SV169 @ SV132 ) )
| ~ ( in @ ( sK7_D @ SY390 @ SV169 @ SV132 ) @ SV132 ) ) ) )
= $false )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(938,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) ) )
| ~ ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) ) )
= $false )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(939,plain,
! [SV171: $i,SV56: $i,SV192: $i] :
( ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false )
| ( ( ~ ( ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV192 )
| ( in @ SY418 @ SV56 )
| ( in @ SY418 @ SV171 ) )
| ~ ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV56 )
| ( in @ SY419 @ SV192 ) )
| ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV171 )
| ( in @ SY420 @ SV192 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(940,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) ) ) )
= $false )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(941,plain,
! [SV173: $i,SV57: $i,SV194: $i] :
( ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false )
| ( ( ~ ( ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV57 )
| ( in @ SY421 @ SV173 )
| ( in @ SY421 @ SV194 ) )
| ~ ~ ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV194 )
| ( in @ SY422 @ SV57 ) )
| ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV194 )
| ~ ( in @ SY423 @ SV173 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(942,plain,
! [SV218: $i,SV195: $i,SV99: $i,SV58: $i] :
( ( ( ( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SV195 @ SV218 ) ) )
= $true )
| ( ( SV58 = SV195 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(943,plain,
! [SV209: $i,SV196: $i,SV99: $i,SV58: $i] :
( ( ( ( ( ordered_pair @ SV58 @ SV99 )
!= ( ordered_pair @ SV196 @ SV209 ) ) )
= $true )
| ( ( SV99 = SV209 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(944,plain,
! [SV133: $i,SV174: $i] :
( ( ( in @ SV174 @ SV133 )
= $false )
| ( ( ( set_difference @ SV133 @ ( singleton @ SV174 ) )
= SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(945,plain,
! [SV176: $i,SV197: $i,SV59: $i] :
( ( ( ~ ( in @ SV59 @ SV197 ) )
= $true )
| ( ( ~ ( in @ SV176 @ SV197 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV59 @ SV176 ) @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(946,plain,
! [SV219: $i,SV59: $i] :
( ( ! [SY437: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SV219 ) @ SY437 )
| ( in @ SV59 @ SY437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(947,plain,
! [SV220: $i,SV59: $i] :
( ( ! [SY438: $i] :
( ~ ( subset @ ( unordered_pair @ SV59 @ SV220 ) @ SY438 )
| ( in @ SV220 @ SY438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(948,plain,
! [SV180: $i,SV138: $i,SV210: $i] :
( ( ( in @ SV210 @ ( set_intersection2 @ SV138 @ SV180 ) )
= $false )
| ( ( ~ ( disjoint @ SV138 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(949,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
| ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) ) ) )
= $false )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(950,plain,
! [SV182: $i,SV60: $i,SV199: $i] :
( ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false )
| ( ( ~ ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV60 )
| ~ ( in @ SY426 @ SV182 )
| ( in @ SY426 @ SV199 ) )
| ~ ~ ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV199 )
| ( in @ SY427 @ SV60 ) )
| ~ ! [SY428: $i] :
( ~ ( in @ SY428 @ SV199 )
| ( in @ SY428 @ SV182 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(951,plain,
! [SV185: $i,SV141: $i] :
( ( ( subset @ SV141 @ SV185 )
= $false )
| ( ( ~ ( subset @ SV185 @ SV141 ) )
= $true )
| ( ( SV141 = SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(952,plain,
! [SV221: $i,SV211: $i] :
( ( ( SV211 != SV221 )
| ( subset @ SV211 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(953,plain,
! [SV222: $i,SV212: $i] :
( ( ( SV212 != SV222 )
| ( subset @ SV222 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(954,plain,
! [SV200: $i] :
( ( ( SV200 = empty_set )
= $false )
| ( ( ! [SY429: $i] : ( subset @ SV200 @ ( singleton @ SY429 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(955,plain,
! [SV213: $i,SV201: $i] :
( ( ( ( SV201
!= ( singleton @ SV213 ) ) )
= $true )
| ( ( subset @ SV201 @ ( singleton @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(956,plain,
! [SV202: $i,SV97: $i,SV186: $i,SV52: $i] :
( ( ( ~ ( in @ SV52 @ SV186 ) )
= $true )
| ( ( ~ ( in @ SV97 @ SV202 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV186 @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(957,plain,
! [SV223: $i,SV97: $i,SV52: $i] :
( ( ! [SY439: $i] :
~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV223 @ SY439 ) )
| ( in @ SV52 @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(958,plain,
! [SV224: $i,SV97: $i,SV52: $i] :
( ( ! [SY440: $i] :
( ~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV224 @ SY440 ) )
| ( in @ SV97 @ SY440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(959,plain,
! [SV203: $i] :
( ( ( SV203 = empty_set )
= $false )
| ( ( ! [SY431: $i] : ( subset @ SV203 @ ( singleton @ SY431 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(960,plain,
! [SV214: $i,SV204: $i] :
( ( ( ( SV204
!= ( singleton @ SV214 ) ) )
= $true )
| ( ( subset @ SV204 @ ( singleton @ SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(961,plain,
! [SV187: $i,SV147: $i,SV53: $i] :
( ( ( ~ ( ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ SV53 )
| ~ ( in @ SY410 @ SV147 )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ SY409 @ SY410 ) ) )
| ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) ) )
= $false )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[914]) ).
thf(962,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) @ SV147 ) )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) ) ) )
| ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) ) )
= $false )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[914]) ).
thf(963,plain,
! [SV188: $i,SV148: $i,SV53: $i] :
( ( ( ~ ! [SY411: $i] :
( ! [SY373: $i,SY374: $i] :
( ~ ( in @ SY373 @ SV53 )
| ~ ( in @ SY374 @ SV148 )
| ( SY411
!= ( ordered_pair @ SY373 @ SY374 ) ) )
| ( in @ SY411 @ SV188 ) )
| ~ ! [SY414: $i] :
( ~ ( in @ SY414 @ SV188 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY414 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SY414 @ SV188 @ SV148 @ SV53 ) @ SV148 ) )
| ( SY414
!= ( ordered_pair @ ( sK12_E @ SY414 @ SV188 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SY414 @ SV188 @ SV148 @ SV53 ) ) ) ) ) )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(964,plain,
! [SV116: $i,SV153: $i] :
( ( ( in @ ( sK11_C @ SV153 @ SV116 ) @ SV116 )
= $true )
| ( ( subset @ SV116 @ SV153 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(965,plain,
! [SV116: $i,SV153: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV153 @ SV116 ) @ SV153 ) )
= $true )
| ( ( subset @ SV116 @ SV153 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(966,plain,
! [SV154: $i,SV117: $i,SV215: $i] :
( ( ( ~ ( in @ SV215 @ SV117 ) )
= $true )
| ( ( in @ SV215 @ SV154 )
= $true )
| ( ( subset @ SV117 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(967,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV54 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV155 ) ) ) )
= $false )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[919]) ).
thf(968,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ~ ( ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV54 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV155 ) ) )
= $false )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[919]) ).
thf(969,plain,
! [SV156: $i,SV54: $i,SV190: $i] :
( ( ( ~ ! [SY415: $i] :
( ~ ( in @ SY415 @ SV190 )
| ( SY415 = SV54 )
| ( SY415 = SV156 ) )
| ~ ~ ( ~ ! [SY416: $i] :
( ( SY416 != SV54 )
| ( in @ SY416 @ SV190 ) )
| ~ ! [SY417: $i] :
( ( SY417 != SV156 )
| ( in @ SY417 @ SV190 ) ) ) )
= $false )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(970,plain,
! [SV124: $i,SV161: $i] :
( ( ( ( ( sK21_C @ SV161 @ SV124 )
!= SV124 )
| ~ ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 ) )
= $true )
| ( ( SV161
= ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(971,plain,
! [SV124: $i,SV161: $i] :
( ( ( ( ( sK21_C @ SV161 @ SV124 )
= SV124 )
| ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 ) )
= $true )
| ( ( SV161
= ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[923]) ).
thf(972,plain,
! [SV162: $i,SV125: $i] :
( ( ( ~ ! [SY382: $i] :
( ( SY382 != SV125 )
| ( in @ SY382 @ SV162 ) ) )
= $false )
| ( ( SV162
= ( singleton @ SV125 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(973,plain,
! [SV125: $i,SV162: $i] :
( ( ( ~ ! [SY383: $i] :
( ~ ( in @ SY383 @ SV162 )
| ( SY383 = SV125 ) ) )
= $false )
| ( ( SV162
= ( singleton @ SV125 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[924]) ).
thf(974,plain,
! [SV216: $i,SV206: $i] :
( ( ( ~ ( proper_subset @ SV206 @ SV216 ) )
= $true )
| ( ( ( SV206 != SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(975,plain,
! [SV217: $i,SV207: $i] :
( ( ( ~ ( proper_subset @ SV207 @ SV217 ) )
= $true )
| ( ( subset @ SV207 @ SV217 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(976,plain,
! [SV127: $i,SV164: $i] :
( ( ( in @ ( sK23_C @ SV164 @ SV127 ) @ SV127 )
= $true )
| ( ( disjoint @ SV127 @ SV164 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[928]) ).
