TSTP Solution File: SEU160+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU160+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 : n006.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 12:07:20 EDT 2022
% Result : Theorem 1.03s 1.27s
% Output : CNFRefutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 128
% Syntax : Number of formulae : 2241 (1156 unt; 38 typ; 0 def)
% Number of atoms : 14965 (5933 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 32675 (6061 ~;5289 |; 250 &;20954 @)
% ( 65 <=>; 56 =>; 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 : 6763 ( 0 ^6749 !; 14 ?;6763 :)
% 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_SY186,type,
sK13_SY186: $i > $i > $i > $i > $i ).
thf(tp_sK14_D,type,
sK14_D: $i > $i > $i > $i ).
thf(tp_sK15_SY189,type,
sK15_SY189: $i > $i > $i > $i ).
thf(tp_sK16_SY191,type,
sK16_SY191: $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_SY183,type,
sK2_SY183: $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_SY185,type,
sK9_SY185: $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(5,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(7,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(8,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(11,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(12,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(19,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(41,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(53,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(55,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(57,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(62,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(68,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(71,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(74,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(77,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(87,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(89,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(90,conjecture,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(91,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[90]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[91]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(96,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(97,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(99,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(100,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(101,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(102,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(103,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(104,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(106,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(111,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(112,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(113,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(114,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(115,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(116,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(117,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(118,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(119,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(120,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(121,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(122,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(123,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(124,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(125,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(126,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(127,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(128,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(129,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(130,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(131,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(132,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(133,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(134,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(135,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(137,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(138,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(139,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(141,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(142,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(143,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(144,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(145,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(146,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(147,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(148,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(149,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(150,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)],[58]) ).
thf(151,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(152,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(153,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(154,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(155,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(156,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(157,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)],[65]) ).
thf(158,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(159,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(160,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(161,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)],[69]) ).
thf(162,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)],[70]) ).
thf(163,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(164,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(165,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)],[73]) ).
thf(166,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(167,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(168,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)],[76]) ).
thf(169,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(170,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(171,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)],[79]) ).
thf(172,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)],[80]) ).
thf(173,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(174,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(175,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)],[83]) ).
thf(176,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(177,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(178,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(179,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(180,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(181,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(182,plain,
( ( ! [SY183: $i] :
( ( subset @ sK1_A @ ( singleton @ SY183 ) )
<=> ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ SY183 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(183,plain,
( ( ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) )
<=> ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY183 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[182]) ).
thf(184,plain,
( ( ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) )
=> ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY183 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[183]) ).
thf(185,plain,
( ( ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY183 ) ) )
=> ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[183]) ).
thf(186,plain,
( ( ~ ( ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) )
=> ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY183 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[184]) ).
thf(187,plain,
( ( ~ ( ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY183 ) ) )
=> ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[185]) ).
thf(188,plain,
( ( ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) )
& ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY183 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(189,plain,
( ( ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY183 ) ) )
& ~ ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[187]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(191,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(192,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(193,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)],[98]) ).
thf(194,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(195,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(196,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(197,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(198,plain,
( ( ! [A: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(199,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(200,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(201,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(202,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(203,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)],[122]) ).
thf(204,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)],[123]) ).
thf(205,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)],[125]) ).
thf(206,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY184: $i] :
( ~ ( in @ ( sK8_C @ B @ A ) @ SY184 )
| ~ ( in @ SY184 @ A ) )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK8_C @ B @ A ) @ ( sK9_SY185 @ B @ A ) )
& ( in @ ( sK9_SY185 @ 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)],[126]) ).
thf(207,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)],[127]) ).
thf(208,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)],[128]) ).
thf(209,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY187: $i,SY188: $i] :
( ~ ( in @ SY187 @ A )
| ~ ( in @ SY188 @ B )
| ( ( sK14_D @ C @ B @ A )
!= ( ordered_pair @ SY187 @ SY188 ) ) )
| ~ ( in @ ( sK14_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK15_SY189 @ C @ B @ A ) @ A )
& ( in @ ( sK16_SY191 @ C @ B @ A ) @ B )
& ( ( sK14_D @ C @ B @ A )
= ( ordered_pair @ ( sK15_SY189 @ C @ B @ A ) @ ( sK16_SY191 @ 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_SY186 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK12_E @ D @ C @ B @ A ) @ ( sK13_SY186 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[129]) ).
thf(210,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)],[130]) ).
thf(211,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)],[131]) ).
thf(212,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)],[132]) ).
thf(213,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)],[133]) ).
thf(214,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)],[134]) ).
thf(215,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)],[135]) ).
thf(216,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(217,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[140]) ).
thf(218,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(219,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(220,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)],[143]) ).
thf(221,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)],[144]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(223,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(225,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)],[150]) ).
thf(226,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(227,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[154]) ).
thf(228,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)],[155]) ).
thf(229,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)],[157]) ).
thf(230,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)],[158]) ).
thf(231,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)],[159]) ).
thf(232,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)],[161]) ).
thf(233,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)],[162]) ).
thf(234,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(235,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)],[165]) ).
thf(236,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(237,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)],[168]) ).
thf(238,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[170]) ).
thf(239,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)],[171]) ).
thf(240,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)],[172]) ).
thf(241,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[173]) ).
thf(242,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)],[174]) ).
thf(243,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)],[175]) ).
thf(244,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)],[176]) ).
thf(245,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)],[177]) ).
thf(246,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(247,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(248,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[180]) ).
thf(249,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(250,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(251,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(252,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(253,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(254,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)],[245]) ).
thf(255,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)],[244]) ).
thf(256,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)],[243]) ).
thf(257,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)],[242]) ).
thf(258,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(259,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)],[240]) ).
thf(260,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)],[239]) ).
thf(261,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(263,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(264,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(265,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(266,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(267,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(268,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(269,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(270,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)],[232]) ).
thf(271,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(272,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)],[231]) ).
thf(273,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)],[230]) ).
thf(274,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)],[229]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(276,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)],[228]) ).
thf(277,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(278,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(279,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(280,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(281,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)],[225]) ).
thf(282,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(283,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(284,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(285,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(286,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(287,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)],[221]) ).
thf(288,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(289,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(290,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(291,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(292,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(293,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(294,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(295,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(296,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)],[215]) ).
thf(297,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)],[214]) ).
thf(298,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)],[213]) ).
thf(299,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)],[212]) ).
thf(300,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)],[211]) ).
thf(301,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)],[210]) ).
thf(302,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY187: $i,SY188: $i] :
( ~ ( in @ SY187 @ A )
| ~ ( in @ SY188 @ B )
| ( ( sK14_D @ C @ B @ A )
!= ( ordered_pair @ SY187 @ SY188 ) ) )
| ~ ( in @ ( sK14_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK15_SY189 @ C @ B @ A ) @ A )
& ( in @ ( sK16_SY191 @ C @ B @ A ) @ B )
& ( ( sK14_D @ C @ B @ A )
= ( ordered_pair @ ( sK15_SY189 @ C @ B @ A ) @ ( sK16_SY191 @ 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_SY186 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK12_E @ D @ C @ B @ A ) @ ( sK13_SY186 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(303,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)],[208]) ).
thf(304,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)],[207]) ).
thf(305,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY184: $i] :
( ~ ( in @ ( sK8_C @ B @ A ) @ SY184 )
| ~ ( in @ SY184 @ A ) )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK8_C @ B @ A ) @ ( sK9_SY185 @ B @ A ) )
& ( in @ ( sK9_SY185 @ 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)],[206]) ).
thf(306,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)],[205]) ).
thf(307,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(308,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)],[204]) ).
thf(309,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)],[203]) ).
thf(310,plain,
$true = $true,
inference(copy,[status(thm)],[121]) ).
thf(311,plain,
$true = $true,
inference(copy,[status(thm)],[120]) ).
thf(312,plain,
$true = $true,
inference(copy,[status(thm)],[119]) ).
thf(313,plain,
$true = $true,
inference(copy,[status(thm)],[118]) ).
thf(314,plain,
$true = $true,
inference(copy,[status(thm)],[117]) ).
thf(315,plain,
$true = $true,
inference(copy,[status(thm)],[116]) ).
thf(316,plain,
$true = $true,
inference(copy,[status(thm)],[115]) ).
thf(317,plain,
$true = $true,
inference(copy,[status(thm)],[114]) ).
thf(318,plain,
$true = $true,
inference(copy,[status(thm)],[113]) ).
thf(319,plain,
$true = $true,
inference(copy,[status(thm)],[112]) ).
thf(320,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(321,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(322,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(323,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(324,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(325,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(326,plain,
( ( ! [A: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(327,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(328,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(329,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(330,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(331,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(332,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(333,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)],[193]) ).
thf(334,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(335,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(336,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(337,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(338,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(339,plain,
( ( ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) )
& ( sK1_A != empty_set )
& ( sK1_A
!= ( singleton @ sK2_SY183 ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(340,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)],[287]) ).
thf(341,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)],[255]) ).
thf(342,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)],[300]) ).
thf(343,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)],[304]) ).
thf(344,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)],[299]) ).
thf(345,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)],[254]) ).
thf(346,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)],[309]) ).
thf(347,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)],[298]) ).
thf(348,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)],[281]) ).
thf(349,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)],[274]) ).
thf(350,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)],[259]) ).
thf(351,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)],[296]) ).
thf(352,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)],[306]) ).
thf(353,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)],[301]) ).
thf(354,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)],[308]) ).
thf(355,plain,
( ( ~ ( ~ ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) )
| ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY183 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(356,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)],[257]) ).
thf(357,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)],[273]) ).
thf(358,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)],[303]) ).
thf(359,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)],[270]) ).
thf(360,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)],[333]) ).
thf(361,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)],[276]) ).
thf(362,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)],[297]) ).
thf(363,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_SY185 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_SY185 @ 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)],[305]) ).
thf(364,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)],[272]) ).
thf(365,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_SY189 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK16_SY191 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK14_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK15_SY189 @ SX2 @ SX1 @ SX0 ) @ ( sK16_SY191 @ 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_SY186 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK12_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY186 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(366,plain,
! [SV1: $i] :
( ( ( ( singleton @ SV1 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(367,plain,
! [SV2: $i] :
( ( ! [SY192: $i] :
( ~ ( in @ SV2 @ SY192 )
| ( ( set_union2 @ ( singleton @ SV2 ) @ SY192 )
= SY192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(368,plain,
! [SV3: $i] :
( ( ! [SY193: $i] :
( ~ ( disjoint @ ( singleton @ SV3 ) @ SY193 )
| ~ ( in @ SV3 @ SY193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(369,plain,
! [SV4: $i] :
( ( ! [SY194: $i] :
( ( in @ SV4 @ SY194 )
| ( disjoint @ ( singleton @ SV4 ) @ SY194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(370,plain,
! [SV5: $i] :
( ( ! [SY195: $i] :
( ~ ( subset @ SV5 @ SY195 )
| ! [SY196: $i] :
( ( in @ SY196 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SY195 @ ( singleton @ SY196 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(371,plain,
! [SV6: $i] :
( ( ! [SY197: $i] :
( ~ ( in @ SV6 @ SY197 )
| ( subset @ SV6 @ ( union @ SY197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(372,plain,
! [SV7: $i] :
( ( ! [SY198: $i,SY199: $i,SY200: $i] :
( ( SV7 = SY200 )
| ( SV7 = SY199 )
| ( ( unordered_pair @ SV7 @ SY198 )
!= ( unordered_pair @ SY199 @ SY200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(373,plain,
! [SV8: $i] :
( ( ! [SY201: $i] :
( ~ ( subset @ SV8 @ SY201 )
| ( ( set_union2 @ SV8 @ SY201 )
= SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(374,plain,
! [SV9: $i] :
( ( ! [SY202: $i] : ( subset @ ( set_intersection2 @ SV9 @ SY202 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(375,plain,
! [SV10: $i] :
( ( ! [SY203: $i,SY204: $i] :
( ~ ( subset @ SV10 @ SY203 )
| ~ ( subset @ SV10 @ SY204 )
| ( subset @ SV10 @ ( set_intersection2 @ SY203 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(376,plain,
! [SV11: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ~ ( subset @ SV11 @ SY205 )
| ~ ( subset @ SY205 @ SY206 )
| ( subset @ SV11 @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(377,plain,
! [SV12: $i] :
( ( ! [SY207: $i] :
( ~ ( subset @ SV12 @ SY207 )
| ! [SY208: $i] : ( subset @ ( set_intersection2 @ SV12 @ SY208 ) @ ( set_intersection2 @ SY207 @ SY208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(378,plain,
! [SV13: $i] :
( ( ! [SY209: $i] :
( ~ ( subset @ SV13 @ SY209 )
| ( ( set_intersection2 @ SV13 @ SY209 )
= SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(379,plain,
! [SV14: $i] :
( ( subset @ empty_set @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(380,plain,
! [SV15: $i] :
( ( ! [SY210: $i] :
( ~ ( subset @ SV15 @ SY210 )
| ! [SY211: $i] : ( subset @ ( set_difference @ SV15 @ SY211 ) @ ( set_difference @ SY210 @ SY211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(381,plain,
! [SV16: $i] :
( ( ! [SY212: $i] : ( subset @ ( set_difference @ SV16 @ SY212 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(382,plain,
! [SV17: $i] :
( ( ! [SY213: $i] :
( ( set_union2 @ SV17 @ ( set_difference @ SY213 @ SV17 ) )
= ( set_union2 @ SV17 @ SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(383,plain,
! [SV18: $i] :
( ( ~ ( subset @ SV18 @ empty_set )
| ( SV18 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(384,plain,
! [SV19: $i] :
( ( ! [SY214: $i] :
( ( set_difference @ ( set_union2 @ SV19 @ SY214 ) @ SY214 )
= ( set_difference @ SV19 @ SY214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(385,plain,
! [SV20: $i] :
( ( ! [SY215: $i] :
( ~ ( subset @ SV20 @ SY215 )
| ( SY215
= ( set_union2 @ SV20 @ ( set_difference @ SY215 @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(386,plain,
! [SV21: $i] :
( ( ! [SY216: $i] :
( ( set_difference @ SV21 @ ( set_difference @ SV21 @ SY216 ) )
= ( set_intersection2 @ SV21 @ SY216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(387,plain,
! [SV22: $i] :
( ( ! [SY217: $i] :
( ~ ( proper_subset @ SY217 @ SV22 )
| ~ ( subset @ SV22 @ SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(388,plain,
! [SV23: $i] :
( ( ! [SY218: $i,SY219: $i] :
( ~ ( disjoint @ SY218 @ SY219 )
| ~ ( subset @ SV23 @ SY218 )
| ( disjoint @ SV23 @ SY219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(389,plain,
! [SV24: $i] :
( ( ( unordered_pair @ SV24 @ SV24 )
= ( singleton @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(390,plain,
! [SV25: $i] :
( ( ! [SY220: $i] :
( ~ ( subset @ ( singleton @ SV25 ) @ ( singleton @ SY220 ) )
| ( SV25 = SY220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(391,plain,
! [SV26: $i] :
( ( ! [SY221: $i] : ( subset @ SV26 @ ( set_union2 @ SV26 @ SY221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(392,plain,
! [SV27: $i] :
( ( ! [SY222: $i,SY223: $i] :
( ~ ( subset @ SV27 @ SY222 )
| ~ ( subset @ SY223 @ SY222 )
| ( subset @ ( set_union2 @ SV27 @ SY223 ) @ SY222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(393,plain,
! [SV28: $i] :
( ( ! [SY224: $i] :
( ! [SY225: $i] :
( ( singleton @ SV28 )
!= ( unordered_pair @ SY224 @ SY225 ) )
| ( SV28 = SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(394,plain,
! [SV29: $i] :
( ( ! [SY226: $i,SY227: $i] :
( ( ( singleton @ SV29 )
!= ( unordered_pair @ SY226 @ SY227 ) )
| ( SY226 = SY227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(395,plain,
! [SV30: $i] :
( ( ! [SY228: $i] :
( ~ ( in @ SV30 @ SY228 )
| ~ ( in @ SY228 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(396,plain,
! [SV31: $i] :
( ( ! [SY229: $i] :
( ~ ( proper_subset @ SV31 @ SY229 )
| ~ ( proper_subset @ SY229 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(397,plain,
! [SV32: $i] :
( ( ! [SY230: $i] :
( ( unordered_pair @ SV32 @ SY230 )
= ( unordered_pair @ SY230 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(398,plain,
! [SV33: $i] :
( ( ! [SY231: $i] :
( ( set_union2 @ SV33 @ SY231 )
= ( set_union2 @ SY231 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(399,plain,
! [SV34: $i] :
( ( ! [SY232: $i] :
( ( set_intersection2 @ SV34 @ SY232 )
= ( set_intersection2 @ SY232 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(400,plain,
! [SV35: $i] :
( ( ! [SY233: $i] :
( ( ordered_pair @ SV35 @ SY233 )
= ( unordered_pair @ ( unordered_pair @ SV35 @ SY233 ) @ ( singleton @ SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(401,plain,
! [SV36: $i] :
( ( ! [SY234: $i] :
~ ( empty @ ( ordered_pair @ SV36 @ SY234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(402,plain,
! [SV37: $i] :
( ( ( empty @ SV37 )
| ! [SY235: $i] :
~ ( empty @ ( set_union2 @ SV37 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(403,plain,
! [SV38: $i] :
( ( ( empty @ SV38 )
| ! [SY236: $i] :
~ ( empty @ ( set_union2 @ SY236 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(404,plain,
! [SV39: $i] :
( ( ( set_union2 @ SV39 @ SV39 )
= SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(405,plain,
! [SV40: $i] :
( ( ( set_intersection2 @ SV40 @ SV40 )
= SV40 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(406,plain,
! [SV41: $i] :
( ( ~ ( proper_subset @ SV41 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(407,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(408,plain,
! [SV42: $i] :
( ( subset @ SV42 @ SV42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(409,plain,
! [SV43: $i] :
( ( ! [SY237: $i] :
( ~ ( disjoint @ SV43 @ SY237 )
| ( disjoint @ SY237 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(410,plain,
! [SV44: $i] :
( ( ( set_union2 @ SV44 @ empty_set )
= SV44 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(411,plain,
! [SV45: $i] :
( ( ( set_intersection2 @ SV45 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(412,plain,
! [SV46: $i] :
( ( ( set_difference @ SV46 @ empty_set )
= SV46 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(413,plain,
! [SV47: $i] :
( ( ( set_difference @ empty_set @ SV47 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(414,plain,
! [SV48: $i] :
( ( ~ ( empty @ SV48 )
| ( SV48 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(415,plain,
! [SV49: $i] :
( ( ! [SY238: $i] :
( ~ ( empty @ SY238 )
| ~ ( in @ SV49 @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(416,plain,
! [SV50: $i] :
( ( ! [SY239: $i] :
( ( SV50 = SY239 )
| ~ ( empty @ SV50 )
| ~ ( empty @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(417,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)],[340]) ).
thf(418,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)],[341]) ).
thf(419,plain,
! [SV51: $i] :
( ( ~ ( ~ ! [SY240: $i,SY241: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY241 @ SY240 @ SV51 ) @ SY241 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY241 @ SY240 @ SV51 ) @ SY241 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
!= SY240 ) ) )
| ~ ( ( in @ ( sK18_D @ SY241 @ SY240 @ SV51 ) @ SY241 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
= SV51 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
= SY240 ) ) )
| ( SY241
= ( unordered_pair @ SV51 @ SY240 ) ) )
| ~ ! [SY242: $i,SY243: $i] :
( ( SY243
!= ( unordered_pair @ SV51 @ SY242 ) )
| ~ ( ~ ! [SY244: $i] :
( ~ ( in @ SY244 @ SY243 )
| ( SY244 = SV51 )
| ( SY244 = SY242 ) )
| ~ ~ ( ~ ! [SY245: $i] :
( ( SY245 != SV51 )
| ( in @ SY245 @ SY243 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY242 )
| ( in @ SX3 @ SY243 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(420,plain,
! [SV52: $i] :
( ( ~ ( ~ ! [SY247: $i,SY248: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SV52 )
| ~ ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY247 )
| ~ ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY248 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY248 ) )
| ~ ( ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY247 )
| ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY248 ) ) ) )
| ( SY248
= ( set_intersection2 @ SV52 @ SY247 ) ) )
| ~ ! [SY249: $i,SY250: $i] :
( ( SY250
!= ( set_intersection2 @ SV52 @ SY249 ) )
| ~ ( ~ ! [SY251: $i] :
( ~ ( in @ SY251 @ SV52 )
| ~ ( in @ SY251 @ SY249 )
| ( in @ SY251 @ SY250 ) )
| ~ ~ ( ~ ! [SY252: $i] :
( ~ ( in @ SY252 @ SY250 )
| ( in @ SY252 @ SV52 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(421,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)],[344]) ).
thf(422,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)],[345]) ).
thf(423,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)],[346]) ).
thf(424,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)],[347]) ).
thf(425,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)],[348]) ).
thf(426,plain,
! [SV53: $i] :
( ( ~ ( ~ ! [SY254: $i,SY255: $i] :
( ~ ( in @ SV53 @ SY255 )
| ~ ( in @ SY254 @ SY255 )
| ( subset @ ( unordered_pair @ SV53 @ SY254 ) @ SY255 ) )
| ~ ~ ( ~ ! [SY256: $i,SY257: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY256 ) @ SY257 )
| ( in @ SV53 @ SY257 ) )
| ~ ! [SY258: $i,SY259: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY258 ) @ SY259 )
| ( in @ SY258 @ SY259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(427,plain,
! [SV54: $i] :
( ( ! [SY260: $i] :
~ ( ~ ! [SY261: $i,SY262: $i] :
( ~ ( in @ SV54 @ SY261 )
| ~ ( in @ SY260 @ SY262 )
| ( in @ ( ordered_pair @ SV54 @ SY260 ) @ ( cartesian_product2 @ SY261 @ SY262 ) ) )
| ~ ~ ( ~ ! [SY263: $i] :
( ! [SY264: $i] :
~ ( in @ ( ordered_pair @ SV54 @ SY260 ) @ ( cartesian_product2 @ SY263 @ SY264 ) )
| ( in @ SV54 @ SY263 ) )
| ~ ! [SY265: $i,SY266: $i] :
( ~ ( in @ ( ordered_pair @ SV54 @ SY260 ) @ ( cartesian_product2 @ SY265 @ SY266 ) )
| ( in @ SY260 @ SY266 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(428,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)],[351]) ).
thf(429,plain,
! [SV55: $i] :
( ( ~ ( ~ ! [SY267: $i,SY268: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY267 )
| ~ ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY268 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY268 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY267 )
| ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY268 ) ) ) )
| ( SY268
= ( set_difference @ SV55 @ SY267 ) ) )
| ~ ! [SY269: $i,SY270: $i] :
( ( SY270
!= ( set_difference @ SV55 @ SY269 ) )
| ~ ( ~ ! [SY271: $i] :
( ~ ( in @ SY271 @ SV55 )
| ( in @ SY271 @ SY269 )
| ( in @ SY271 @ SY270 ) )
| ~ ~ ( ~ ! [SY272: $i] :
( ~ ( in @ SY272 @ SY270 )
| ( in @ SY272 @ SV55 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY270 )
| ~ ( in @ SX3 @ SY269 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(430,plain,
! [SV56: $i] :
( ( ~ ( ~ ! [SY274: $i,SY275: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY275 )
| ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY275 )
| ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY274 ) ) )
| ~ ( ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY275 )
| ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY274 ) ) )
| ( SY275
= ( set_union2 @ SV56 @ SY274 ) ) )
| ~ ! [SY276: $i,SY277: $i] :
( ( SY277
!= ( set_union2 @ SV56 @ SY276 ) )
| ~ ( ~ ! [SY278: $i] :
( ~ ( in @ SY278 @ SY277 )
| ( in @ SY278 @ SV56 )
| ( in @ SY278 @ SY276 ) )
| ~ ~ ( ~ ! [SY279: $i] :
( ~ ( in @ SY279 @ SV56 )
| ( in @ SY279 @ SY277 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY276 )
| ( in @ SX3 @ SY277 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(431,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)],[354]) ).
thf(432,plain,
( ( ~ ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) )
| ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY183 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(433,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)],[356]) ).
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)],[357]) ).
thf(435,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)],[358]) ).
thf(436,plain,
! [SV57: $i] :
( ( ! [SY281: $i] :
~ ( ~ ! [SY282: $i] :
( ! [SY283: $i] :
( ( ordered_pair @ SV57 @ SY281 )
!= ( ordered_pair @ SY282 @ SY283 ) )
| ( SV57 = SY282 ) )
| ~ ! [SY284: $i,SY285: $i] :
( ( ( ordered_pair @ SV57 @ SY281 )
!= ( ordered_pair @ SY284 @ SY285 ) )
| ( SY281 = SY285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(437,plain,
! [SV58: $i] :
( ( ! [SY286: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SY286 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK3_C @ SY286 @ SV58 ) @ SY286 ) )
| ~ ( ( in @ ( sK3_C @ SY286 @ SV58 ) @ SV58 )
| ( in @ ( sK3_C @ SY286 @ SV58 ) @ SY286 ) ) )
| ( SV58 = SY286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(438,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)],[361]) ).
thf(439,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)],[362]) ).
thf(440,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_SY185 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_SY185 @ 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)],[363]) ).
thf(441,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)],[364]) ).