thf(977,plain,
! [SV127: $i,SV164: $i] :
( ( ( in @ ( sK23_C @ SV164 @ SV127 ) @ SV164 )
= $true )
| ( ( disjoint @ SV127 @ SV164 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(978,plain,
! [SV165: $i,SV128: $i,SV208: $i] :
( ( ( in @ SV208 @ SV128 )
= $false )
| ( ( ~ ( in @ SV208 @ SV165 ) )
= $true )
| ( ( ~ ( disjoint @ SV128 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(979,plain,
! [SV55: $i,SV98: $i] :
( ( ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV98 )
= $false )
| ( ( in @ ( sK3_C @ SV98 @ SV55 ) @ SV55 )
= $false )
| ( ( SV55 = SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(980,plain,
! [SV129: $i,SV166: $i] :
( ( ( ~ ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
| ~ ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 ) )
= $true )
| ( ( SV166
= ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(981,plain,
! [SV129: $i,SV166: $i] :
( ( ( ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
| ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 ) )
= $true )
| ( ( SV166
= ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[933]) ).
thf(982,plain,
! [SV130: $i,SV167: $i] :
( ( ( ~ ! [SY385: $i] :
( ~ ( in @ SY385 @ SV167 )
| ( subset @ SY385 @ SV130 ) ) )
= $false )
| ( ( SV167
= ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[934]) ).
thf(983,plain,
! [SV167: $i,SV130: $i] :
( ( ( ~ ! [SY386: $i] :
( ~ ( subset @ SY386 @ SV130 )
| ( in @ SY386 @ SV167 ) ) )
= $false )
| ( ( SV167
= ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[934]) ).
thf(984,plain,
! [SV131: $i,SV168: $i] :
( ( ( ! [SY387: $i] :
( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SY387 )
| ~ ( in @ SY387 @ SV131 ) )
| ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(985,plain,
! [SV131: $i,SV168: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ ( sK9_SY191 @ SV168 @ SV131 ) )
| ~ ( in @ ( sK9_SY191 @ SV168 @ SV131 ) @ SV131 ) )
| ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[936]) ).
thf(986,plain,
! [SV169: $i,SV132: $i] :
( ( ( ~ ! [SY388: $i] :
( ! [SY356: $i] :
( ~ ( in @ SY388 @ SY356 )
| ~ ( in @ SY356 @ SV132 ) )
| ( in @ SY388 @ SV169 ) ) )
= $false )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(987,plain,
! [SV132: $i,SV169: $i] :
( ( ( ~ ! [SY390: $i] :
( ~ ( in @ SY390 @ SV169 )
| ~ ( ~ ( in @ SY390 @ ( sK7_D @ SY390 @ SV169 @ SV132 ) )
| ~ ( in @ ( sK7_D @ SY390 @ SV169 @ SV132 ) @ SV132 ) ) ) )
= $false )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[937]) ).
thf(988,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) ) ) )
= $false )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(989,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ~ ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) ) )
= $false )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[938]) ).
thf(990,plain,
! [SV171: $i,SV56: $i,SV192: $i] :
( ( ( ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV192 )
| ( in @ SY418 @ SV56 )
| ( in @ SY418 @ SV171 ) )
| ~ ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV56 )
| ( in @ SY419 @ SV192 ) )
| ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV171 )
| ( in @ SY420 @ SV192 ) ) ) )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(991,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) ) )
= $false )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(992,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) ) ) )
= $false )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[940]) ).
thf(993,plain,
! [SV194: $i,SV173: $i,SV57: $i] :
( ( ( ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV57 )
| ( in @ SY421 @ SV173 )
| ( in @ SY421 @ SV194 ) )
| ~ ~ ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV194 )
| ( in @ SY422 @ SV57 ) )
| ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV194 )
| ~ ( in @ SY423 @ SV173 ) ) ) )
= $false )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(994,plain,
! [SV218: $i,SV195: $i,SV99: $i,SV58: $i] :
( ( ( ( ordered_pair @ SV58 @ SV99 )
= ( ordered_pair @ SV195 @ SV218 ) )
= $false )
| ( ( SV58 = SV195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(995,plain,
! [SV209: $i,SV196: $i,SV99: $i,SV58: $i] :
( ( ( ( ordered_pair @ SV58 @ SV99 )
= ( ordered_pair @ SV196 @ SV209 ) )
= $false )
| ( ( SV99 = SV209 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(996,plain,
! [SV176: $i,SV197: $i,SV59: $i] :
( ( ( in @ SV59 @ SV197 )
= $false )
| ( ( ~ ( in @ SV176 @ SV197 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV59 @ SV176 ) @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(997,plain,
! [SV225: $i,SV219: $i,SV59: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV59 @ SV219 ) @ SV225 )
| ( in @ SV59 @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(998,plain,
! [SV226: $i,SV220: $i,SV59: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV59 @ SV220 ) @ SV226 )
| ( in @ SV220 @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(999,plain,
! [SV210: $i,SV180: $i,SV138: $i] :
( ( ( disjoint @ SV138 @ SV180 )
= $false )
| ( ( in @ SV210 @ ( set_intersection2 @ SV138 @ SV180 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(1000,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) ) )
= $false )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1001,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
| ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) ) ) )
= $false )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[949]) ).
thf(1002,plain,
! [SV199: $i,SV182: $i,SV60: $i] :
( ( ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV60 )
| ~ ( in @ SY426 @ SV182 )
| ( in @ SY426 @ SV199 ) )
| ~ ~ ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV199 )
| ( in @ SY427 @ SV60 ) )
| ~ ! [SY428: $i] :
( ~ ( in @ SY428 @ SV199 )
| ( in @ SY428 @ SV182 ) ) ) )
= $false )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(1003,plain,
! [SV141: $i,SV185: $i] :
( ( ( subset @ SV185 @ SV141 )
= $false )
| ( ( subset @ SV141 @ SV185 )
= $false )
| ( ( SV141 = SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[951]) ).
thf(1004,plain,
! [SV221: $i,SV211: $i] :
( ( ( ( SV211 != SV221 ) )
= $true )
| ( ( subset @ SV211 @ SV221 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(1005,plain,
! [SV222: $i,SV212: $i] :
( ( ( ( SV212 != SV222 ) )
= $true )
| ( ( subset @ SV222 @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1006,plain,
! [SV227: $i,SV200: $i] :
( ( ( subset @ SV200 @ ( singleton @ SV227 ) )
= $true )
| ( ( SV200 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1007,plain,
! [SV213: $i,SV201: $i] :
( ( ( SV201
= ( singleton @ SV213 ) )
= $false )
| ( ( subset @ SV201 @ ( singleton @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(1008,plain,
! [SV202: $i,SV97: $i,SV186: $i,SV52: $i] :
( ( ( in @ SV52 @ SV186 )
= $false )
| ( ( ~ ( in @ SV97 @ SV202 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV186 @ SV202 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1009,plain,
! [SV223: $i,SV97: $i,SV52: $i] :
( ( ( ! [SY439: $i] :
~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV223 @ SY439 ) ) )
= $true )
| ( ( in @ SV52 @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1010,plain,
! [SV228: $i,SV224: $i,SV97: $i,SV52: $i] :
( ( ~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV224 @ SV228 ) )
| ( in @ SV97 @ SV228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1011,plain,
! [SV229: $i,SV203: $i] :
( ( ( subset @ SV203 @ ( singleton @ SV229 ) )
= $true )
| ( ( SV203 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1012,plain,
! [SV214: $i,SV204: $i] :
( ( ( SV204
= ( singleton @ SV214 ) )
= $false )
| ( ( subset @ SV204 @ ( singleton @ SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1013,plain,
! [SV187: $i,SV147: $i,SV53: $i] :
( ( ( ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ SV53 )
| ~ ( in @ SY410 @ SV147 )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ SY409 @ SY410 ) ) )
| ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[961]) ).
thf(1014,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) @ SV147 ) )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) ) ) )
| ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[962]) ).
thf(1015,plain,
! [SV188: $i,SV148: $i,SV53: $i] :
( ( ( ~ ! [SY411: $i] :
( ! [SY373: $i,SY374: $i] :
( ~ ( in @ SY373 @ SV53 )
| ~ ( in @ SY374 @ SV148 )
| ( SY411
!= ( ordered_pair @ SY373 @ SY374 ) ) )
| ( in @ SY411 @ SV188 ) ) )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(1016,plain,
! [SV53: $i,SV148: $i,SV188: $i] :
( ( ( ~ ! [SY414: $i] :
( ~ ( in @ SY414 @ SV188 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY414 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SY414 @ SV188 @ SV148 @ SV53 ) @ SV148 ) )
| ( SY414
!= ( ordered_pair @ ( sK12_E @ SY414 @ SV188 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SY414 @ SV188 @ SV148 @ SV53 ) ) ) ) ) )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(1017,plain,
! [SV116: $i,SV153: $i] :
( ( ( in @ ( sK11_C @ SV153 @ SV116 ) @ SV153 )
= $false )
| ( ( subset @ SV116 @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1018,plain,
! [SV154: $i,SV117: $i,SV215: $i] :
( ( ( in @ SV215 @ SV117 )
= $false )
| ( ( in @ SV215 @ SV154 )
= $true )
| ( ( subset @ SV117 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1019,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV54 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV155 ) ) ) )
= $true )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[967]) ).
thf(1020,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV54 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV155 ) )
= $true )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[968]) ).
thf(1021,plain,
! [SV156: $i,SV54: $i,SV190: $i] :
( ( ( ~ ! [SY415: $i] :
( ~ ( in @ SY415 @ SV190 )
| ( SY415 = SV54 )
| ( SY415 = SV156 ) ) )
= $false )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[969]) ).
thf(1022,plain,
! [SV156: $i,SV190: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ! [SY416: $i] :
( ( SY416 != SV54 )
| ( in @ SY416 @ SV190 ) )
| ~ ! [SY417: $i] :
( ( SY417 != SV156 )
| ( in @ SY417 @ SV190 ) ) ) )
= $false )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[969]) ).
thf(1023,plain,
! [SV124: $i,SV161: $i] :
( ( ( ( ( sK21_C @ SV161 @ SV124 )
!= SV124 ) )
= $true )
| ( ( ~ ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 ) )
= $true )
| ( ( SV161
= ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1024,plain,
! [SV124: $i,SV161: $i] :
( ( ( ( sK21_C @ SV161 @ SV124 )
= SV124 )
= $true )
| ( ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 )
= $true )
| ( ( SV161
= ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1025,plain,
! [SV162: $i,SV125: $i] :
( ( ( ! [SY382: $i] :
( ( SY382 != SV125 )
| ( in @ SY382 @ SV162 ) ) )
= $true )
| ( ( SV162
= ( singleton @ SV125 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(1026,plain,
! [SV125: $i,SV162: $i] :
( ( ( ! [SY383: $i] :
( ~ ( in @ SY383 @ SV162 )
| ( SY383 = SV125 ) ) )
= $true )
| ( ( SV162
= ( singleton @ SV125 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1027,plain,
! [SV216: $i,SV206: $i] :
( ( ( proper_subset @ SV206 @ SV216 )
= $false )
| ( ( ( SV206 != SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1028,plain,
! [SV217: $i,SV207: $i] :
( ( ( proper_subset @ SV207 @ SV217 )
= $false )
| ( ( subset @ SV207 @ SV217 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(1029,plain,
! [SV128: $i,SV165: $i,SV208: $i] :
( ( ( in @ SV208 @ SV165 )
= $false )
| ( ( in @ SV208 @ SV128 )
= $false )
| ( ( ~ ( disjoint @ SV128 @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1030,plain,
! [SV129: $i,SV166: $i] :
( ( ( ~ ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 ) )
= $true )
| ( ( ~ ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 ) )
= $true )
| ( ( SV166
= ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1031,plain,
! [SV129: $i,SV166: $i] :
( ( ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
= $true )
| ( ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 )
= $true )
| ( ( SV166
= ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1032,plain,
! [SV130: $i,SV167: $i] :
( ( ( ! [SY385: $i] :
( ~ ( in @ SY385 @ SV167 )
| ( subset @ SY385 @ SV130 ) ) )
= $true )
| ( ( SV167
= ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[982]) ).
thf(1033,plain,
! [SV167: $i,SV130: $i] :
( ( ( ! [SY386: $i] :
( ~ ( subset @ SY386 @ SV130 )
| ( in @ SY386 @ SV167 ) ) )
= $true )
| ( ( SV167
= ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1034,plain,
! [SV131: $i,SV168: $i] :
( ( ( ! [SY387: $i] :
( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SY387 )
| ~ ( in @ SY387 @ SV131 ) ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1035,plain,
! [SV131: $i,SV168: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ ( sK9_SY191 @ SV168 @ SV131 ) )
| ~ ( in @ ( sK9_SY191 @ SV168 @ SV131 ) @ SV131 ) ) )
= $true )
| ( ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1036,plain,
! [SV169: $i,SV132: $i] :
( ( ( ! [SY388: $i] :
( ! [SY356: $i] :
( ~ ( in @ SY388 @ SY356 )
| ~ ( in @ SY356 @ SV132 ) )
| ( in @ SY388 @ SV169 ) ) )
= $true )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[986]) ).
thf(1037,plain,
! [SV132: $i,SV169: $i] :
( ( ( ! [SY390: $i] :
( ~ ( in @ SY390 @ SV169 )
| ~ ( ~ ( in @ SY390 @ ( sK7_D @ SY390 @ SV169 @ SV132 ) )
| ~ ( in @ ( sK7_D @ SY390 @ SV169 @ SV132 ) @ SV132 ) ) ) )
= $true )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[987]) ).
thf(1038,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) ) ) )
= $true )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1039,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) )
= $true )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1040,plain,
! [SV171: $i,SV56: $i,SV192: $i] :
( ( ( ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV192 )
| ( in @ SY418 @ SV56 )
| ( in @ SY418 @ SV171 ) ) )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1041,plain,
! [SV171: $i,SV192: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV56 )
| ( in @ SY419 @ SV192 ) )
| ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV171 )
| ( in @ SY420 @ SV192 ) ) ) )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1042,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
= $true )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[991]) ).
thf(1043,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) ) ) )
= $true )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1044,plain,
! [SV194: $i,SV173: $i,SV57: $i] :
( ( ( ~ ! [SY421: $i] :
( ~ ( in @ SY421 @ SV57 )
| ( in @ SY421 @ SV173 )
| ( in @ SY421 @ SV194 ) ) )
= $false )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1045,plain,
! [SV173: $i,SV57: $i,SV194: $i] :
( ( ( ~ ~ ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV194 )
| ( in @ SY422 @ SV57 ) )
| ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV194 )
| ~ ( in @ SY423 @ SV173 ) ) ) )
= $false )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1046,plain,
! [SV59: $i,SV197: $i,SV176: $i] :
( ( ( in @ SV176 @ SV197 )
= $false )
| ( ( in @ SV59 @ SV197 )
= $false )
| ( ( subset @ ( unordered_pair @ SV59 @ SV176 ) @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[996]) ).
thf(1047,plain,
! [SV225: $i,SV219: $i,SV59: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV59 @ SV219 ) @ SV225 ) )
= $true )
| ( ( in @ SV59 @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1048,plain,
! [SV226: $i,SV220: $i,SV59: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV59 @ SV220 ) @ SV226 ) )
= $true )
| ( ( in @ SV220 @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1049,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
= $true )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1050,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
| ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) ) ) )
= $true )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1051,plain,
! [SV199: $i,SV182: $i,SV60: $i] :
( ( ( ~ ! [SY426: $i] :
( ~ ( in @ SY426 @ SV60 )
| ~ ( in @ SY426 @ SV182 )
| ( in @ SY426 @ SV199 ) ) )
= $false )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1052,plain,
! [SV182: $i,SV60: $i,SV199: $i] :
( ( ( ~ ~ ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV199 )
| ( in @ SY427 @ SV60 ) )
| ~ ! [SY428: $i] :
( ~ ( in @ SY428 @ SV199 )
| ( in @ SY428 @ SV182 ) ) ) )
= $false )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1002]) ).
thf(1053,plain,
! [SV221: $i,SV211: $i] :
( ( ( SV211 = SV221 )
= $false )
| ( ( subset @ SV211 @ SV221 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1054,plain,
! [SV222: $i,SV212: $i] :
( ( ( SV212 = SV222 )
= $false )
| ( ( subset @ SV222 @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1055,plain,
! [SV186: $i,SV52: $i,SV202: $i,SV97: $i] :
( ( ( in @ SV97 @ SV202 )
= $false )
| ( ( in @ SV52 @ SV186 )
= $false )
| ( ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV186 @ SV202 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1056,plain,
! [SV230: $i,SV223: $i,SV97: $i,SV52: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV223 @ SV230 ) ) )
= $true )
| ( ( in @ SV52 @ SV223 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1057,plain,
! [SV228: $i,SV224: $i,SV97: $i,SV52: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV224 @ SV228 ) ) )
= $true )
| ( ( in @ SV97 @ SV228 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1058,plain,
! [SV187: $i,SV147: $i,SV53: $i] :
( ( ( ! [SY409: $i,SY410: $i] :
( ~ ( in @ SY409 @ SV53 )
| ~ ( in @ SY410 @ SV147 )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ SY409 @ SY410 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1059,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) @ SV147 ) )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) ) ) ) )
= $true )
| ( ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1060,plain,
! [SV188: $i,SV148: $i,SV53: $i] :
( ( ( ! [SY411: $i] :
( ! [SY373: $i,SY374: $i] :
( ~ ( in @ SY373 @ SV53 )
| ~ ( in @ SY374 @ SV148 )
| ( SY411
!= ( ordered_pair @ SY373 @ SY374 ) ) )
| ( in @ SY411 @ SV188 ) ) )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1015]) ).