thf(442,plain,
! [SV59: $i] :
( ( ~ ( ~ ! [SY287: $i,SY288: $i] :
( ~ ( ~ ( ! [SY289: $i,SY290: $i] :
( ~ ( in @ SY289 @ SV59 )
| ~ ( in @ SY290 @ SY287 )
| ( ( sK14_D @ SY288 @ SY287 @ SV59 )
!= ( ordered_pair @ SY289 @ SY290 ) ) )
| ~ ( in @ ( sK14_D @ SY288 @ SY287 @ SV59 ) @ SY288 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SY288 @ SY287 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SY288 @ SY287 @ SV59 ) @ SY287 ) )
| ( ( sK14_D @ SY288 @ SY287 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SY288 @ SY287 @ SV59 ) @ ( sK16_SY191 @ SY288 @ SY287 @ SV59 ) ) ) )
| ( in @ ( sK14_D @ SY288 @ SY287 @ SV59 ) @ SY288 ) ) )
| ( SY288
= ( cartesian_product2 @ SV59 @ SY287 ) ) )
| ~ ! [SY291: $i,SY292: $i] :
( ( SY292
!= ( cartesian_product2 @ SV59 @ SY291 ) )
| ~ ( ~ ! [SY293: $i] :
( ! [SY294: $i,SY295: $i] :
( ~ ( in @ SY294 @ SV59 )
| ~ ( in @ SY295 @ SY291 )
| ( SY293
!= ( ordered_pair @ SY294 @ SY295 ) ) )
| ( in @ SY293 @ SY292 ) )
| ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ SY292 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY296 @ SY292 @ SY291 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SY296 @ SY292 @ SY291 @ SV59 ) @ SY291 ) )
| ( SY296
!= ( ordered_pair @ ( sK12_E @ SY296 @ SY292 @ SY291 @ SV59 ) @ ( sK13_SY186 @ SY296 @ SY292 @ SY291 @ SV59 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(443,plain,
! [SV1: $i] :
( ( ( singleton @ SV1 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(444,plain,
! [SV60: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV60 )
| ( ( set_union2 @ ( singleton @ SV2 ) @ SV60 )
= SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(445,plain,
! [SV61: $i,SV3: $i] :
( ( ~ ( disjoint @ ( singleton @ SV3 ) @ SV61 )
| ~ ( in @ SV3 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(446,plain,
! [SV62: $i,SV4: $i] :
( ( ( in @ SV4 @ SV62 )
| ( disjoint @ ( singleton @ SV4 ) @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(447,plain,
! [SV63: $i,SV5: $i] :
( ( ~ ( subset @ SV5 @ SV63 )
| ! [SY297: $i] :
( ( in @ SY297 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV63 @ ( singleton @ SY297 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(448,plain,
! [SV64: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV64 )
| ( subset @ SV6 @ ( union @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(449,plain,
! [SV65: $i,SV7: $i] :
( ( ! [SY298: $i,SY299: $i] :
( ( SV7 = SY299 )
| ( SV7 = SY298 )
| ( ( unordered_pair @ SV7 @ SV65 )
!= ( unordered_pair @ SY298 @ SY299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(450,plain,
! [SV66: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ SV66 )
| ( ( set_union2 @ SV8 @ SV66 )
= SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(451,plain,
! [SV67: $i,SV9: $i] :
( ( subset @ ( set_intersection2 @ SV9 @ SV67 ) @ SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(452,plain,
! [SV68: $i,SV10: $i] :
( ( ! [SY300: $i] :
( ~ ( subset @ SV10 @ SV68 )
| ~ ( subset @ SV10 @ SY300 )
| ( subset @ SV10 @ ( set_intersection2 @ SV68 @ SY300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(453,plain,
! [SV69: $i,SV11: $i] :
( ( ! [SY301: $i] :
( ~ ( subset @ SV11 @ SV69 )
| ~ ( subset @ SV69 @ SY301 )
| ( subset @ SV11 @ SY301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(454,plain,
! [SV70: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV70 )
| ! [SY302: $i] : ( subset @ ( set_intersection2 @ SV12 @ SY302 ) @ ( set_intersection2 @ SV70 @ SY302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(455,plain,
! [SV71: $i,SV13: $i] :
( ( ~ ( subset @ SV13 @ SV71 )
| ( ( set_intersection2 @ SV13 @ SV71 )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(456,plain,
! [SV72: $i,SV15: $i] :
( ( ~ ( subset @ SV15 @ SV72 )
| ! [SY303: $i] : ( subset @ ( set_difference @ SV15 @ SY303 ) @ ( set_difference @ SV72 @ SY303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(457,plain,
! [SV73: $i,SV16: $i] :
( ( subset @ ( set_difference @ SV16 @ SV73 ) @ SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(458,plain,
! [SV74: $i,SV17: $i] :
( ( ( set_union2 @ SV17 @ ( set_difference @ SV74 @ SV17 ) )
= ( set_union2 @ SV17 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(459,plain,
! [SV18: $i] :
( ( ( ~ ( subset @ SV18 @ empty_set ) )
= $true )
| ( ( SV18 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(460,plain,
! [SV75: $i,SV19: $i] :
( ( ( set_difference @ ( set_union2 @ SV19 @ SV75 ) @ SV75 )
= ( set_difference @ SV19 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(461,plain,
! [SV76: $i,SV20: $i] :
( ( ~ ( subset @ SV20 @ SV76 )
| ( SV76
= ( set_union2 @ SV20 @ ( set_difference @ SV76 @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(462,plain,
! [SV77: $i,SV21: $i] :
( ( ( set_difference @ SV21 @ ( set_difference @ SV21 @ SV77 ) )
= ( set_intersection2 @ SV21 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(463,plain,
! [SV22: $i,SV78: $i] :
( ( ~ ( proper_subset @ SV78 @ SV22 )
| ~ ( subset @ SV22 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(464,plain,
! [SV23: $i,SV79: $i] :
( ( ! [SY304: $i] :
( ~ ( disjoint @ SV79 @ SY304 )
| ~ ( subset @ SV23 @ SV79 )
| ( disjoint @ SV23 @ SY304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(465,plain,
! [SV80: $i,SV25: $i] :
( ( ~ ( subset @ ( singleton @ SV25 ) @ ( singleton @ SV80 ) )
| ( SV25 = SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(466,plain,
! [SV81: $i,SV26: $i] :
( ( subset @ SV26 @ ( set_union2 @ SV26 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(467,plain,
! [SV82: $i,SV27: $i] :
( ( ! [SY305: $i] :
( ~ ( subset @ SV27 @ SV82 )
| ~ ( subset @ SY305 @ SV82 )
| ( subset @ ( set_union2 @ SV27 @ SY305 ) @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(468,plain,
! [SV83: $i,SV28: $i] :
( ( ! [SY306: $i] :
( ( singleton @ SV28 )
!= ( unordered_pair @ SV83 @ SY306 ) )
| ( SV28 = SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(469,plain,
! [SV84: $i,SV29: $i] :
( ( ! [SY307: $i] :
( ( ( singleton @ SV29 )
!= ( unordered_pair @ SV84 @ SY307 ) )
| ( SV84 = SY307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(470,plain,
! [SV85: $i,SV30: $i] :
( ( ~ ( in @ SV30 @ SV85 )
| ~ ( in @ SV85 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(471,plain,
! [SV86: $i,SV31: $i] :
( ( ~ ( proper_subset @ SV31 @ SV86 )
| ~ ( proper_subset @ SV86 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(472,plain,
! [SV87: $i,SV32: $i] :
( ( ( unordered_pair @ SV32 @ SV87 )
= ( unordered_pair @ SV87 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(473,plain,
! [SV88: $i,SV33: $i] :
( ( ( set_union2 @ SV33 @ SV88 )
= ( set_union2 @ SV88 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(474,plain,
! [SV89: $i,SV34: $i] :
( ( ( set_intersection2 @ SV34 @ SV89 )
= ( set_intersection2 @ SV89 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(475,plain,
! [SV90: $i,SV35: $i] :
( ( ( ordered_pair @ SV35 @ SV90 )
= ( unordered_pair @ ( unordered_pair @ SV35 @ SV90 ) @ ( singleton @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(476,plain,
! [SV91: $i,SV36: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV36 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(477,plain,
! [SV37: $i] :
( ( ( empty @ SV37 )
= $true )
| ( ( ! [SY235: $i] :
~ ( empty @ ( set_union2 @ SV37 @ SY235 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(478,plain,
! [SV38: $i] :
( ( ( empty @ SV38 )
= $true )
| ( ( ! [SY236: $i] :
~ ( empty @ ( set_union2 @ SY236 @ SV38 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(479,plain,
! [SV41: $i] :
( ( proper_subset @ SV41 @ SV41 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(480,plain,
! [SV92: $i,SV43: $i] :
( ( ~ ( disjoint @ SV43 @ SV92 )
| ( disjoint @ SV92 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(481,plain,
! [SV48: $i] :
( ( ( ~ ( empty @ SV48 ) )
= $true )
| ( ( SV48 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(482,plain,
! [SV49: $i,SV93: $i] :
( ( ~ ( empty @ SV93 )
| ~ ( in @ SV49 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(483,plain,
! [SV94: $i,SV50: $i] :
( ( ( SV50 = SV94 )
| ~ ( empty @ SV50 )
| ~ ( empty @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(484,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(485,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(486,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(487,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(488,plain,
! [SV51: $i] :
( ( ~ ! [SY240: $i,SY241: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY241 @ SY240 @ SV51 ) @ SY241 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY241 @ SY240 @ SV51 ) @ SY241 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
!= SY240 ) ) )
| ~ ( ( in @ ( sK18_D @ SY241 @ SY240 @ SV51 ) @ SY241 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
= SV51 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
= SY240 ) ) )
| ( SY241
= ( unordered_pair @ SV51 @ SY240 ) ) )
| ~ ! [SY242: $i,SY243: $i] :
( ( SY243
!= ( unordered_pair @ SV51 @ SY242 ) )
| ~ ( ~ ! [SY244: $i] :
( ~ ( in @ SY244 @ SY243 )
| ( SY244 = SV51 )
| ( SY244 = SY242 ) )
| ~ ~ ( ~ ! [SY245: $i] :
( ( SY245 != SV51 )
| ( in @ SY245 @ SY243 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY242 )
| ( in @ SX3 @ SY243 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(489,plain,
! [SV52: $i] :
( ( ~ ! [SY247: $i,SY248: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SV52 )
| ~ ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY247 )
| ~ ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY248 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY248 ) )
| ~ ( ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY247 )
| ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY248 ) ) ) )
| ( SY248
= ( set_intersection2 @ SV52 @ SY247 ) ) )
| ~ ! [SY249: $i,SY250: $i] :
( ( SY250
!= ( set_intersection2 @ SV52 @ SY249 ) )
| ~ ( ~ ! [SY251: $i] :
( ~ ( in @ SY251 @ SV52 )
| ~ ( in @ SY251 @ SY249 )
| ( in @ SY251 @ SY250 ) )
| ~ ~ ( ~ ! [SY252: $i] :
( ~ ( in @ SY252 @ SY250 )
| ( in @ SY252 @ SV52 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(490,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)],[421]) ).
thf(491,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)],[421]) ).
thf(492,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(493,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(494,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(495,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)],[423]) ).
thf(496,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK20_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(497,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(498,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK22_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(499,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(500,plain,
! [SV53: $i] :
( ( ~ ! [SY254: $i,SY255: $i] :
( ~ ( in @ SV53 @ SY255 )
| ~ ( in @ SY254 @ SY255 )
| ( subset @ ( unordered_pair @ SV53 @ SY254 ) @ SY255 ) )
| ~ ~ ( ~ ! [SY256: $i,SY257: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY256 ) @ SY257 )
| ( in @ SV53 @ SY257 ) )
| ~ ! [SY258: $i,SY259: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY258 ) @ SY259 )
| ( in @ SY258 @ SY259 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(501,plain,
! [SV95: $i,SV54: $i] :
( ( ~ ( ~ ! [SY308: $i,SY309: $i] :
( ~ ( in @ SV54 @ SY308 )
| ~ ( in @ SV95 @ SY309 )
| ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY308 @ SY309 ) ) )
| ~ ~ ( ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY310 @ SY311 ) )
| ( in @ SV54 @ SY310 ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY312 @ SY313 ) )
| ( in @ SV95 @ SY313 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(502,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(503,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)],[428]) ).
thf(504,plain,
! [SV55: $i] :
( ( ~ ! [SY267: $i,SY268: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY267 )
| ~ ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY268 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY268 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY267 )
| ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY268 ) ) ) )
| ( SY268
= ( set_difference @ SV55 @ SY267 ) ) )
| ~ ! [SY269: $i,SY270: $i] :
( ( SY270
!= ( set_difference @ SV55 @ SY269 ) )
| ~ ( ~ ! [SY271: $i] :
( ~ ( in @ SY271 @ SV55 )
| ( in @ SY271 @ SY269 )
| ( in @ SY271 @ SY270 ) )
| ~ ~ ( ~ ! [SY272: $i] :
( ~ ( in @ SY272 @ SY270 )
| ( in @ SY272 @ SV55 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY270 )
| ~ ( in @ SX3 @ SY269 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(505,plain,
! [SV56: $i] :
( ( ~ ! [SY274: $i,SY275: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY275 )
| ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY275 )
| ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY274 ) ) )
| ~ ( ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY275 )
| ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY274 ) ) )
| ( SY275
= ( set_union2 @ SV56 @ SY274 ) ) )
| ~ ! [SY276: $i,SY277: $i] :
( ( SY277
!= ( set_union2 @ SV56 @ SY276 ) )
| ~ ( ~ ! [SY278: $i] :
( ~ ( in @ SY278 @ SY277 )
| ( in @ SY278 @ SV56 )
| ( in @ SY278 @ SY276 ) )
| ~ ~ ( ~ ! [SY279: $i] :
( ~ ( in @ SY279 @ SV56 )
| ( in @ SY279 @ SY277 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY276 )
| ( in @ SX3 @ SY277 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(506,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(507,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(508,plain,
( ( ~ ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(509,plain,
( ( ~ ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY183 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(510,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(511,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)],[433]) ).
thf(512,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(513,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(514,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)],[435]) ).
thf(515,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(516,plain,
! [SV96: $i,SV57: $i] :
( ( ~ ( ~ ! [SY314: $i] :
( ! [SY315: $i] :
( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SY314 @ SY315 ) )
| ( SV57 = SY314 ) )
| ~ ! [SY316: $i,SY317: $i] :
( ( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SY316 @ SY317 ) )
| ( SV96 = SY317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(517,plain,
! [SV58: $i,SV97: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 ) )
| ~ ( ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
| ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 ) ) )
| ( SV58 = SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(518,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)],[438]) ).
thf(519,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[438]) ).
thf(520,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)],[439]) ).
thf(521,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)],[439]) ).
thf(522,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_SY185 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_SY185 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(523,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)],[440]) ).
thf(524,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(525,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(526,plain,
! [SV59: $i] :
( ( ~ ! [SY287: $i,SY288: $i] :
( ~ ( ~ ( ! [SY289: $i,SY290: $i] :
( ~ ( in @ SY289 @ SV59 )
| ~ ( in @ SY290 @ SY287 )
| ( ( sK14_D @ SY288 @ SY287 @ SV59 )
!= ( ordered_pair @ SY289 @ SY290 ) ) )
| ~ ( in @ ( sK14_D @ SY288 @ SY287 @ SV59 ) @ SY288 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SY288 @ SY287 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SY288 @ SY287 @ SV59 ) @ SY287 ) )
| ( ( sK14_D @ SY288 @ SY287 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SY288 @ SY287 @ SV59 ) @ ( sK16_SY191 @ SY288 @ SY287 @ SV59 ) ) ) )
| ( in @ ( sK14_D @ SY288 @ SY287 @ SV59 ) @ SY288 ) ) )
| ( SY288
= ( cartesian_product2 @ SV59 @ SY287 ) ) )
| ~ ! [SY291: $i,SY292: $i] :
( ( SY292
!= ( cartesian_product2 @ SV59 @ SY291 ) )
| ~ ( ~ ! [SY293: $i] :
( ! [SY294: $i,SY295: $i] :
( ~ ( in @ SY294 @ SV59 )
| ~ ( in @ SY295 @ SY291 )
| ( SY293
!= ( ordered_pair @ SY294 @ SY295 ) ) )
| ( in @ SY293 @ SY292 ) )
| ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ SY292 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY296 @ SY292 @ SY291 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SY296 @ SY292 @ SY291 @ SV59 ) @ SY291 ) )
| ( SY296
!= ( ordered_pair @ ( sK12_E @ SY296 @ SY292 @ SY291 @ SV59 ) @ ( sK13_SY186 @ SY296 @ SY292 @ SY291 @ SV59 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(527,plain,
! [SV60: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV60 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV2 ) @ SV60 )
= SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(528,plain,
! [SV61: $i,SV3: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV3 ) @ SV61 ) )
= $true )
| ( ( ~ ( in @ SV3 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(529,plain,
! [SV62: $i,SV4: $i] :
( ( ( in @ SV4 @ SV62 )
= $true )
| ( ( disjoint @ ( singleton @ SV4 ) @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(530,plain,
! [SV63: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ SV63 ) )
= $true )
| ( ( ! [SY297: $i] :
( ( in @ SY297 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV63 @ ( singleton @ SY297 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(531,plain,
! [SV64: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV64 ) )
= $true )
| ( ( subset @ SV6 @ ( union @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(532,plain,
! [SV65: $i,SV98: $i,SV7: $i] :
( ( ! [SY318: $i] :
( ( SV7 = SY318 )
| ( SV7 = SV98 )
| ( ( unordered_pair @ SV7 @ SV65 )
!= ( unordered_pair @ SV98 @ SY318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(533,plain,
! [SV66: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV66 ) )
= $true )
| ( ( ( set_union2 @ SV8 @ SV66 )
= SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(534,plain,
! [SV99: $i,SV68: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV68 )
| ~ ( subset @ SV10 @ SV99 )
| ( subset @ SV10 @ ( set_intersection2 @ SV68 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(535,plain,
! [SV100: $i,SV69: $i,SV11: $i] :
( ( ~ ( subset @ SV11 @ SV69 )
| ~ ( subset @ SV69 @ SV100 )
| ( subset @ SV11 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(536,plain,
! [SV70: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV70 ) )
= $true )
| ( ( ! [SY302: $i] : ( subset @ ( set_intersection2 @ SV12 @ SY302 ) @ ( set_intersection2 @ SV70 @ SY302 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(537,plain,
! [SV71: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV71 ) )
= $true )
| ( ( ( set_intersection2 @ SV13 @ SV71 )
= SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(538,plain,
! [SV72: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV72 ) )
= $true )
| ( ( ! [SY303: $i] : ( subset @ ( set_difference @ SV15 @ SY303 ) @ ( set_difference @ SV72 @ SY303 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(539,plain,
! [SV18: $i] :
( ( ( subset @ SV18 @ empty_set )
= $false )
| ( ( SV18 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(540,plain,
! [SV76: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV76 ) )
= $true )
| ( ( SV76
= ( set_union2 @ SV20 @ ( set_difference @ SV76 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(541,plain,
! [SV22: $i,SV78: $i] :
( ( ( ~ ( proper_subset @ SV78 @ SV22 ) )
= $true )
| ( ( ~ ( subset @ SV22 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(542,plain,
! [SV23: $i,SV101: $i,SV79: $i] :
( ( ~ ( disjoint @ SV79 @ SV101 )
| ~ ( subset @ SV23 @ SV79 )
| ( disjoint @ SV23 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(543,plain,
! [SV80: $i,SV25: $i] :
( ( ( ~ ( subset @ ( singleton @ SV25 ) @ ( singleton @ SV80 ) ) )
= $true )
| ( ( SV25 = SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(544,plain,
! [SV102: $i,SV82: $i,SV27: $i] :
( ( ~ ( subset @ SV27 @ SV82 )
| ~ ( subset @ SV102 @ SV82 )
| ( subset @ ( set_union2 @ SV27 @ SV102 ) @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(545,plain,
! [SV83: $i,SV28: $i] :
( ( ( ! [SY306: $i] :
( ( singleton @ SV28 )
!= ( unordered_pair @ SV83 @ SY306 ) ) )
= $true )
| ( ( SV28 = SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(546,plain,
! [SV103: $i,SV84: $i,SV29: $i] :
( ( ( ( singleton @ SV29 )
!= ( unordered_pair @ SV84 @ SV103 ) )
| ( SV84 = SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(547,plain,
! [SV85: $i,SV30: $i] :
( ( ( ~ ( in @ SV30 @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV85 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(548,plain,
! [SV86: $i,SV31: $i] :
( ( ( ~ ( proper_subset @ SV31 @ SV86 ) )
= $true )
| ( ( ~ ( proper_subset @ SV86 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(549,plain,
! [SV91: $i,SV36: $i] :
( ( empty @ ( ordered_pair @ SV36 @ SV91 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(550,plain,
! [SV104: $i,SV37: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV37 @ SV104 ) ) )
= $true )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(551,plain,
! [SV38: $i,SV105: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV105 @ SV38 ) ) )
= $true )
| ( ( empty @ SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(552,plain,
! [SV92: $i,SV43: $i] :
( ( ( ~ ( disjoint @ SV43 @ SV92 ) )
= $true )
| ( ( disjoint @ SV92 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(553,plain,
! [SV48: $i] :
( ( ( empty @ SV48 )
= $false )
| ( ( SV48 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(554,plain,
! [SV49: $i,SV93: $i] :
( ( ( ~ ( empty @ SV93 ) )
= $true )
| ( ( ~ ( in @ SV49 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(555,plain,
! [SV94: $i,SV50: $i] :
( ( ( ( SV50 = SV94 )
| ~ ( empty @ SV50 ) )
= $true )
| ( ( ~ ( empty @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(556,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(557,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(558,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(559,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(560,plain,
! [SV51: $i] :
( ( ~ ! [SY240: $i,SY241: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY241 @ SY240 @ SV51 ) @ SY241 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY241 @ SY240 @ SV51 ) @ SY241 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
!= SY240 ) ) )
| ~ ( ( in @ ( sK18_D @ SY241 @ SY240 @ SV51 ) @ SY241 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
= SV51 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
= SY240 ) ) )
| ( SY241
= ( unordered_pair @ SV51 @ SY240 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(561,plain,
! [SV51: $i] :
( ( ~ ! [SY242: $i,SY243: $i] :
( ( SY243
!= ( unordered_pair @ SV51 @ SY242 ) )
| ~ ( ~ ! [SY244: $i] :
( ~ ( in @ SY244 @ SY243 )
| ( SY244 = SV51 )
| ( SY244 = SY242 ) )
| ~ ~ ( ~ ! [SY245: $i] :
( ( SY245 != SV51 )
| ( in @ SY245 @ SY243 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY242 )
| ( in @ SX3 @ SY243 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(562,plain,
! [SV52: $i] :
( ( ~ ! [SY247: $i,SY248: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SV52 )
| ~ ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY247 )
| ~ ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY248 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY248 ) )
| ~ ( ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY247 )
| ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY248 ) ) ) )
| ( SY248
= ( set_intersection2 @ SV52 @ SY247 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(563,plain,
! [SV52: $i] :
( ( ~ ! [SY249: $i,SY250: $i] :
( ( SY250
!= ( set_intersection2 @ SV52 @ SY249 ) )
| ~ ( ~ ! [SY251: $i] :
( ~ ( in @ SY251 @ SV52 )
| ~ ( in @ SY251 @ SY249 )
| ( in @ SY251 @ SY250 ) )
| ~ ~ ( ~ ! [SY252: $i] :
( ~ ( in @ SY252 @ SY250 )
| ( in @ SY252 @ SV52 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(564,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)],[490]) ).
thf(565,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)],[491]) ).
thf(566,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(567,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(568,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(569,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)],[495]) ).
thf(570,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK20_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(571,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(572,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK22_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(573,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(574,plain,
! [SV53: $i] :
( ( ~ ! [SY254: $i,SY255: $i] :
( ~ ( in @ SV53 @ SY255 )
| ~ ( in @ SY254 @ SY255 )
| ( subset @ ( unordered_pair @ SV53 @ SY254 ) @ SY255 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(575,plain,
! [SV53: $i] :
( ( ~ ~ ( ~ ! [SY256: $i,SY257: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY256 ) @ SY257 )
| ( in @ SV53 @ SY257 ) )
| ~ ! [SY258: $i,SY259: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY258 ) @ SY259 )
| ( in @ SY258 @ SY259 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(576,plain,
! [SV95: $i,SV54: $i] :
( ( ~ ! [SY308: $i,SY309: $i] :
( ~ ( in @ SV54 @ SY308 )
| ~ ( in @ SV95 @ SY309 )
| ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY308 @ SY309 ) ) )
| ~ ~ ( ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY310 @ SY311 ) )
| ( in @ SV54 @ SY310 ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY312 @ SY313 ) )
| ( in @ SV95 @ SY313 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(577,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(578,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)],[503]) ).
thf(579,plain,
! [SV55: $i] :
( ( ~ ! [SY267: $i,SY268: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY267 )
| ~ ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY268 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY268 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY267 )
| ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY268 ) ) ) )
| ( SY268
= ( set_difference @ SV55 @ SY267 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(580,plain,
! [SV55: $i] :
( ( ~ ! [SY269: $i,SY270: $i] :
( ( SY270
!= ( set_difference @ SV55 @ SY269 ) )
| ~ ( ~ ! [SY271: $i] :
( ~ ( in @ SY271 @ SV55 )
| ( in @ SY271 @ SY269 )
| ( in @ SY271 @ SY270 ) )
| ~ ~ ( ~ ! [SY272: $i] :
( ~ ( in @ SY272 @ SY270 )
| ( in @ SY272 @ SV55 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY270 )
| ~ ( in @ SX3 @ SY269 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(581,plain,
! [SV56: $i] :
( ( ~ ! [SY274: $i,SY275: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY275 )
| ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY275 )
| ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY274 ) ) )
| ~ ( ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY275 )
| ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY274 ) ) )
| ( SY275
= ( set_union2 @ SV56 @ SY274 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(582,plain,
! [SV56: $i] :
( ( ~ ! [SY276: $i,SY277: $i] :
( ( SY277
!= ( set_union2 @ SV56 @ SY276 ) )
| ~ ( ~ ! [SY278: $i] :
( ~ ( in @ SY278 @ SY277 )
| ( in @ SY278 @ SV56 )
| ( in @ SY278 @ SY276 ) )
| ~ ~ ( ~ ! [SY279: $i] :
( ~ ( in @ SY279 @ SV56 )
| ( in @ SY279 @ SY277 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY276 )
| ( in @ SX3 @ SY277 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(583,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(584,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(585,plain,
( ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(586,plain,
( ( ~ ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY183 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(587,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(588,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)],[511]) ).
thf(589,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(590,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(591,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)],[514]) ).
thf(592,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(593,plain,
! [SV96: $i,SV57: $i] :
( ( ~ ! [SY314: $i] :
( ! [SY315: $i] :
( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SY314 @ SY315 ) )
| ( SV57 = SY314 ) )
| ~ ! [SY316: $i,SY317: $i] :
( ( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SY316 @ SY317 ) )
| ( SV96 = SY317 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(594,plain,
! [SV58: $i,SV97: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 ) )
| ~ ( ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
| ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 ) ) ) )
= $true )
| ( ( SV58 = SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(595,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)],[518]) ).
thf(596,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(597,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)],[520]) ).
thf(598,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)],[521]) ).
thf(599,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_SY185 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_SY185 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(600,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)],[523]) ).
thf(601,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(602,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(603,plain,
! [SV59: $i] :
( ( ~ ! [SY287: $i,SY288: $i] :
( ~ ( ~ ( ! [SY289: $i,SY290: $i] :
( ~ ( in @ SY289 @ SV59 )
| ~ ( in @ SY290 @ SY287 )
| ( ( sK14_D @ SY288 @ SY287 @ SV59 )
!= ( ordered_pair @ SY289 @ SY290 ) ) )
| ~ ( in @ ( sK14_D @ SY288 @ SY287 @ SV59 ) @ SY288 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SY288 @ SY287 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SY288 @ SY287 @ SV59 ) @ SY287 ) )
| ( ( sK14_D @ SY288 @ SY287 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SY288 @ SY287 @ SV59 ) @ ( sK16_SY191 @ SY288 @ SY287 @ SV59 ) ) ) )
| ( in @ ( sK14_D @ SY288 @ SY287 @ SV59 ) @ SY288 ) ) )
| ( SY288
= ( cartesian_product2 @ SV59 @ SY287 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(604,plain,
! [SV59: $i] :
( ( ~ ! [SY291: $i,SY292: $i] :
( ( SY292
!= ( cartesian_product2 @ SV59 @ SY291 ) )
| ~ ( ~ ! [SY293: $i] :
( ! [SY294: $i,SY295: $i] :
( ~ ( in @ SY294 @ SV59 )
| ~ ( in @ SY295 @ SY291 )
| ( SY293
!= ( ordered_pair @ SY294 @ SY295 ) ) )
| ( in @ SY293 @ SY292 ) )
| ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ SY292 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY296 @ SY292 @ SY291 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SY296 @ SY292 @ SY291 @ SV59 ) @ SY291 ) )
| ( SY296
!= ( ordered_pair @ ( sK12_E @ SY296 @ SY292 @ SY291 @ SV59 ) @ ( sK13_SY186 @ SY296 @ SY292 @ SY291 @ SV59 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[526]) ).