thf(1061,plain,
! [SV53: $i,SV148: $i,SV188: $i] :
( ( ( ! [SY414: $i] :
( ~ ( in @ SY414 @ SV188 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY414 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SY414 @ SV188 @ SV148 @ SV53 ) @ SV148 ) )
| ( SY414
!= ( ordered_pair @ ( sK12_E @ SY414 @ SV188 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SY414 @ SV188 @ SV148 @ SV53 ) ) ) ) ) )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1062,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV54 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV155 ) ) )
= $false )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1063,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
= $true )
| ( ( ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV54 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV155 ) )
= $true )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1064,plain,
! [SV156: $i,SV54: $i,SV190: $i] :
( ( ( ! [SY415: $i] :
( ~ ( in @ SY415 @ SV190 )
| ( SY415 = SV54 )
| ( SY415 = SV156 ) ) )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1065,plain,
! [SV156: $i,SV190: $i,SV54: $i] :
( ( ( ~ ( ~ ! [SY416: $i] :
( ( SY416 != SV54 )
| ( in @ SY416 @ SV190 ) )
| ~ ! [SY417: $i] :
( ( SY417 != SV156 )
| ( in @ SY417 @ SV190 ) ) ) )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1022]) ).
thf(1066,plain,
! [SV124: $i,SV161: $i] :
( ( ( ( sK21_C @ SV161 @ SV124 )
= SV124 )
= $false )
| ( ( ~ ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 ) )
= $true )
| ( ( SV161
= ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1067,plain,
! [SV162: $i,SV125: $i,SV231: $i] :
( ( ( ( SV231 != SV125 )
| ( in @ SV231 @ SV162 ) )
= $true )
| ( ( SV162
= ( singleton @ SV125 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1068,plain,
! [SV125: $i,SV162: $i,SV232: $i] :
( ( ( ~ ( in @ SV232 @ SV162 )
| ( SV232 = SV125 ) )
= $true )
| ( ( SV162
= ( singleton @ SV125 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1069,plain,
! [SV216: $i,SV206: $i] :
( ( ( SV206 = SV216 )
= $false )
| ( ( proper_subset @ SV206 @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1070,plain,
! [SV208: $i,SV165: $i,SV128: $i] :
( ( ( disjoint @ SV128 @ SV165 )
= $false )
| ( ( in @ SV208 @ SV128 )
= $false )
| ( ( in @ SV208 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1071,plain,
! [SV129: $i,SV166: $i] :
( ( ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
= $false )
| ( ( ~ ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 ) )
= $true )
| ( ( SV166
= ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1072,plain,
! [SV130: $i,SV167: $i,SV233: $i] :
( ( ( ~ ( in @ SV233 @ SV167 )
| ( subset @ SV233 @ SV130 ) )
= $true )
| ( ( SV167
= ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1073,plain,
! [SV167: $i,SV130: $i,SV234: $i] :
( ( ( ~ ( subset @ SV234 @ SV130 )
| ( in @ SV234 @ SV167 ) )
= $true )
| ( ( SV167
= ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1074,plain,
! [SV235: $i,SV131: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV235 )
| ~ ( in @ SV235 @ SV131 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1075,plain,
! [SV131: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ ( sK9_SY191 @ SV168 @ SV131 ) )
| ~ ( in @ ( sK9_SY191 @ SV168 @ SV131 ) @ SV131 ) )
= $false )
| ( ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1076,plain,
! [SV169: $i,SV132: $i,SV236: $i] :
( ( ( ! [SY441: $i] :
( ~ ( in @ SV236 @ SY441 )
| ~ ( in @ SY441 @ SV132 ) )
| ( in @ SV236 @ SV169 ) )
= $true )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1077,plain,
! [SV132: $i,SV169: $i,SV237: $i] :
( ( ( ~ ( in @ SV237 @ SV169 )
| ~ ( ~ ( in @ SV237 @ ( sK7_D @ SV237 @ SV169 @ SV132 ) )
| ~ ( in @ ( sK7_D @ SV237 @ SV169 @ SV132 ) @ SV132 ) ) )
= $true )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1078,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) ) )
= $false )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1079,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
= $true )
| ( ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) )
= $true )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1080,plain,
! [SV171: $i,SV56: $i,SV192: $i] :
( ( ( ! [SY418: $i] :
( ~ ( in @ SY418 @ SV192 )
| ( in @ SY418 @ SV56 )
| ( in @ SY418 @ SV171 ) ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1081,plain,
! [SV171: $i,SV192: $i,SV56: $i] :
( ( ( ~ ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV56 )
| ( in @ SY419 @ SV192 ) )
| ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV171 )
| ( in @ SY420 @ SV192 ) ) ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1082,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
= $true )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1083,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) ) )
= $false )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1084,plain,
! [SV194: $i,SV173: $i,SV57: $i] :
( ( ( ! [SY421: $i] :
( ~ ( in @ SY421 @ SV57 )
| ( in @ SY421 @ SV173 )
| ( in @ SY421 @ SV194 ) ) )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1044]) ).
thf(1085,plain,
! [SV173: $i,SV57: $i,SV194: $i] :
( ( ( ~ ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV194 )
| ( in @ SY422 @ SV57 ) )
| ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV194 )
| ~ ( in @ SY423 @ SV173 ) ) ) )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1086,plain,
! [SV225: $i,SV219: $i,SV59: $i] :
( ( ( subset @ ( unordered_pair @ SV59 @ SV219 ) @ SV225 )
= $false )
| ( ( in @ SV59 @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1087,plain,
! [SV226: $i,SV220: $i,SV59: $i] :
( ( ( subset @ ( unordered_pair @ SV59 @ SV220 ) @ SV226 )
= $false )
| ( ( in @ SV220 @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1088,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
= $true )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1089,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
| ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) ) )
= $false )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1090,plain,
! [SV199: $i,SV182: $i,SV60: $i] :
( ( ( ! [SY426: $i] :
( ~ ( in @ SY426 @ SV60 )
| ~ ( in @ SY426 @ SV182 )
| ( in @ SY426 @ SV199 ) ) )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1051]) ).
thf(1091,plain,
! [SV182: $i,SV60: $i,SV199: $i] :
( ( ( ~ ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV199 )
| ( in @ SY427 @ SV60 ) )
| ~ ! [SY428: $i] :
( ~ ( in @ SY428 @ SV199 )
| ( in @ SY428 @ SV182 ) ) ) )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1092,plain,
! [SV230: $i,SV223: $i,SV97: $i,SV52: $i] :
( ( ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV223 @ SV230 ) )
= $false )
| ( ( in @ SV52 @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1093,plain,
! [SV228: $i,SV224: $i,SV97: $i,SV52: $i] :
( ( ( in @ ( ordered_pair @ SV52 @ SV97 ) @ ( cartesian_product2 @ SV224 @ SV228 ) )
= $false )
| ( ( in @ SV97 @ SV228 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1094,plain,
! [SV187: $i,SV147: $i,SV53: $i,SV238: $i] :
( ( ( ! [SY442: $i] :
( ~ ( in @ SV238 @ SV53 )
| ~ ( in @ SY442 @ SV147 )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ SV238 @ SY442 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1095,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) @ SV147 ) )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) ) ) )
= $false )
| ( ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1096,plain,
! [SV188: $i,SV239: $i,SV148: $i,SV53: $i] :
( ( ( ! [SY443: $i,SY444: $i] :
( ~ ( in @ SY443 @ SV53 )
| ~ ( in @ SY444 @ SV148 )
| ( SV239
!= ( ordered_pair @ SY443 @ SY444 ) ) )
| ( in @ SV239 @ SV188 ) )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1097,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ SV188 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV148 ) )
| ( SV240
!= ( ordered_pair @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) ) ) ) )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1098,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV54 ) ) )
= $false )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1099,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV155 ) ) )
= $false )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1100,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV54 )
= $true )
| ( ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV155 )
= $true )
| ( ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
= $true )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1101,plain,
! [SV156: $i,SV54: $i,SV190: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV190 )
| ( SV241 = SV54 )
| ( SV241 = SV156 ) )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1102,plain,
! [SV156: $i,SV190: $i,SV54: $i] :
( ( ( ~ ! [SY416: $i] :
( ( SY416 != SV54 )
| ( in @ SY416 @ SV190 ) )
| ~ ! [SY417: $i] :
( ( SY417 != SV156 )
| ( in @ SY417 @ SV190 ) ) )
= $false )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1103,plain,
! [SV124: $i,SV161: $i] :
( ( ( in @ ( sK21_C @ SV161 @ SV124 ) @ SV161 )
= $false )
| ( ( ( sK21_C @ SV161 @ SV124 )
= SV124 )
= $false )
| ( ( SV161
= ( singleton @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1104,plain,
! [SV162: $i,SV125: $i,SV231: $i] :
( ( ( ( SV231 != SV125 ) )
= $true )
| ( ( in @ SV231 @ SV162 )
= $true )
| ( ( SV162
= ( singleton @ SV125 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1067]) ).