thf(605,plain,
! [SV60: $i,SV2: $i] :
( ( ( in @ SV2 @ SV60 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV2 ) @ SV60 )
= SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(606,plain,
! [SV61: $i,SV3: $i] :
( ( ( disjoint @ ( singleton @ SV3 ) @ SV61 )
= $false )
| ( ( ~ ( in @ SV3 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(607,plain,
! [SV63: $i,SV5: $i] :
( ( ( subset @ SV5 @ SV63 )
= $false )
| ( ( ! [SY297: $i] :
( ( in @ SY297 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV63 @ ( singleton @ SY297 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(608,plain,
! [SV64: $i,SV6: $i] :
( ( ( in @ SV6 @ SV64 )
= $false )
| ( ( subset @ SV6 @ ( union @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(609,plain,
! [SV65: $i,SV98: $i,SV106: $i,SV7: $i] :
( ( ( SV7 = SV106 )
| ( SV7 = SV98 )
| ( ( unordered_pair @ SV7 @ SV65 )
!= ( unordered_pair @ SV98 @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(610,plain,
! [SV66: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV66 )
= $false )
| ( ( ( set_union2 @ SV8 @ SV66 )
= SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(611,plain,
! [SV99: $i,SV68: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV68 )
| ~ ( subset @ SV10 @ SV99 ) )
= $true )
| ( ( subset @ SV10 @ ( set_intersection2 @ SV68 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(612,plain,
! [SV100: $i,SV69: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV69 )
| ~ ( subset @ SV69 @ SV100 ) )
= $true )
| ( ( subset @ SV11 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(613,plain,
! [SV70: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV70 )
= $false )
| ( ( ! [SY302: $i] : ( subset @ ( set_intersection2 @ SV12 @ SY302 ) @ ( set_intersection2 @ SV70 @ SY302 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(614,plain,
! [SV71: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV71 )
= $false )
| ( ( ( set_intersection2 @ SV13 @ SV71 )
= SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(615,plain,
! [SV72: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV72 )
= $false )
| ( ( ! [SY303: $i] : ( subset @ ( set_difference @ SV15 @ SY303 ) @ ( set_difference @ SV72 @ SY303 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(616,plain,
! [SV76: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV76 )
= $false )
| ( ( SV76
= ( set_union2 @ SV20 @ ( set_difference @ SV76 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(617,plain,
! [SV22: $i,SV78: $i] :
( ( ( proper_subset @ SV78 @ SV22 )
= $false )
| ( ( ~ ( subset @ SV22 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(618,plain,
! [SV23: $i,SV101: $i,SV79: $i] :
( ( ( ~ ( disjoint @ SV79 @ SV101 )
| ~ ( subset @ SV23 @ SV79 ) )
= $true )
| ( ( disjoint @ SV23 @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(619,plain,
! [SV80: $i,SV25: $i] :
( ( ( subset @ ( singleton @ SV25 ) @ ( singleton @ SV80 ) )
= $false )
| ( ( SV25 = SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(620,plain,
! [SV102: $i,SV82: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ SV82 )
| ~ ( subset @ SV102 @ SV82 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV27 @ SV102 ) @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(621,plain,
! [SV107: $i,SV83: $i,SV28: $i] :
( ( ( ( ( singleton @ SV28 )
!= ( unordered_pair @ SV83 @ SV107 ) ) )
= $true )
| ( ( SV28 = SV83 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(622,plain,
! [SV103: $i,SV84: $i,SV29: $i] :
( ( ( ( ( singleton @ SV29 )
!= ( unordered_pair @ SV84 @ SV103 ) ) )
= $true )
| ( ( SV84 = SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(623,plain,
! [SV85: $i,SV30: $i] :
( ( ( in @ SV30 @ SV85 )
= $false )
| ( ( ~ ( in @ SV85 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(624,plain,
! [SV86: $i,SV31: $i] :
( ( ( proper_subset @ SV31 @ SV86 )
= $false )
| ( ( ~ ( proper_subset @ SV86 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(625,plain,
! [SV104: $i,SV37: $i] :
( ( ( empty @ ( set_union2 @ SV37 @ SV104 ) )
= $false )
| ( ( empty @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(626,plain,
! [SV38: $i,SV105: $i] :
( ( ( empty @ ( set_union2 @ SV105 @ SV38 ) )
= $false )
| ( ( empty @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(627,plain,
! [SV92: $i,SV43: $i] :
( ( ( disjoint @ SV43 @ SV92 )
= $false )
| ( ( disjoint @ SV92 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(628,plain,
! [SV49: $i,SV93: $i] :
( ( ( empty @ SV93 )
= $false )
| ( ( ~ ( in @ SV49 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(629,plain,
! [SV94: $i,SV50: $i] :
( ( ( SV50 = SV94 )
= $true )
| ( ( ~ ( empty @ SV50 ) )
= $true )
| ( ( ~ ( empty @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(630,plain,
! [SV108: $i] :
( ( ! [SY319: $i] :
( ( ( set_difference @ SV108 @ SY319 )
!= SV108 )
| ( disjoint @ SV108 @ SY319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(631,plain,
! [SV109: $i] :
( ( ! [SY320: $i] :
( ~ ( disjoint @ SV109 @ SY320 )
| ( ( set_difference @ SV109 @ SY320 )
= SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(632,plain,
! [SV110: $i] :
( ( ! [SY321: $i] :
( ( ( set_difference @ SV110 @ SY321 )
!= empty_set )
| ( subset @ SV110 @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(633,plain,
! [SV111: $i] :
( ( ! [SY322: $i] :
( ~ ( subset @ SV111 @ SY322 )
| ( ( set_difference @ SV111 @ SY322 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(634,plain,
! [SV51: $i] :
( ( ! [SY240: $i,SY241: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY241 @ SY240 @ SV51 ) @ SY241 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY241 @ SY240 @ SV51 ) @ SY241 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
!= SY240 ) ) )
| ~ ( ( in @ ( sK18_D @ SY241 @ SY240 @ SV51 ) @ SY241 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
= SV51 )
| ( ( sK18_D @ SY241 @ SY240 @ SV51 )
= SY240 ) ) )
| ( SY241
= ( unordered_pair @ SV51 @ SY240 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(635,plain,
! [SV51: $i] :
( ( ! [SY242: $i,SY243: $i] :
( ( SY243
!= ( unordered_pair @ SV51 @ SY242 ) )
| ~ ( ~ ! [SY244: $i] :
( ~ ( in @ SY244 @ SY243 )
| ( SY244 = SV51 )
| ( SY244 = SY242 ) )
| ~ ~ ( ~ ! [SY245: $i] :
( ( SY245 != SV51 )
| ( in @ SY245 @ SY243 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY242 )
| ( in @ SX3 @ SY243 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(636,plain,
! [SV52: $i] :
( ( ! [SY247: $i,SY248: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SV52 )
| ~ ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY247 )
| ~ ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY248 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY248 ) )
| ~ ( ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY247 )
| ( in @ ( sK10_D @ SY248 @ SY247 @ SV52 ) @ SY248 ) ) ) )
| ( SY248
= ( set_intersection2 @ SV52 @ SY247 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(637,plain,
! [SV52: $i] :
( ( ! [SY249: $i,SY250: $i] :
( ( SY250
!= ( set_intersection2 @ SV52 @ SY249 ) )
| ~ ( ~ ! [SY251: $i] :
( ~ ( in @ SY251 @ SV52 )
| ~ ( in @ SY251 @ SY249 )
| ( in @ SY251 @ SY250 ) )
| ~ ~ ( ~ ! [SY252: $i] :
( ~ ( in @ SY252 @ SY250 )
| ( in @ SY252 @ SV52 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY250 )
| ( in @ SX3 @ SY249 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(638,plain,
! [SV112: $i] :
( ( ! [SY323: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_C @ SY323 @ SV112 ) @ SY323 )
| ~ ( subset @ ( sK19_C @ SY323 @ SV112 ) @ SV112 ) )
| ~ ( ( in @ ( sK19_C @ SY323 @ SV112 ) @ SY323 )
| ( subset @ ( sK19_C @ SY323 @ SV112 ) @ SV112 ) ) )
| ( SY323
= ( powerset @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(639,plain,
! [SV113: $i] :
( ( ! [SY324: $i] :
( ( SY324
!= ( powerset @ SV113 ) )
| ~ ( ~ ! [SY325: $i] :
( ~ ( in @ SY325 @ SY324 )
| ( subset @ SY325 @ SV113 ) )
| ~ ! [SY326: $i] :
( ~ ( subset @ SY326 @ SV113 )
| ( in @ SY326 @ SY324 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(640,plain,
! [SV114: $i] :
( ( ! [SY327: $i] :
( ~ ( in @ SV114 @ SY327 )
| ( subset @ ( singleton @ SV114 ) @ SY327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(641,plain,
! [SV115: $i] :
( ( ! [SY328: $i] :
( ~ ( subset @ ( singleton @ SV115 ) @ SY328 )
| ( in @ SV115 @ SY328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(642,plain,
! [SV116: $i] :
( ( ! [SY329: $i] :
( ( SV116 = SY329 )
| ~ ( subset @ SV116 @ SY329 )
| ( proper_subset @ SV116 @ SY329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(643,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)],[569]) ).
thf(644,plain,
! [SV117: $i] :
( ( ( in @ ( sK20_B @ SV117 ) @ SV117 )
| ( SV117 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(645,plain,
! [SV118: $i] :
( ( ( SV118 != empty_set )
| ! [SY330: $i] :
~ ( in @ SY330 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(646,plain,
! [SV119: $i] :
( ( ! [SY331: $i] :
( ( disjoint @ SV119 @ SY331 )
| ( in @ ( sK22_C @ SY331 @ SV119 ) @ ( set_intersection2 @ SV119 @ SY331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(647,plain,
! [SV120: $i] :
( ( ! [SY332: $i] :
( ! [SY333: $i] :
~ ( in @ SY333 @ ( set_intersection2 @ SV120 @ SY332 ) )
| ~ ( disjoint @ SV120 @ SY332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(648,plain,
! [SV53: $i] :
( ( ! [SY254: $i,SY255: $i] :
( ~ ( in @ SV53 @ SY255 )
| ~ ( in @ SY254 @ SY255 )
| ( subset @ ( unordered_pair @ SV53 @ SY254 ) @ SY255 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(649,plain,
! [SV53: $i] :
( ( ~ ( ~ ! [SY256: $i,SY257: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY256 ) @ SY257 )
| ( in @ SV53 @ SY257 ) )
| ~ ! [SY258: $i,SY259: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY258 ) @ SY259 )
| ( in @ SY258 @ SY259 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(650,plain,
! [SV95: $i,SV54: $i] :
( ( ~ ! [SY308: $i,SY309: $i] :
( ~ ( in @ SV54 @ SY308 )
| ~ ( in @ SV95 @ SY309 )
| ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY308 @ SY309 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[576]) ).
thf(651,plain,
! [SV95: $i,SV54: $i] :
( ( ~ ~ ( ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY310 @ SY311 ) )
| ( in @ SV54 @ SY310 ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY312 @ SY313 ) )
| ( in @ SV95 @ SY313 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[576]) ).
thf(652,plain,
! [SV121: $i] :
( ( ! [SY334: $i] :
( ~ ( subset @ SV121 @ SY334 )
| ~ ( subset @ SY334 @ SV121 )
| ( SV121 = SY334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(653,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)],[578]) ).
thf(654,plain,
! [SV55: $i] :
( ( ! [SY267: $i,SY268: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY267 )
| ~ ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY268 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY268 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY267 )
| ( in @ ( sK6_D @ SY268 @ SY267 @ SV55 ) @ SY268 ) ) ) )
| ( SY268
= ( set_difference @ SV55 @ SY267 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(655,plain,
! [SV55: $i] :
( ( ! [SY269: $i,SY270: $i] :
( ( SY270
!= ( set_difference @ SV55 @ SY269 ) )
| ~ ( ~ ! [SY271: $i] :
( ~ ( in @ SY271 @ SV55 )
| ( in @ SY271 @ SY269 )
| ( in @ SY271 @ SY270 ) )
| ~ ~ ( ~ ! [SY272: $i] :
( ~ ( in @ SY272 @ SY270 )
| ( in @ SY272 @ SV55 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY270 )
| ~ ( in @ SX3 @ SY269 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(656,plain,
! [SV56: $i] :
( ( ! [SY274: $i,SY275: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY275 )
| ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY275 )
| ~ ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY274 ) ) )
| ~ ( ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY275 )
| ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SY275 @ SY274 @ SV56 ) @ SY274 ) ) )
| ( SY275
= ( set_union2 @ SV56 @ SY274 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(657,plain,
! [SV56: $i] :
( ( ! [SY276: $i,SY277: $i] :
( ( SY277
!= ( set_union2 @ SV56 @ SY276 ) )
| ~ ( ~ ! [SY278: $i] :
( ~ ( in @ SY278 @ SY277 )
| ( in @ SY278 @ SV56 )
| ( in @ SY278 @ SY276 ) )
| ~ ~ ( ~ ! [SY279: $i] :
( ~ ( in @ SY279 @ SV56 )
| ( in @ SY279 @ SY277 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY276 )
| ( in @ SX3 @ SY277 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(658,plain,
! [SV122: $i] :
( ( ! [SY335: $i] :
( ( ( set_intersection2 @ SV122 @ SY335 )
!= empty_set )
| ( disjoint @ SV122 @ SY335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(659,plain,
! [SV123: $i] :
( ( ! [SY336: $i] :
( ~ ( disjoint @ SV123 @ SY336 )
| ( ( set_intersection2 @ SV123 @ SY336 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(660,plain,
( ( ~ ( ( sK1_A != empty_set ) )
| ~ ( ( sK1_A
!= ( singleton @ sK2_SY183 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(661,plain,
! [SV124: $i] :
( ( ! [SY337: $i] :
( ~ ( subset @ SV124 @ ( singleton @ SY337 ) )
| ( SV124 = empty_set )
| ( SV124
= ( singleton @ SY337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(662,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)],[588]) ).
thf(663,plain,
! [SV125: $i] :
( ( ! [SY338: $i] :
( ~ ( in @ SV125 @ SY338 )
| ( subset @ ( singleton @ SV125 ) @ SY338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(664,plain,
! [SV126: $i] :
( ( ! [SY339: $i] :
( ~ ( subset @ ( singleton @ SV126 ) @ SY339 )
| ( in @ SV126 @ SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(665,plain,
! [SV127: $i] :
( ( ! [SY340: $i] :
( ~ ( ~ ( in @ ( sK11_C @ SY340 @ SV127 ) @ SV127 )
| ~ ~ ( in @ ( sK11_C @ SY340 @ SV127 ) @ SY340 ) )
| ( subset @ SV127 @ SY340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(666,plain,
! [SV128: $i] :
( ( ! [SY341: $i] :
( ~ ( subset @ SV128 @ SY341 )
| ! [SY342: $i] :
( ~ ( in @ SY342 @ SV128 )
| ( in @ SY342 @ SY341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(667,plain,
! [SV96: $i,SV57: $i] :
( ( ~ ! [SY314: $i] :
( ! [SY315: $i] :
( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SY314 @ SY315 ) )
| ( SV57 = SY314 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[593]) ).
thf(668,plain,
! [SV96: $i,SV57: $i] :
( ( ~ ! [SY316: $i,SY317: $i] :
( ( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SY316 @ SY317 ) )
| ( SV96 = SY317 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[593]) ).
thf(669,plain,
! [SV58: $i,SV97: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 ) )
| ~ ( ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
| ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 ) ) )
= $false )
| ( ( SV58 = SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(670,plain,
! [SV129: $i] :
( ( ! [SY343: $i] :
( ( disjoint @ SV129 @ SY343 )
| ~ ( ~ ( in @ ( sK23_C @ SY343 @ SV129 ) @ SV129 )
| ~ ( in @ ( sK23_C @ SY343 @ SV129 ) @ SY343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(671,plain,
! [SV130: $i] :
( ( ! [SY344: $i] :
( ! [SY345: $i] :
( ~ ( in @ SY345 @ SV130 )
| ~ ( in @ SY345 @ SY344 ) )
| ~ ( disjoint @ SV130 @ SY344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(672,plain,
! [SV131: $i] :
( ( ! [SY346: $i] :
( ~ ( ~ ( ( ( sK21_C @ SY346 @ SV131 )
!= SV131 )
| ~ ( in @ ( sK21_C @ SY346 @ SV131 ) @ SY346 ) )
| ~ ( ( ( sK21_C @ SY346 @ SV131 )
= SV131 )
| ( in @ ( sK21_C @ SY346 @ SV131 ) @ SY346 ) ) )
| ( SY346
= ( singleton @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(673,plain,
! [SV132: $i] :
( ( ! [SY347: $i] :
( ( SY347
!= ( singleton @ SV132 ) )
| ~ ( ~ ! [SY348: $i] :
( ( SY348 != SV132 )
| ( in @ SY348 @ SY347 ) )
| ~ ! [SY349: $i] :
( ~ ( in @ SY349 @ SY347 )
| ( SY349 = SV132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(674,plain,
! [SV133: $i] :
( ( ! [SY350: $i] :
( ~ ( ~ ( ! [SY351: $i] :
( ~ ( in @ ( sK8_C @ SY350 @ SV133 ) @ SY351 )
| ~ ( in @ SY351 @ SV133 ) )
| ~ ( in @ ( sK8_C @ SY350 @ SV133 ) @ SY350 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SY350 @ SV133 ) @ ( sK9_SY185 @ SY350 @ SV133 ) )
| ~ ( in @ ( sK9_SY185 @ SY350 @ SV133 ) @ SV133 ) )
| ( in @ ( sK8_C @ SY350 @ SV133 ) @ SY350 ) ) )
| ( SY350
= ( union @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(675,plain,
! [SV134: $i] :
( ( ! [SY352: $i] :
( ( SY352
!= ( union @ SV134 ) )
| ~ ( ~ ! [SY353: $i] :
( ! [SY354: $i] :
( ~ ( in @ SY353 @ SY354 )
| ~ ( in @ SY354 @ SV134 ) )
| ( in @ SY353 @ SY352 ) )
| ~ ! [SY355: $i] :
( ~ ( in @ SY355 @ SY352 )
| ~ ( ~ ( in @ SY355 @ ( sK7_D @ SY355 @ SY352 @ SV134 ) )
| ~ ( in @ ( sK7_D @ SY355 @ SY352 @ SV134 ) @ SV134 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(676,plain,
! [SV135: $i] :
( ( ! [SY356: $i] :
( ( ( set_difference @ SV135 @ SY356 )
!= empty_set )
| ( subset @ SV135 @ SY356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(677,plain,
! [SV136: $i] :
( ( ! [SY357: $i] :
( ~ ( subset @ SV136 @ SY357 )
| ( ( set_difference @ SV136 @ SY357 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(678,plain,
! [SV59: $i] :
( ( ! [SY287: $i,SY288: $i] :
( ~ ( ~ ( ! [SY289: $i,SY290: $i] :
( ~ ( in @ SY289 @ SV59 )
| ~ ( in @ SY290 @ SY287 )
| ( ( sK14_D @ SY288 @ SY287 @ SV59 )
!= ( ordered_pair @ SY289 @ SY290 ) ) )
| ~ ( in @ ( sK14_D @ SY288 @ SY287 @ SV59 ) @ SY288 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SY288 @ SY287 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SY288 @ SY287 @ SV59 ) @ SY287 ) )
| ( ( sK14_D @ SY288 @ SY287 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SY288 @ SY287 @ SV59 ) @ ( sK16_SY191 @ SY288 @ SY287 @ SV59 ) ) ) )
| ( in @ ( sK14_D @ SY288 @ SY287 @ SV59 ) @ SY288 ) ) )
| ( SY288
= ( cartesian_product2 @ SV59 @ SY287 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[603]) ).
thf(679,plain,
! [SV59: $i] :
( ( ! [SY291: $i,SY292: $i] :
( ( SY292
!= ( cartesian_product2 @ SV59 @ SY291 ) )
| ~ ( ~ ! [SY293: $i] :
( ! [SY294: $i,SY295: $i] :
( ~ ( in @ SY294 @ SV59 )
| ~ ( in @ SY295 @ SY291 )
| ( SY293
!= ( ordered_pair @ SY294 @ SY295 ) ) )
| ( in @ SY293 @ SY292 ) )
| ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ SY292 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY296 @ SY292 @ SY291 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SY296 @ SY292 @ SY291 @ SV59 ) @ SY291 ) )
| ( SY296
!= ( ordered_pair @ ( sK12_E @ SY296 @ SY292 @ SY291 @ SV59 ) @ ( sK13_SY186 @ SY296 @ SY292 @ SY291 @ SV59 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[604]) ).
thf(680,plain,
! [SV61: $i,SV3: $i] :
( ( ( in @ SV3 @ SV61 )
= $false )
| ( ( disjoint @ ( singleton @ SV3 ) @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(681,plain,
! [SV63: $i,SV5: $i,SV137: $i] :
( ( ( ( in @ SV137 @ SV5 )
| ( subset @ SV5 @ ( set_difference @ SV63 @ ( singleton @ SV137 ) ) ) )
= $true )
| ( ( subset @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(682,plain,
! [SV65: $i,SV98: $i,SV106: $i,SV7: $i] :
( ( ( SV7 = SV106 )
= $true )
| ( ( ( SV7 = SV98 )
| ( ( unordered_pair @ SV7 @ SV65 )
!= ( unordered_pair @ SV98 @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(683,plain,
! [SV99: $i,SV68: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV68 ) )
= $true )
| ( ( ~ ( subset @ SV10 @ SV99 ) )
= $true )
| ( ( subset @ SV10 @ ( set_intersection2 @ SV68 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(684,plain,
! [SV100: $i,SV69: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV69 ) )
= $true )
| ( ( ~ ( subset @ SV69 @ SV100 ) )
= $true )
| ( ( subset @ SV11 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(685,plain,
! [SV70: $i,SV138: $i,SV12: $i] :
( ( ( subset @ ( set_intersection2 @ SV12 @ SV138 ) @ ( set_intersection2 @ SV70 @ SV138 ) )
= $true )
| ( ( subset @ SV12 @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(686,plain,
! [SV72: $i,SV139: $i,SV15: $i] :
( ( ( subset @ ( set_difference @ SV15 @ SV139 ) @ ( set_difference @ SV72 @ SV139 ) )
= $true )
| ( ( subset @ SV15 @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(687,plain,
! [SV78: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV78 )
= $false )
| ( ( proper_subset @ SV78 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(688,plain,
! [SV23: $i,SV101: $i,SV79: $i] :
( ( ( ~ ( disjoint @ SV79 @ SV101 ) )
= $true )
| ( ( ~ ( subset @ SV23 @ SV79 ) )
= $true )
| ( ( disjoint @ SV23 @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(689,plain,
! [SV102: $i,SV82: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ SV82 ) )
= $true )
| ( ( ~ ( subset @ SV102 @ SV82 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV27 @ SV102 ) @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(690,plain,
! [SV107: $i,SV83: $i,SV28: $i] :
( ( ( ( singleton @ SV28 )
= ( unordered_pair @ SV83 @ SV107 ) )
= $false )
| ( ( SV28 = SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(691,plain,
! [SV103: $i,SV84: $i,SV29: $i] :
( ( ( ( singleton @ SV29 )
= ( unordered_pair @ SV84 @ SV103 ) )
= $false )
| ( ( SV84 = SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(692,plain,
! [SV30: $i,SV85: $i] :
( ( ( in @ SV85 @ SV30 )
= $false )
| ( ( in @ SV30 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(693,plain,
! [SV31: $i,SV86: $i] :
( ( ( proper_subset @ SV86 @ SV31 )
= $false )
| ( ( proper_subset @ SV31 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(694,plain,
! [SV93: $i,SV49: $i] :
( ( ( in @ SV49 @ SV93 )
= $false )
| ( ( empty @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(695,plain,
! [SV94: $i,SV50: $i] :
( ( ( empty @ SV50 )
= $false )
| ( ( SV50 = SV94 )
= $true )
| ( ( ~ ( empty @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(696,plain,
! [SV140: $i,SV108: $i] :
( ( ( ( set_difference @ SV108 @ SV140 )
!= SV108 )
| ( disjoint @ SV108 @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(697,plain,
! [SV141: $i,SV109: $i] :
( ( ~ ( disjoint @ SV109 @ SV141 )
| ( ( set_difference @ SV109 @ SV141 )
= SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(698,plain,
! [SV142: $i,SV110: $i] :
( ( ( ( set_difference @ SV110 @ SV142 )
!= empty_set )
| ( subset @ SV110 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(699,plain,
! [SV143: $i,SV111: $i] :
( ( ~ ( subset @ SV111 @ SV143 )
| ( ( set_difference @ SV111 @ SV143 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(700,plain,
! [SV51: $i,SV144: $i] :
( ( ! [SY358: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY358 @ SV144 @ SV51 ) @ SY358 )
| ( ( sK18_D @ SY358 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY358 @ SV144 @ SV51 ) @ SY358 )
| ( ( sK18_D @ SY358 @ SV144 @ SV51 )
!= SV144 ) ) )
| ~ ( ( in @ ( sK18_D @ SY358 @ SV144 @ SV51 ) @ SY358 )
| ( ( sK18_D @ SY358 @ SV144 @ SV51 )
= SV51 )
| ( ( sK18_D @ SY358 @ SV144 @ SV51 )
= SV144 ) ) )
| ( SY358
= ( unordered_pair @ SV51 @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(701,plain,
! [SV145: $i,SV51: $i] :
( ( ! [SY359: $i] :
( ( SY359
!= ( unordered_pair @ SV51 @ SV145 ) )
| ~ ( ~ ! [SY360: $i] :
( ~ ( in @ SY360 @ SY359 )
| ( SY360 = SV51 )
| ( SY360 = SV145 ) )
| ~ ~ ( ~ ! [SY245: $i] :
( ( SY245 != SV51 )
| ( in @ SY245 @ SY359 ) )
| ~ ! [SY362: $i] :
( ( SY362 != SV145 )
| ( in @ SY362 @ SY359 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(702,plain,
! [SV52: $i,SV146: $i] :
( ( ! [SY363: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY363 @ SV146 @ SV52 ) @ SV52 )
| ~ ( in @ ( sK10_D @ SY363 @ SV146 @ SV52 ) @ SV146 )
| ~ ( in @ ( sK10_D @ SY363 @ SV146 @ SV52 ) @ SY363 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY363 @ SV146 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SY363 @ SV146 @ SV52 ) @ SY363 ) )
| ~ ( ( in @ ( sK10_D @ SY363 @ SV146 @ SV52 ) @ SV146 )
| ( in @ ( sK10_D @ SY363 @ SV146 @ SV52 ) @ SY363 ) ) ) )
| ( SY363
= ( set_intersection2 @ SV52 @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(703,plain,
! [SV147: $i,SV52: $i] :
( ( ! [SY364: $i] :
( ( SY364
!= ( set_intersection2 @ SV52 @ SV147 ) )
| ~ ( ~ ! [SY365: $i] :
( ~ ( in @ SY365 @ SV52 )
| ~ ( in @ SY365 @ SV147 )
| ( in @ SY365 @ SY364 ) )
| ~ ~ ( ~ ! [SY252: $i] :
( ~ ( in @ SY252 @ SY364 )
| ( in @ SY252 @ SV52 ) )
| ~ ! [SY367: $i] :
( ~ ( in @ SY367 @ SY364 )
| ( in @ SY367 @ SV147 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(704,plain,
! [SV112: $i,SV148: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
| ~ ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 ) )
| ~ ( ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
| ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 ) ) )
| ( SV148
= ( powerset @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(705,plain,
! [SV113: $i,SV149: $i] :
( ( ( SV149
!= ( powerset @ SV113 ) )
| ~ ( ~ ! [SY368: $i] :
( ~ ( in @ SY368 @ SV149 )
| ( subset @ SY368 @ SV113 ) )
| ~ ! [SY369: $i] :
( ~ ( subset @ SY369 @ SV113 )
| ( in @ SY369 @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(706,plain,
! [SV150: $i,SV114: $i] :
( ( ~ ( in @ SV114 @ SV150 )
| ( subset @ ( singleton @ SV114 ) @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(707,plain,
! [SV151: $i,SV115: $i] :
( ( ~ ( subset @ ( singleton @ SV115 ) @ SV151 )
| ( in @ SV115 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(708,plain,
! [SV152: $i,SV116: $i] :
( ( ( SV116 = SV152 )
| ~ ( subset @ SV116 @ SV152 )
| ( proper_subset @ SV116 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(709,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(710,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(711,plain,
! [SV117: $i] :
( ( ( in @ ( sK20_B @ SV117 ) @ SV117 )
= $true )