thf(1105,plain,
! [SV125: $i,SV162: $i,SV232: $i] :
( ( ( ~ ( in @ SV232 @ SV162 ) )
= $true )
| ( ( SV232 = SV125 )
= $true )
| ( ( SV162
= ( singleton @ SV125 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1106,plain,
! [SV129: $i,SV166: $i] :
( ( ( subset @ ( sK19_C @ SV166 @ SV129 ) @ SV129 )
= $false )
| ( ( in @ ( sK19_C @ SV166 @ SV129 ) @ SV166 )
= $false )
| ( ( SV166
= ( powerset @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1107,plain,
! [SV130: $i,SV167: $i,SV233: $i] :
( ( ( ~ ( in @ SV233 @ SV167 ) )
= $true )
| ( ( subset @ SV233 @ SV130 )
= $true )
| ( ( SV167
= ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1108,plain,
! [SV167: $i,SV130: $i,SV234: $i] :
( ( ( ~ ( subset @ SV234 @ SV130 ) )
= $true )
| ( ( in @ SV234 @ SV167 )
= $true )
| ( ( SV167
= ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1073]) ).
thf(1109,plain,
! [SV235: $i,SV131: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV235 ) )
= $true )
| ( ( ~ ( in @ SV235 @ SV131 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1110,plain,
! [SV131: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ ( sK9_SY191 @ SV168 @ SV131 ) ) )
= $false )
| ( ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1111,plain,
! [SV131: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK9_SY191 @ SV168 @ SV131 ) @ SV131 ) )
= $false )
| ( ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1112,plain,
! [SV169: $i,SV132: $i,SV236: $i] :
( ( ( ! [SY441: $i] :
( ~ ( in @ SV236 @ SY441 )
| ~ ( in @ SY441 @ SV132 ) ) )
= $true )
| ( ( in @ SV236 @ SV169 )
= $true )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1113,plain,
! [SV132: $i,SV169: $i,SV237: $i] :
( ( ( ~ ( in @ SV237 @ SV169 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV237 @ ( sK7_D @ SV237 @ SV169 @ SV132 ) )
| ~ ( in @ ( sK7_D @ SV237 @ SV169 @ SV132 ) @ SV132 ) ) )
= $true )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1077]) ).
thf(1114,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 ) ) )
= $false )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1078]) ).
thf(1115,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) ) )
= $false )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1078]) ).
thf(1116,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 )
= $true )
| ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 )
= $true )
| ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
= $true )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1079]) ).
thf(1117,plain,
! [SV171: $i,SV56: $i,SV192: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV192 )
| ( in @ SV242 @ SV56 )
| ( in @ SV242 @ SV171 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1118,plain,
! [SV171: $i,SV192: $i,SV56: $i] :
( ( ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV56 )
| ( in @ SY419 @ SV192 ) )
| ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV171 )
| ( in @ SY420 @ SV192 ) ) )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1119,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 ) )
= $true )
| ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
= $true )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1120,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) ) )
= $false )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1121,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) ) )
= $false )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1083]) ).
thf(1122,plain,
! [SV194: $i,SV173: $i,SV57: $i,SV243: $i] :
( ( ( ~ ( in @ SV243 @ SV57 )
| ( in @ SV243 @ SV173 )
| ( in @ SV243 @ SV194 ) )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1123,plain,
! [SV173: $i,SV57: $i,SV194: $i] :
( ( ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV194 )
| ( in @ SY422 @ SV57 ) )
| ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV194 )
| ~ ( in @ SY423 @ SV173 ) ) )
= $false )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1124,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
= $true )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1125,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) ) )
= $false )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1126,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) ) )
= $false )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1089]) ).
thf(1127,plain,
! [SV199: $i,SV182: $i,SV60: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV60 )
| ~ ( in @ SV244 @ SV182 )
| ( in @ SV244 @ SV199 ) )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1128,plain,
! [SV182: $i,SV60: $i,SV199: $i] :
( ( ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV199 )
| ( in @ SY427 @ SV60 ) )
| ~ ! [SY428: $i] :
( ~ ( in @ SY428 @ SV199 )
| ( in @ SY428 @ SV182 ) ) )
= $false )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1129,plain,
! [SV187: $i,SV147: $i,SV245: $i,SV53: $i,SV238: $i] :
( ( ( ~ ( in @ SV238 @ SV53 )
| ~ ( in @ SV245 @ SV147 )
| ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ SV238 @ SV245 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1130,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) @ SV147 ) ) )
= $false )
| ( ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1131,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) ) ) )
= $false )
| ( ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1132,plain,
! [SV188: $i,SV239: $i,SV148: $i,SV53: $i] :
( ( ( ! [SY443: $i,SY444: $i] :
( ~ ( in @ SY443 @ SV53 )
| ~ ( in @ SY444 @ SV148 )
| ( SV239
!= ( ordered_pair @ SY443 @ SY444 ) ) ) )
= $true )
| ( ( in @ SV239 @ SV188 )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1133,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ SV188 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV148 ) )
| ( SV240
!= ( ordered_pair @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) ) ) ) )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1134,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV54 ) )
= $true )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1135,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
| ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV155 ) )
= $true )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1136,plain,
! [SV156: $i,SV54: $i,SV190: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV190 ) )
= $true )
| ( ( ( SV241 = SV54 )
| ( SV241 = SV156 ) )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1137,plain,
! [SV156: $i,SV190: $i,SV54: $i] :
( ( ( ~ ! [SY416: $i] :
( ( SY416 != SV54 )
| ( in @ SY416 @ SV190 ) ) )
= $false )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1102]) ).
thf(1138,plain,
! [SV54: $i,SV190: $i,SV156: $i] :
( ( ( ~ ! [SY417: $i] :
( ( SY417 != SV156 )
| ( in @ SY417 @ SV190 ) ) )
= $false )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1102]) ).
thf(1139,plain,
! [SV162: $i,SV125: $i,SV231: $i] :
( ( ( SV231 = SV125 )
= $false )
| ( ( in @ SV231 @ SV162 )
= $true )
| ( ( SV162
= ( singleton @ SV125 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1140,plain,
! [SV125: $i,SV162: $i,SV232: $i] :
( ( ( in @ SV232 @ SV162 )
= $false )
| ( ( SV232 = SV125 )
= $true )
| ( ( SV162
= ( singleton @ SV125 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1141,plain,
! [SV130: $i,SV167: $i,SV233: $i] :
( ( ( in @ SV233 @ SV167 )
= $false )
| ( ( subset @ SV233 @ SV130 )
= $true )
| ( ( SV167
= ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1142,plain,
! [SV167: $i,SV130: $i,SV234: $i] :
( ( ( subset @ SV234 @ SV130 )
= $false )
| ( ( in @ SV234 @ SV167 )
= $true )
| ( ( SV167
= ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1108]) ).
thf(1143,plain,
! [SV235: $i,SV131: $i,SV168: $i] :
( ( ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV235 )
= $false )
| ( ( ~ ( in @ SV235 @ SV131 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1144,plain,
! [SV131: $i,SV168: $i] :
( ( ( in @ ( sK8_C @ SV168 @ SV131 ) @ ( sK9_SY191 @ SV168 @ SV131 ) )
= $true )
| ( ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1145,plain,
! [SV131: $i,SV168: $i] :
( ( ( in @ ( sK9_SY191 @ SV168 @ SV131 ) @ SV131 )
= $true )
| ( ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1146,plain,
! [SV169: $i,SV132: $i,SV246: $i,SV236: $i] :
( ( ( ~ ( in @ SV236 @ SV246 )
| ~ ( in @ SV246 @ SV132 ) )
= $true )
| ( ( in @ SV236 @ SV169 )
= $true )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1147,plain,
! [SV132: $i,SV169: $i,SV237: $i] :
( ( ( in @ SV237 @ SV169 )
= $false )
| ( ( ~ ( ~ ( in @ SV237 @ ( sK7_D @ SV237 @ SV169 @ SV132 ) )
| ~ ( in @ ( sK7_D @ SV237 @ SV169 @ SV132 ) @ SV132 ) ) )
= $true )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1148,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 ) )
= $true )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1114]) ).
thf(1149,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
| ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) )
= $true )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1115]) ).
thf(1150,plain,
! [SV171: $i,SV56: $i,SV192: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV192 ) )
= $true )
| ( ( ( in @ SV242 @ SV56 )
| ( in @ SV242 @ SV171 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1117]) ).