| ( ( SV117 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(712,plain,
! [SV118: $i] :
( ( ( ( SV118 != empty_set ) )
= $true )
| ( ( ! [SY330: $i] :
~ ( in @ SY330 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(713,plain,
! [SV153: $i,SV119: $i] :
( ( ( disjoint @ SV119 @ SV153 )
| ( in @ ( sK22_C @ SV153 @ SV119 ) @ ( set_intersection2 @ SV119 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(714,plain,
! [SV154: $i,SV120: $i] :
( ( ! [SY370: $i] :
~ ( in @ SY370 @ ( set_intersection2 @ SV120 @ SV154 ) )
| ~ ( disjoint @ SV120 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(715,plain,
! [SV155: $i,SV53: $i] :
( ( ! [SY371: $i] :
( ~ ( in @ SV53 @ SY371 )
| ~ ( in @ SV155 @ SY371 )
| ( subset @ ( unordered_pair @ SV53 @ SV155 ) @ SY371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(716,plain,
! [SV53: $i] :
( ( ~ ! [SY256: $i,SY257: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY256 ) @ SY257 )
| ( in @ SV53 @ SY257 ) )
| ~ ! [SY258: $i,SY259: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY258 ) @ SY259 )
| ( in @ SY258 @ SY259 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(717,plain,
! [SV95: $i,SV54: $i] :
( ( ! [SY308: $i,SY309: $i] :
( ~ ( in @ SV54 @ SY308 )
| ~ ( in @ SV95 @ SY309 )
| ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY308 @ SY309 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(718,plain,
! [SV95: $i,SV54: $i] :
( ( ~ ( ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY310 @ SY311 ) )
| ( in @ SV54 @ SY310 ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY312 @ SY313 ) )
| ( in @ SV95 @ SY313 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(719,plain,
! [SV156: $i,SV121: $i] :
( ( ~ ( subset @ SV121 @ SV156 )
| ~ ( subset @ SV156 @ SV121 )
| ( SV121 = SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(720,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(721,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(722,plain,
! [SV55: $i,SV157: $i] :
( ( ! [SY372: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY372 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SY372 @ SV157 @ SV55 ) @ SV157 )
| ~ ( in @ ( sK6_D @ SY372 @ SV157 @ SV55 ) @ SY372 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY372 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SY372 @ SV157 @ SV55 ) @ SY372 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY372 @ SV157 @ SV55 ) @ SV157 )
| ( in @ ( sK6_D @ SY372 @ SV157 @ SV55 ) @ SY372 ) ) ) )
| ( SY372
= ( set_difference @ SV55 @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(723,plain,
! [SV158: $i,SV55: $i] :
( ( ! [SY373: $i] :
( ( SY373
!= ( set_difference @ SV55 @ SV158 ) )
| ~ ( ~ ! [SY374: $i] :
( ~ ( in @ SY374 @ SV55 )
| ( in @ SY374 @ SV158 )
| ( in @ SY374 @ SY373 ) )
| ~ ~ ( ~ ! [SY272: $i] :
( ~ ( in @ SY272 @ SY373 )
| ( in @ SY272 @ SV55 ) )
| ~ ! [SY376: $i] :
( ~ ( in @ SY376 @ SY373 )
| ~ ( in @ SY376 @ SV158 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(724,plain,
! [SV56: $i,SV159: $i] :
( ( ! [SY377: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY377 @ SV159 @ SV56 ) @ SY377 )
| ~ ( in @ ( sK17_D @ SY377 @ SV159 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY377 @ SV159 @ SV56 ) @ SY377 )
| ~ ( in @ ( sK17_D @ SY377 @ SV159 @ SV56 ) @ SV159 ) ) )
| ~ ( ( in @ ( sK17_D @ SY377 @ SV159 @ SV56 ) @ SY377 )
| ( in @ ( sK17_D @ SY377 @ SV159 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SY377 @ SV159 @ SV56 ) @ SV159 ) ) )
| ( SY377
= ( set_union2 @ SV56 @ SV159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(725,plain,
! [SV160: $i,SV56: $i] :
( ( ! [SY378: $i] :
( ( SY378
!= ( set_union2 @ SV56 @ SV160 ) )
| ~ ( ~ ! [SY379: $i] :
( ~ ( in @ SY379 @ SY378 )
| ( in @ SY379 @ SV56 )
| ( in @ SY379 @ SV160 ) )
| ~ ~ ( ~ ! [SY279: $i] :
( ~ ( in @ SY279 @ SV56 )
| ( in @ SY279 @ SY378 ) )
| ~ ! [SY381: $i] :
( ~ ( in @ SY381 @ SV160 )
| ( in @ SY381 @ SY378 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(726,plain,
! [SV161: $i,SV122: $i] :
( ( ( ( set_intersection2 @ SV122 @ SV161 )
!= empty_set )
| ( disjoint @ SV122 @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(727,plain,
! [SV162: $i,SV123: $i] :
( ( ~ ( disjoint @ SV123 @ SV162 )
| ( ( set_intersection2 @ SV123 @ SV162 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(728,plain,
( ( ~ ( ( sK1_A != empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[660]) ).
thf(729,plain,
( ( ~ ( ( sK1_A
!= ( singleton @ sK2_SY183 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[660]) ).
thf(730,plain,
! [SV163: $i,SV124: $i] :
( ( ~ ( subset @ SV124 @ ( singleton @ SV163 ) )
| ( SV124 = empty_set )
| ( SV124
= ( singleton @ SV163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(731,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(732,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(733,plain,
! [SV164: $i,SV125: $i] :
( ( ~ ( in @ SV125 @ SV164 )
| ( subset @ ( singleton @ SV125 ) @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(734,plain,
! [SV165: $i,SV126: $i] :
( ( ~ ( subset @ ( singleton @ SV126 ) @ SV165 )
| ( in @ SV126 @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(735,plain,
! [SV127: $i,SV166: $i] :
( ( ~ ( ~ ( in @ ( sK11_C @ SV166 @ SV127 ) @ SV127 )
| ~ ~ ( in @ ( sK11_C @ SV166 @ SV127 ) @ SV166 ) )
| ( subset @ SV127 @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(736,plain,
! [SV167: $i,SV128: $i] :
( ( ~ ( subset @ SV128 @ SV167 )
| ! [SY382: $i] :
( ~ ( in @ SY382 @ SV128 )
| ( in @ SY382 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(737,plain,
! [SV96: $i,SV57: $i] :
( ( ! [SY314: $i] :
( ! [SY315: $i] :
( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SY314 @ SY315 ) )
| ( SV57 = SY314 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[667]) ).
thf(738,plain,
! [SV96: $i,SV57: $i] :
( ( ! [SY316: $i,SY317: $i] :
( ( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SY316 @ SY317 ) )
| ( SV96 = SY317 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(739,plain,
! [SV58: $i,SV97: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 ) ) )
= $false )
| ( ( SV58 = SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[669]) ).
thf(740,plain,
! [SV58: $i,SV97: $i] :
( ( ( ~ ( ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
| ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 ) ) )
= $false )
| ( ( SV58 = SV97 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[669]) ).
thf(741,plain,
! [SV168: $i,SV129: $i] :
( ( ( disjoint @ SV129 @ SV168 )
| ~ ( ~ ( in @ ( sK23_C @ SV168 @ SV129 ) @ SV129 )
| ~ ( in @ ( sK23_C @ SV168 @ SV129 ) @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(742,plain,
! [SV169: $i,SV130: $i] :
( ( ! [SY383: $i] :
( ~ ( in @ SY383 @ SV130 )
| ~ ( in @ SY383 @ SV169 ) )
| ~ ( disjoint @ SV130 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(743,plain,
! [SV131: $i,SV170: $i] :
( ( ~ ( ~ ( ( ( sK21_C @ SV170 @ SV131 )
!= SV131 )
| ~ ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 ) )
| ~ ( ( ( sK21_C @ SV170 @ SV131 )
= SV131 )
| ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 ) ) )
| ( SV170
= ( singleton @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(744,plain,
! [SV132: $i,SV171: $i] :
( ( ( SV171
!= ( singleton @ SV132 ) )
| ~ ( ~ ! [SY384: $i] :
( ( SY384 != SV132 )
| ( in @ SY384 @ SV171 ) )
| ~ ! [SY385: $i] :
( ~ ( in @ SY385 @ SV171 )
| ( SY385 = SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(745,plain,
! [SV133: $i,SV172: $i] :
( ( ~ ( ~ ( ! [SY386: $i] :
( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SY386 )
| ~ ( in @ SY386 @ SV133 ) )
| ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ ( sK9_SY185 @ SV172 @ SV133 ) )
| ~ ( in @ ( sK9_SY185 @ SV172 @ SV133 ) @ SV133 ) )
| ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) ) )
| ( SV172
= ( union @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(746,plain,
! [SV134: $i,SV173: $i] :
( ( ( SV173
!= ( union @ SV134 ) )
| ~ ( ~ ! [SY387: $i] :
( ! [SY354: $i] :
( ~ ( in @ SY387 @ SY354 )
| ~ ( in @ SY354 @ SV134 ) )
| ( in @ SY387 @ SV173 ) )
| ~ ! [SY389: $i] :
( ~ ( in @ SY389 @ SV173 )
| ~ ( ~ ( in @ SY389 @ ( sK7_D @ SY389 @ SV173 @ SV134 ) )
| ~ ( in @ ( sK7_D @ SY389 @ SV173 @ SV134 ) @ SV134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(747,plain,
! [SV174: $i,SV135: $i] :
( ( ( ( set_difference @ SV135 @ SV174 )
!= empty_set )
| ( subset @ SV135 @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(748,plain,
! [SV175: $i,SV136: $i] :
( ( ~ ( subset @ SV136 @ SV175 )
| ( ( set_difference @ SV136 @ SV175 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(749,plain,
! [SV176: $i,SV59: $i] :
( ( ! [SY390: $i] :
( ~ ( ~ ( ! [SY391: $i,SY392: $i] :
( ~ ( in @ SY391 @ SV59 )
| ~ ( in @ SY392 @ SV176 )
| ( ( sK14_D @ SY390 @ SV176 @ SV59 )
!= ( ordered_pair @ SY391 @ SY392 ) ) )
| ~ ( in @ ( sK14_D @ SY390 @ SV176 @ SV59 ) @ SY390 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SY390 @ SV176 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SY390 @ SV176 @ SV59 ) @ SV176 ) )
| ( ( sK14_D @ SY390 @ SV176 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SY390 @ SV176 @ SV59 ) @ ( sK16_SY191 @ SY390 @ SV176 @ SV59 ) ) ) )
| ( in @ ( sK14_D @ SY390 @ SV176 @ SV59 ) @ SY390 ) ) )
| ( SY390
= ( cartesian_product2 @ SV59 @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(750,plain,
! [SV177: $i,SV59: $i] :
( ( ! [SY393: $i] :
( ( SY393
!= ( cartesian_product2 @ SV59 @ SV177 ) )
| ~ ( ~ ! [SY394: $i] :
( ! [SY395: $i,SY396: $i] :
( ~ ( in @ SY395 @ SV59 )
| ~ ( in @ SY396 @ SV177 )
| ( SY394
!= ( ordered_pair @ SY395 @ SY396 ) ) )
| ( in @ SY394 @ SY393 ) )
| ~ ! [SY397: $i] :
( ~ ( in @ SY397 @ SY393 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY397 @ SY393 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SY397 @ SY393 @ SV177 @ SV59 ) @ SV177 ) )
| ( SY397
!= ( ordered_pair @ ( sK12_E @ SY397 @ SY393 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SY397 @ SY393 @ SV177 @ SV59 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(751,plain,
! [SV63: $i,SV5: $i,SV137: $i] :
( ( ( in @ SV137 @ SV5 )
= $true )
| ( ( subset @ SV5 @ ( set_difference @ SV63 @ ( singleton @ SV137 ) ) )
= $true )
| ( ( subset @ SV5 @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(752,plain,
! [SV106: $i,SV65: $i,SV98: $i,SV7: $i] :
( ( ( SV7 = SV98 )
= $true )
| ( ( ( ( unordered_pair @ SV7 @ SV65 )
!= ( unordered_pair @ SV98 @ SV106 ) ) )
= $true )
| ( ( SV7 = SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(753,plain,
! [SV99: $i,SV68: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV68 )
= $false )
| ( ( ~ ( subset @ SV10 @ SV99 ) )
= $true )
| ( ( subset @ SV10 @ ( set_intersection2 @ SV68 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(754,plain,
! [SV100: $i,SV69: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV69 )
= $false )
| ( ( ~ ( subset @ SV69 @ SV100 ) )
= $true )
| ( ( subset @ SV11 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(755,plain,
! [SV23: $i,SV101: $i,SV79: $i] :
( ( ( disjoint @ SV79 @ SV101 )
= $false )
| ( ( ~ ( subset @ SV23 @ SV79 ) )
= $true )
| ( ( disjoint @ SV23 @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(756,plain,
! [SV102: $i,SV82: $i,SV27: $i] :
( ( ( subset @ SV27 @ SV82 )
= $false )
| ( ( ~ ( subset @ SV102 @ SV82 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV27 @ SV102 ) @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(757,plain,
! [SV50: $i,SV94: $i] :
( ( ( empty @ SV94 )
= $false )
| ( ( SV50 = SV94 )
= $true )
| ( ( empty @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(758,plain,
! [SV140: $i,SV108: $i] :
( ( ( ( ( set_difference @ SV108 @ SV140 )
!= SV108 ) )
= $true )
| ( ( disjoint @ SV108 @ SV140 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(759,plain,
! [SV141: $i,SV109: $i] :
( ( ( ~ ( disjoint @ SV109 @ SV141 ) )
= $true )
| ( ( ( set_difference @ SV109 @ SV141 )
= SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(760,plain,
! [SV142: $i,SV110: $i] :
( ( ( ( ( set_difference @ SV110 @ SV142 )
!= empty_set ) )
= $true )
| ( ( subset @ SV110 @ SV142 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(761,plain,
! [SV143: $i,SV111: $i] :
( ( ( ~ ( subset @ SV111 @ SV143 ) )
= $true )
| ( ( ( set_difference @ SV111 @ SV143 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(762,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV144 ) ) )