thf(1151,plain,
! [SV171: $i,SV192: $i,SV56: $i] :
( ( ( ~ ! [SY419: $i] :
( ~ ( in @ SY419 @ SV56 )
| ( in @ SY419 @ SV192 ) ) )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1152,plain,
! [SV56: $i,SV192: $i,SV171: $i] :
( ( ( ~ ! [SY420: $i] :
( ~ ( in @ SY420 @ SV171 )
| ( in @ SY420 @ SV192 ) ) )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1153,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
= $false )
| ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
= $true )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1154,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
= $true )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1155,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
| ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 ) )
= $true )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1156,plain,
! [SV194: $i,SV173: $i,SV57: $i,SV243: $i] :
( ( ( ~ ( in @ SV243 @ SV57 )
| ( in @ SV243 @ SV173 ) )
= $true )
| ( ( in @ SV243 @ SV194 )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1157,plain,
! [SV173: $i,SV57: $i,SV194: $i] :
( ( ( ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SV194 )
| ( in @ SY422 @ SV57 ) ) )
= $false )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1123]) ).
thf(1158,plain,
! [SV57: $i,SV173: $i,SV194: $i] :
( ( ( ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV194 )
| ~ ( in @ SY423 @ SV173 ) ) )
= $false )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1123]) ).
thf(1159,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
= $false )
| ( ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
= $true )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1160,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
= $true )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1125]) ).
thf(1161,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
| ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
= $true )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1126]) ).
thf(1162,plain,
! [SV199: $i,SV182: $i,SV60: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV60 )
| ~ ( in @ SV244 @ SV182 ) )
= $true )
| ( ( in @ SV244 @ SV199 )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1163,plain,
! [SV182: $i,SV60: $i,SV199: $i] :
( ( ( ~ ! [SY427: $i] :
( ~ ( in @ SY427 @ SV199 )
| ( in @ SY427 @ SV60 ) ) )
= $false )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1164,plain,
! [SV60: $i,SV182: $i,SV199: $i] :
( ( ( ~ ! [SY428: $i] :
( ~ ( in @ SY428 @ SV199 )
| ( in @ SY428 @ SV182 ) ) )
= $false )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1128]) ).
thf(1165,plain,
! [SV187: $i,SV147: $i,SV245: $i,SV53: $i,SV238: $i] :
( ( ( ~ ( in @ SV238 @ SV53 )
| ~ ( in @ SV245 @ SV147 ) )
= $true )
| ( ( ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ SV238 @ SV245 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1166,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) @ SV147 ) ) )
= $true )
| ( ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1167,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( ( sK14_D @ SV187 @ SV147 @ SV53 )
= ( ordered_pair @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) ) )
= $true )
| ( ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1131]) ).
thf(1168,plain,
! [SV188: $i,SV239: $i,SV148: $i,SV53: $i,SV247: $i] :
( ( ( ! [SY445: $i] :
( ~ ( in @ SV247 @ SV53 )
| ~ ( in @ SY445 @ SV148 )
| ( SV239
!= ( ordered_pair @ SV247 @ SY445 ) ) ) )
= $true )
| ( ( in @ SV239 @ SV188 )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1169,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( in @ SV240 @ SV188 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV148 ) )
| ( SV240
!= ( ordered_pair @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) ) ) ) )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1170,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 ) )
= $true )
| ( ( ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV54 ) )
= $true )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1134]) ).
thf(1171,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 ) )
= $true )
| ( ( ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV155 ) )
= $true )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1172,plain,
! [SV156: $i,SV54: $i,SV190: $i,SV241: $i] :
( ( ( in @ SV241 @ SV190 )
= $false )
| ( ( ( SV241 = SV54 )
| ( SV241 = SV156 ) )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1173,plain,
! [SV156: $i,SV190: $i,SV54: $i] :
( ( ( ! [SY416: $i] :
( ( SY416 != SV54 )
| ( in @ SY416 @ SV190 ) ) )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1137]) ).
thf(1174,plain,
! [SV54: $i,SV190: $i,SV156: $i] :
( ( ( ! [SY417: $i] :
( ( SY417 != SV156 )
| ( in @ SY417 @ SV190 ) ) )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1138]) ).
thf(1175,plain,
! [SV168: $i,SV131: $i,SV235: $i] :
( ( ( in @ SV235 @ SV131 )
= $false )
| ( ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV235 )
= $false )
| ( ( ~ ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 ) )
= $true )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1176,plain,
! [SV169: $i,SV132: $i,SV246: $i,SV236: $i] :
( ( ( ~ ( in @ SV236 @ SV246 ) )
= $true )
| ( ( ~ ( in @ SV246 @ SV132 ) )
= $true )
| ( ( in @ SV236 @ SV169 )
= $true )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1177,plain,
! [SV132: $i,SV169: $i,SV237: $i] :
( ( ( ~ ( in @ SV237 @ ( sK7_D @ SV237 @ SV169 @ SV132 ) )
| ~ ( in @ ( sK7_D @ SV237 @ SV169 @ SV132 ) @ SV132 ) )
= $false )
| ( ( in @ SV237 @ SV169 )
= $false )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1178,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 ) )
= $true )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1179,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) )
= $true )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1180,plain,
! [SV171: $i,SV56: $i,SV192: $i,SV242: $i] :
( ( ( in @ SV242 @ SV192 )
= $false )
| ( ( ( in @ SV242 @ SV56 )
| ( in @ SV242 @ SV171 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1181,plain,
! [SV171: $i,SV192: $i,SV56: $i] :
( ( ( ! [SY419: $i] :
( ~ ( in @ SY419 @ SV56 )
| ( in @ SY419 @ SV192 ) ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1182,plain,
! [SV56: $i,SV192: $i,SV171: $i] :
( ( ( ! [SY420: $i] :
( ~ ( in @ SY420 @ SV171 )
| ( in @ SY420 @ SV192 ) ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1152]) ).
thf(1183,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 )
= $false )
| ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
= $true )
| ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
= $false )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1184,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV57 )
= $true )
| ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 )
= $true )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1185,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 ) )
= $true )
| ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 )
= $true )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1186,plain,
! [SV194: $i,SV173: $i,SV57: $i,SV243: $i] :
( ( ( ~ ( in @ SV243 @ SV57 ) )
= $true )
| ( ( in @ SV243 @ SV173 )
= $true )
| ( ( in @ SV243 @ SV194 )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1187,plain,
! [SV173: $i,SV57: $i,SV194: $i] :
( ( ( ! [SY422: $i] :
( ~ ( in @ SY422 @ SV194 )
| ( in @ SY422 @ SV57 ) ) )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1157]) ).
thf(1188,plain,
! [SV57: $i,SV173: $i,SV194: $i] :
( ( ( ! [SY423: $i] :
( ~ ( in @ SY423 @ SV194 )
| ~ ( in @ SY423 @ SV173 ) ) )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1158]) ).
thf(1189,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
= $false )
| ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
= $false )
| ( ( ~ ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 ) )
= $true )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1190,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
= $true )
| ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 )
= $true )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1191,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
= $true )
| ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 )
= $true )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1192,plain,
! [SV199: $i,SV182: $i,SV60: $i,SV244: $i] :
( ( ( ~ ( in @ SV244 @ SV60 ) )
= $true )
| ( ( ~ ( in @ SV244 @ SV182 ) )
= $true )
| ( ( in @ SV244 @ SV199 )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1193,plain,
! [SV182: $i,SV60: $i,SV199: $i] :
( ( ( ! [SY427: $i] :
( ~ ( in @ SY427 @ SV199 )
| ( in @ SY427 @ SV60 ) ) )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1163]) ).
thf(1194,plain,
! [SV60: $i,SV182: $i,SV199: $i] :
( ( ( ! [SY428: $i] :
( ~ ( in @ SY428 @ SV199 )
| ( in @ SY428 @ SV182 ) ) )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1164]) ).
thf(1195,plain,
! [SV187: $i,SV147: $i,SV245: $i,SV53: $i,SV238: $i] :
( ( ( ~ ( in @ SV238 @ SV53 ) )
= $true )
| ( ( ~ ( in @ SV245 @ SV147 ) )
= $true )
| ( ( ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ SV238 @ SV245 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1196,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( ~ ( in @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) @ SV147 ) )
= $false )
| ( ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1166]) ).
thf(1197,plain,
! [SV188: $i,SV239: $i,SV148: $i,SV248: $i,SV53: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV53 )
| ~ ( in @ SV248 @ SV148 )
| ( SV239
!= ( ordered_pair @ SV247 @ SV248 ) ) )
= $true )
| ( ( in @ SV239 @ SV188 )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1198,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV148 ) )
| ( SV240
!= ( ordered_pair @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) ) ) )
= $false )
| ( ( in @ SV240 @ SV188 )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1199,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
= $false )
| ( ( ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV54 ) )
= $true )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1200,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
= $false )
| ( ( ( ( sK18_D @ SV189 @ SV155 @ SV54 )
!= SV155 ) )
= $true )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1201,plain,
! [SV190: $i,SV156: $i,SV54: $i,SV241: $i] :
( ( ( SV241 = SV54 )
= $true )
| ( ( SV241 = SV156 )
= $true )
| ( ( in @ SV241 @ SV190 )
= $false )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1202,plain,
! [SV156: $i,SV190: $i,SV54: $i,SV249: $i] :
( ( ( ( SV249 != SV54 )
| ( in @ SV249 @ SV190 ) )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1203,plain,
! [SV54: $i,SV190: $i,SV156: $i,SV250: $i] :
( ( ( ( SV250 != SV156 )
| ( in @ SV250 @ SV190 ) )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1204,plain,
! [SV235: $i,SV131: $i,SV168: $i] :
( ( ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV168 )
= $false )
| ( ( in @ ( sK8_C @ SV168 @ SV131 ) @ SV235 )
= $false )
| ( ( in @ SV235 @ SV131 )
= $false )
| ( ( SV168
= ( union @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1205,plain,
! [SV169: $i,SV132: $i,SV246: $i,SV236: $i] :
( ( ( in @ SV236 @ SV246 )
= $false )
| ( ( ~ ( in @ SV246 @ SV132 ) )
= $true )
| ( ( in @ SV236 @ SV169 )
= $true )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1206,plain,
! [SV132: $i,SV169: $i,SV237: $i] :
( ( ( ~ ( in @ SV237 @ ( sK7_D @ SV237 @ SV169 @ SV132 ) ) )
= $false )
| ( ( in @ SV237 @ SV169 )
= $false )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1177]) ).
thf(1207,plain,
! [SV132: $i,SV169: $i,SV237: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV237 @ SV169 @ SV132 ) @ SV132 ) )
= $false )
| ( ( in @ SV237 @ SV169 )
= $false )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1177]) ).
thf(1208,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
= $false )
| ( ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 ) )
= $true )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1209,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
= $false )
| ( ( ~ ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 ) )
= $true )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1179]) ).
thf(1210,plain,
! [SV192: $i,SV171: $i,SV56: $i,SV242: $i] :
( ( ( in @ SV242 @ SV56 )
= $true )
| ( ( in @ SV242 @ SV171 )
= $true )
| ( ( in @ SV242 @ SV192 )
= $false )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1180]) ).
thf(1211,plain,
! [SV171: $i,SV192: $i,SV56: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV56 )
| ( in @ SV251 @ SV192 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1212,plain,
! [SV56: $i,SV192: $i,SV171: $i,SV252: $i] :
( ( ( ~ ( in @ SV252 @ SV171 )
| ( in @ SV252 @ SV192 ) )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1213,plain,
! [SV57: $i,SV172: $i,SV193: $i] :
( ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV172 )
= $false )
| ( ( in @ ( sK6_D @ SV193 @ SV172 @ SV57 ) @ SV193 )
= $true )
| ( ( SV193
= ( set_difference @ SV57 @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1214,plain,
! [SV194: $i,SV173: $i,SV57: $i,SV243: $i] :
( ( ( in @ SV243 @ SV57 )
= $false )
| ( ( in @ SV243 @ SV173 )
= $true )
| ( ( in @ SV243 @ SV194 )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1215,plain,
! [SV173: $i,SV57: $i,SV194: $i,SV253: $i] :
( ( ( ~ ( in @ SV253 @ SV194 )
| ( in @ SV253 @ SV57 ) )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1216,plain,
! [SV57: $i,SV173: $i,SV194: $i,SV254: $i] :
( ( ( ~ ( in @ SV254 @ SV194 )
| ~ ( in @ SV254 @ SV173 ) )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1217,plain,
! [SV60: $i,SV181: $i,SV198: $i] :
( ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV198 )
= $false )
| ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV60 )
= $false )
| ( ( in @ ( sK10_D @ SV198 @ SV181 @ SV60 ) @ SV181 )
= $false )
| ( ( SV198
= ( set_intersection2 @ SV60 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1218,plain,
! [SV199: $i,SV182: $i,SV60: $i,SV244: $i] :
( ( ( in @ SV244 @ SV60 )
= $false )
| ( ( ~ ( in @ SV244 @ SV182 ) )
= $true )
| ( ( in @ SV244 @ SV199 )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1219,plain,
! [SV182: $i,SV60: $i,SV199: $i,SV255: $i] :
( ( ( ~ ( in @ SV255 @ SV199 )
| ( in @ SV255 @ SV60 ) )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1220,plain,
! [SV60: $i,SV182: $i,SV199: $i,SV256: $i] :
( ( ( ~ ( in @ SV256 @ SV199 )
| ( in @ SV256 @ SV182 ) )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1221,plain,
! [SV187: $i,SV147: $i,SV245: $i,SV53: $i,SV238: $i] :
( ( ( in @ SV238 @ SV53 )
= $false )
| ( ( ~ ( in @ SV245 @ SV147 ) )
= $true )
| ( ( ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ SV238 @ SV245 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1222,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( ~ ( in @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ SV53 ) )
= $false )
| ( ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1196]) ).
thf(1223,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( ~ ( in @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) @ SV147 ) )
= $false )
| ( ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1196]) ).
thf(1224,plain,
! [SV188: $i,SV239: $i,SV148: $i,SV248: $i,SV53: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV53 )
| ~ ( in @ SV248 @ SV148 ) )
= $true )
| ( ( ( SV239
!= ( ordered_pair @ SV247 @ SV248 ) ) )
= $true )
| ( ( in @ SV239 @ SV188 )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1225,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV148 ) ) )
= $false )
| ( ( in @ SV240 @ SV188 )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1226,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( ( SV240
!= ( ordered_pair @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) ) ) )
= $false )
| ( ( in @ SV240 @ SV188 )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1198]) ).
thf(1227,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV54 )
= $false )
| ( ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
= $false )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1228,plain,
! [SV54: $i,SV155: $i,SV189: $i] :
( ( ( ( sK18_D @ SV189 @ SV155 @ SV54 )
= SV155 )
= $false )
| ( ( in @ ( sK18_D @ SV189 @ SV155 @ SV54 ) @ SV189 )
= $false )
| ( ( SV189
= ( unordered_pair @ SV54 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1229,plain,
! [SV156: $i,SV190: $i,SV54: $i,SV249: $i] :
( ( ( ( SV249 != SV54 ) )
= $true )
| ( ( in @ SV249 @ SV190 )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1230,plain,
! [SV54: $i,SV190: $i,SV156: $i,SV250: $i] :
( ( ( ( SV250 != SV156 ) )
= $true )
| ( ( in @ SV250 @ SV190 )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1231,plain,
! [SV169: $i,SV236: $i,SV132: $i,SV246: $i] :
( ( ( in @ SV246 @ SV132 )
= $false )
| ( ( in @ SV236 @ SV246 )
= $false )
| ( ( in @ SV236 @ SV169 )
= $true )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1205]) ).
thf(1232,plain,
! [SV132: $i,SV169: $i,SV237: $i] :
( ( ( in @ SV237 @ ( sK7_D @ SV237 @ SV169 @ SV132 ) )
= $true )
| ( ( in @ SV237 @ SV169 )
= $false )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1206]) ).
thf(1233,plain,
! [SV132: $i,SV169: $i,SV237: $i] :
( ( ( in @ ( sK7_D @ SV237 @ SV169 @ SV132 ) @ SV132 )
= $true )
| ( ( in @ SV237 @ SV169 )
= $false )
| ( ( SV169
= ( union @ SV132 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1207]) ).
thf(1234,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV56 )
= $false )
| ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
= $false )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1235,plain,
! [SV56: $i,SV170: $i,SV191: $i] :
( ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV170 )
= $false )
| ( ( in @ ( sK17_D @ SV191 @ SV170 @ SV56 ) @ SV191 )
= $false )
| ( ( SV191
= ( set_union2 @ SV56 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1236,plain,
! [SV171: $i,SV192: $i,SV56: $i,SV251: $i] :
( ( ( ~ ( in @ SV251 @ SV56 ) )
= $true )
| ( ( in @ SV251 @ SV192 )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1211]) ).
thf(1237,plain,
! [SV56: $i,SV192: $i,SV171: $i,SV252: $i] :
( ( ( ~ ( in @ SV252 @ SV171 ) )
= $true )
| ( ( in @ SV252 @ SV192 )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1238,plain,
! [SV173: $i,SV57: $i,SV194: $i,SV253: $i] :
( ( ( ~ ( in @ SV253 @ SV194 ) )
= $true )
| ( ( in @ SV253 @ SV57 )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1239,plain,
! [SV57: $i,SV173: $i,SV194: $i,SV254: $i] :
( ( ( ~ ( in @ SV254 @ SV194 ) )
= $true )
| ( ( ~ ( in @ SV254 @ SV173 ) )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1240,plain,
! [SV199: $i,SV60: $i,SV182: $i,SV244: $i] :
( ( ( in @ SV244 @ SV182 )
= $false )
| ( ( in @ SV244 @ SV60 )
= $false )
| ( ( in @ SV244 @ SV199 )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1241,plain,
! [SV182: $i,SV60: $i,SV199: $i,SV255: $i] :
( ( ( ~ ( in @ SV255 @ SV199 ) )
= $true )
| ( ( in @ SV255 @ SV60 )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1219]) ).
thf(1242,plain,
! [SV60: $i,SV182: $i,SV199: $i,SV256: $i] :
( ( ( ~ ( in @ SV256 @ SV199 ) )
= $true )
| ( ( in @ SV256 @ SV182 )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1243,plain,
! [SV187: $i,SV53: $i,SV238: $i,SV147: $i,SV245: $i] :
( ( ( in @ SV245 @ SV147 )
= $false )
| ( ( in @ SV238 @ SV53 )
= $false )
| ( ( ( ( sK14_D @ SV187 @ SV147 @ SV53 )
!= ( ordered_pair @ SV238 @ SV245 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1244,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( in @ ( sK15_SY195 @ SV187 @ SV147 @ SV53 ) @ SV53 )
= $true )
| ( ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1222]) ).
thf(1245,plain,
! [SV53: $i,SV147: $i,SV187: $i] :
( ( ( in @ ( sK16_SY197 @ SV187 @ SV147 @ SV53 ) @ SV147 )
= $true )
| ( ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1223]) ).
thf(1246,plain,
! [SV188: $i,SV239: $i,SV148: $i,SV248: $i,SV53: $i,SV247: $i] :
( ( ( ~ ( in @ SV247 @ SV53 ) )
= $true )
| ( ( ~ ( in @ SV248 @ SV148 ) )
= $true )
| ( ( ( SV239
!= ( ordered_pair @ SV247 @ SV248 ) ) )
= $true )
| ( ( in @ SV239 @ SV188 )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1247,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV148 ) ) )
= $true )
| ( ( in @ SV240 @ SV188 )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1248,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( SV240
= ( ordered_pair @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) ) )
= $true )
| ( ( in @ SV240 @ SV188 )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1226]) ).
thf(1249,plain,
! [SV156: $i,SV190: $i,SV54: $i,SV249: $i] :
( ( ( SV249 = SV54 )
= $false )
| ( ( in @ SV249 @ SV190 )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1250,plain,
! [SV54: $i,SV190: $i,SV156: $i,SV250: $i] :
( ( ( SV250 = SV156 )
= $false )
| ( ( in @ SV250 @ SV190 )
= $true )
| ( ( SV190
= ( unordered_pair @ SV54 @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1251,plain,
! [SV171: $i,SV192: $i,SV56: $i,SV251: $i] :
( ( ( in @ SV251 @ SV56 )
= $false )
| ( ( in @ SV251 @ SV192 )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1252,plain,
! [SV56: $i,SV192: $i,SV171: $i,SV252: $i] :
( ( ( in @ SV252 @ SV171 )
= $false )
| ( ( in @ SV252 @ SV192 )
= $true )
| ( ( SV192
= ( set_union2 @ SV56 @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1253,plain,
! [SV173: $i,SV57: $i,SV194: $i,SV253: $i] :
( ( ( in @ SV253 @ SV194 )
= $false )
| ( ( in @ SV253 @ SV57 )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1254,plain,
! [SV57: $i,SV173: $i,SV194: $i,SV254: $i] :
( ( ( in @ SV254 @ SV194 )
= $false )
| ( ( ~ ( in @ SV254 @ SV173 ) )
= $true )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1239]) ).
thf(1255,plain,
! [SV182: $i,SV60: $i,SV199: $i,SV255: $i] :
( ( ( in @ SV255 @ SV199 )
= $false )
| ( ( in @ SV255 @ SV60 )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1256,plain,
! [SV60: $i,SV182: $i,SV199: $i,SV256: $i] :
( ( ( in @ SV256 @ SV199 )
= $false )
| ( ( in @ SV256 @ SV182 )
= $true )
| ( ( SV199
= ( set_intersection2 @ SV60 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1257,plain,
! [SV245: $i,SV238: $i,SV53: $i,SV147: $i,SV187: $i] :
( ( ( ( sK14_D @ SV187 @ SV147 @ SV53 )
= ( ordered_pair @ SV238 @ SV245 ) )
= $false )
| ( ( in @ SV238 @ SV53 )
= $false )
| ( ( in @ SV245 @ SV147 )
= $false )
| ( ( ~ ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 ) )
= $true )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1243]) ).
thf(1258,plain,
! [SV188: $i,SV239: $i,SV148: $i,SV248: $i,SV53: $i,SV247: $i] :
( ( ( in @ SV247 @ SV53 )
= $false )
| ( ( ~ ( in @ SV248 @ SV148 ) )
= $true )
| ( ( ( SV239
!= ( ordered_pair @ SV247 @ SV248 ) ) )
= $true )
| ( ( in @ SV239 @ SV188 )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1246]) ).
thf(1259,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV53 )
| ~ ( in @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV148 ) )
= $false )
| ( ( in @ SV240 @ SV188 )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1260,plain,
! [SV57: $i,SV194: $i,SV173: $i,SV254: $i] :
( ( ( in @ SV254 @ SV173 )
= $false )
| ( ( in @ SV254 @ SV194 )
= $false )
| ( ( SV194
= ( set_difference @ SV57 @ SV173 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1261,plain,
! [SV238: $i,SV245: $i,SV53: $i,SV147: $i,SV187: $i] :
( ( ( in @ ( sK14_D @ SV187 @ SV147 @ SV53 ) @ SV187 )
= $false )
| ( ( in @ SV245 @ SV147 )
= $false )
| ( ( in @ SV238 @ SV53 )
= $false )
| ( ( ( sK14_D @ SV187 @ SV147 @ SV53 )
= ( ordered_pair @ SV238 @ SV245 ) )
= $false )
| ( ( SV187
= ( cartesian_product2 @ SV53 @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1262,plain,
! [SV188: $i,SV239: $i,SV53: $i,SV247: $i,SV148: $i,SV248: $i] :
( ( ( in @ SV248 @ SV148 )
= $false )
| ( ( in @ SV247 @ SV53 )
= $false )
| ( ( ( SV239
!= ( ordered_pair @ SV247 @ SV248 ) ) )
= $true )
| ( ( in @ SV239 @ SV188 )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1263,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV53 ) )
= $false )
| ( ( in @ SV240 @ SV188 )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1264,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV148 ) )
= $false )
| ( ( in @ SV240 @ SV188 )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1265,plain,
! [SV188: $i,SV148: $i,SV53: $i,SV248: $i,SV247: $i,SV239: $i] :
( ( ( SV239
= ( ordered_pair @ SV247 @ SV248 ) )
= $false )
| ( ( in @ SV247 @ SV53 )
= $false )
| ( ( in @ SV248 @ SV148 )
= $false )
| ( ( in @ SV239 @ SV188 )
= $true )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1266,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( in @ ( sK12_E @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV53 )
= $true )
| ( ( in @ SV240 @ SV188 )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1263]) ).
thf(1267,plain,
! [SV53: $i,SV148: $i,SV188: $i,SV240: $i] :
( ( ( in @ ( sK13_SY192 @ SV240 @ SV188 @ SV148 @ SV53 ) @ SV148 )
= $true )
| ( ( in @ SV240 @ SV188 )
= $false )
| ( ( SV188
= ( cartesian_product2 @ SV53 @ SV148 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1264]) ).
thf(1268,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[271,1267,1266,1265,1261,1260,1256,1255,1253,1252,1251,1250,1249,1248,1245,1244,1240,1235,1234,1233,1232,1231,1228,1227,1217,1214,1213,1210,1204,1201,1191,1190,1184,1183,1167,1145,1144,1142,1141,1140,1139,1116,1106,1103,1100,1093,1092,1087,1086,1070,1069,1055,1054,1053,1046,1031,1028,1024,1018,1017,1012,1011,1007,1006,1003,999,995,994,979,977,976,964,944,925,921,911,905,901,900,896,895,880,871,870,868,867,862,861,860,859,847,846,845,844,843,834,828,784,778,740,718,717,716,715,714,711,710,709,704,648,647,646,640,637,636,634,630,628,625,571,567,556,546,494,490,489,488,487,481,477,474,472,471,465,457,429,425,424,423,422,420,419,417,416,401,390,348,336,329,328,327,326,325,324,323,322,321,320,319]) ).
thf(1269,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU163+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 13:06:22 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.37 ..
% 0.20/0.39
% 0.20/0.39 No.of.Axioms: 92
% 0.20/0.39
% 0.20/0.39 Length.of.Defs: 0
% 0.20/0.39
% 0.20/0.39 Contains.Choice.Funs: false
% 0.20/0.43 ..
% 0.20/0.45 (rf:0,axioms:92,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:94,loop_count:0,foatp_calls:0,translation:fof_full)..........................................................................................
% 0.71/1.00
% 0.71/1.00 ********************************
% 0.71/1.00 * All subproblems solved! *
% 0.71/1.00 ********************************
% 0.71/1.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:93,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:1268,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.13/1.34
% 1.13/1.34 %**** Beginning of derivation protocol ****
% 1.13/1.34 % SZS output start CNFRefutation
% See solution above
% 1.13/1.34
% 1.13/1.34 %**** End of derivation protocol ****
% 1.13/1.34 %**** no. of clauses in derivation: 1269 ****
% 1.13/1.34 %**** clause counter: 1268 ****
% 1.13/1.34
% 1.13/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:93,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:1268,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------