| ~ ( ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV51 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV144 ) ) )
| ( SV178
= ( unordered_pair @ SV51 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(763,plain,
! [SV145: $i,SV51: $i,SV179: $i] :
( ( ( SV179
!= ( unordered_pair @ SV51 @ SV145 ) )
| ~ ( ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SV179 )
| ( SY398 = SV51 )
| ( SY398 = SV145 ) )
| ~ ~ ( ~ ! [SY399: $i] :
( ( SY399 != SV51 )
| ( in @ SY399 @ SV179 ) )
| ~ ! [SY400: $i] :
( ( SY400 != SV145 )
| ( in @ SY400 @ SV179 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(764,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
| ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) ) ) )
| ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(765,plain,
! [SV147: $i,SV52: $i,SV181: $i] :
( ( ( SV181
!= ( set_intersection2 @ SV52 @ SV147 ) )
| ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SV52 )
| ~ ( in @ SY401 @ SV147 )
| ( in @ SY401 @ SV181 ) )
| ~ ~ ( ~ ! [SY402: $i] :
( ~ ( in @ SY402 @ SV181 )
| ( in @ SY402 @ SV52 ) )
| ~ ! [SY403: $i] :
( ~ ( in @ SY403 @ SV181 )
| ( in @ SY403 @ SV147 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(766,plain,
! [SV112: $i,SV148: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
| ~ ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 ) )
| ~ ( ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
| ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 ) ) ) )
= $true )
| ( ( SV148
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(767,plain,
! [SV113: $i,SV149: $i] :
( ( ( ( SV149
!= ( powerset @ SV113 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY368: $i] :
( ~ ( in @ SY368 @ SV149 )
| ( subset @ SY368 @ SV113 ) )
| ~ ! [SY369: $i] :
( ~ ( subset @ SY369 @ SV113 )
| ( in @ SY369 @ SV149 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(768,plain,
! [SV150: $i,SV114: $i] :
( ( ( ~ ( in @ SV114 @ SV150 ) )
= $true )
| ( ( subset @ ( singleton @ SV114 ) @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(769,plain,
! [SV151: $i,SV115: $i] :
( ( ( ~ ( subset @ ( singleton @ SV115 ) @ SV151 ) )
= $true )
| ( ( in @ SV115 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(770,plain,
! [SV152: $i,SV116: $i] :
( ( ( ( SV116 = SV152 )
| ~ ( subset @ SV116 @ SV152 ) )
= $true )
| ( ( proper_subset @ SV116 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(771,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(772,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(773,plain,
! [SV118: $i] :
( ( ( SV118 = empty_set )
= $false )
| ( ( ! [SY330: $i] :
~ ( in @ SY330 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(774,plain,
! [SV153: $i,SV119: $i] :
( ( ( disjoint @ SV119 @ SV153 )
= $true )
| ( ( in @ ( sK22_C @ SV153 @ SV119 ) @ ( set_intersection2 @ SV119 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(775,plain,
! [SV154: $i,SV120: $i] :
( ( ( ! [SY370: $i] :
~ ( in @ SY370 @ ( set_intersection2 @ SV120 @ SV154 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV120 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(776,plain,
! [SV155: $i,SV182: $i,SV53: $i] :
( ( ~ ( in @ SV53 @ SV182 )
| ~ ( in @ SV155 @ SV182 )
| ( subset @ ( unordered_pair @ SV53 @ SV155 ) @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(777,plain,
! [SV53: $i] :
( ( ~ ! [SY256: $i,SY257: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY256 ) @ SY257 )
| ( in @ SV53 @ SY257 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(778,plain,
! [SV53: $i] :
( ( ~ ! [SY258: $i,SY259: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY258 ) @ SY259 )
| ( in @ SY258 @ SY259 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[716]) ).
thf(779,plain,
! [SV95: $i,SV183: $i,SV54: $i] :
( ( ! [SY404: $i] :
( ~ ( in @ SV54 @ SV183 )
| ~ ( in @ SV95 @ SY404 )
| ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV183 @ SY404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(780,plain,
! [SV95: $i,SV54: $i] :
( ( ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY310 @ SY311 ) )
| ( in @ SV54 @ SY310 ) )
| ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY312 @ SY313 ) )
| ( in @ SV95 @ SY313 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(781,plain,
! [SV156: $i,SV121: $i] :
( ( ( ~ ( subset @ SV121 @ SV156 )
| ~ ( subset @ SV156 @ SV121 ) )
= $true )
| ( ( SV121 = SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(782,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(783,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[721]) ).
thf(784,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) ) ) )
| ( SV184
= ( set_difference @ SV55 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(785,plain,
! [SV158: $i,SV55: $i,SV185: $i] :
( ( ( SV185
!= ( set_difference @ SV55 @ SV158 ) )
| ~ ( ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SV55 )
| ( in @ SY405 @ SV158 )
| ( in @ SY405 @ SV185 ) )
| ~ ~ ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SV185 )
| ( in @ SY406 @ SV55 ) )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV185 )
| ~ ( in @ SY407 @ SV158 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(786,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) ) )
| ~ ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) ) )
| ( SV186
= ( set_union2 @ SV56 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(787,plain,
! [SV160: $i,SV56: $i,SV187: $i] :
( ( ( SV187
!= ( set_union2 @ SV56 @ SV160 ) )
| ~ ( ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV187 )
| ( in @ SY408 @ SV56 )
| ( in @ SY408 @ SV160 ) )
| ~ ~ ( ~ ! [SY409: $i] :
( ~ ( in @ SY409 @ SV56 )
| ( in @ SY409 @ SV187 ) )
| ~ ! [SY410: $i] :
( ~ ( in @ SY410 @ SV160 )
| ( in @ SY410 @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(788,plain,
! [SV161: $i,SV122: $i] :
( ( ( ( ( set_intersection2 @ SV122 @ SV161 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV122 @ SV161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(789,plain,
! [SV162: $i,SV123: $i] :
( ( ( ~ ( disjoint @ SV123 @ SV162 ) )
= $true )
| ( ( ( set_intersection2 @ SV123 @ SV162 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(790,plain,
( ( ( sK1_A != empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(791,plain,
( ( ( sK1_A
!= ( singleton @ sK2_SY183 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(792,plain,
! [SV163: $i,SV124: $i] :
( ( ( ~ ( subset @ SV124 @ ( singleton @ SV163 ) ) )
= $true )
| ( ( ( SV124 = empty_set )
| ( SV124
= ( singleton @ SV163 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[730]) ).
thf(793,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[731]) ).
thf(794,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[732]) ).
thf(795,plain,
! [SV164: $i,SV125: $i] :
( ( ( ~ ( in @ SV125 @ SV164 ) )
= $true )
| ( ( subset @ ( singleton @ SV125 ) @ SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(796,plain,
! [SV165: $i,SV126: $i] :
( ( ( ~ ( subset @ ( singleton @ SV126 ) @ SV165 ) )
= $true )
| ( ( in @ SV126 @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(797,plain,
! [SV127: $i,SV166: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_C @ SV166 @ SV127 ) @ SV127 )
| ~ ~ ( in @ ( sK11_C @ SV166 @ SV127 ) @ SV166 ) ) )
= $true )
| ( ( subset @ SV127 @ SV166 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(798,plain,
! [SV167: $i,SV128: $i] :
( ( ( ~ ( subset @ SV128 @ SV167 ) )
= $true )
| ( ( ! [SY382: $i] :
( ~ ( in @ SY382 @ SV128 )
| ( in @ SY382 @ SV167 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(799,plain,
! [SV188: $i,SV96: $i,SV57: $i] :
( ( ! [SY411: $i] :
( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SV188 @ SY411 ) )
| ( SV57 = SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(800,plain,
! [SV189: $i,SV96: $i,SV57: $i] :
( ( ! [SY412: $i] :
( ( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SV189 @ SY412 ) )
| ( SV96 = SY412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(801,plain,
! [SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
| ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 ) )
= $true )
| ( ( SV58 = SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[739]) ).
thf(802,plain,
! [SV58: $i,SV97: $i] :
( ( ( ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
| ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 ) )
= $true )
| ( ( SV58 = SV97 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[740]) ).
thf(803,plain,
! [SV168: $i,SV129: $i] :
( ( ( disjoint @ SV129 @ SV168 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK23_C @ SV168 @ SV129 ) @ SV129 )
| ~ ( in @ ( sK23_C @ SV168 @ SV129 ) @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(804,plain,
! [SV169: $i,SV130: $i] :
( ( ( ! [SY383: $i] :
( ~ ( in @ SY383 @ SV130 )
| ~ ( in @ SY383 @ SV169 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV130 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(805,plain,
! [SV131: $i,SV170: $i] :
( ( ( ~ ( ~ ( ( ( sK21_C @ SV170 @ SV131 )
!= SV131 )
| ~ ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 ) )
| ~ ( ( ( sK21_C @ SV170 @ SV131 )
= SV131 )
| ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 ) ) ) )
= $true )
| ( ( SV170
= ( singleton @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(806,plain,
! [SV132: $i,SV171: $i] :
( ( ( ( SV171
!= ( singleton @ SV132 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY384: $i] :
( ( SY384 != SV132 )
| ( in @ SY384 @ SV171 ) )
| ~ ! [SY385: $i] :
( ~ ( in @ SY385 @ SV171 )
| ( SY385 = SV132 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(807,plain,
! [SV133: $i,SV172: $i] :
( ( ( ~ ( ~ ( ! [SY386: $i] :
( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SY386 )
| ~ ( in @ SY386 @ SV133 ) )
| ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ ( sK9_SY185 @ SV172 @ SV133 ) )
| ~ ( in @ ( sK9_SY185 @ SV172 @ SV133 ) @ SV133 ) )
| ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) ) ) )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(808,plain,
! [SV134: $i,SV173: $i] :
( ( ( ( SV173
!= ( union @ SV134 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY387: $i] :
( ! [SY354: $i] :
( ~ ( in @ SY387 @ SY354 )
| ~ ( in @ SY354 @ SV134 ) )
| ( in @ SY387 @ SV173 ) )
| ~ ! [SY389: $i] :
( ~ ( in @ SY389 @ SV173 )
| ~ ( ~ ( in @ SY389 @ ( sK7_D @ SY389 @ SV173 @ SV134 ) )
| ~ ( in @ ( sK7_D @ SY389 @ SV173 @ SV134 ) @ SV134 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(809,plain,
! [SV174: $i,SV135: $i] :
( ( ( ( ( set_difference @ SV135 @ SV174 )
!= empty_set ) )
= $true )
| ( ( subset @ SV135 @ SV174 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(810,plain,
! [SV175: $i,SV136: $i] :
( ( ( ~ ( subset @ SV136 @ SV175 ) )
= $true )
| ( ( ( set_difference @ SV136 @ SV175 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(811,plain,
! [SV190: $i,SV176: $i,SV59: $i] :
( ( ~ ( ~ ( ! [SY413: $i,SY414: $i] :
( ~ ( in @ SY413 @ SV59 )
| ~ ( in @ SY414 @ SV176 )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ SY413 @ SY414 ) ) )
| ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) @ SV176 ) )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) ) ) )
| ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) ) )
| ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(812,plain,
! [SV177: $i,SV59: $i,SV191: $i] :
( ( ( SV191
!= ( cartesian_product2 @ SV59 @ SV177 ) )
| ~ ( ~ ! [SY415: $i] :
( ! [SY395: $i,SY396: $i] :
( ~ ( in @ SY395 @ SV59 )
| ~ ( in @ SY396 @ SV177 )
| ( SY415
!= ( ordered_pair @ SY395 @ SY396 ) ) )
| ( in @ SY415 @ SV191 ) )
| ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV191 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY418 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SY418 @ SV191 @ SV177 @ SV59 ) @ SV177 ) )
| ( SY418
!= ( ordered_pair @ ( sK12_E @ SY418 @ SV191 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SY418 @ SV191 @ SV177 @ SV59 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(813,plain,
! [SV106: $i,SV98: $i,SV65: $i,SV7: $i] :
( ( ( ( unordered_pair @ SV7 @ SV65 )
= ( unordered_pair @ SV98 @ SV106 ) )
= $false )
| ( ( SV7 = SV98 )
= $true )
| ( ( SV7 = SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(814,plain,
! [SV68: $i,SV99: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV99 )
= $false )
| ( ( subset @ SV10 @ SV68 )
= $false )
| ( ( subset @ SV10 @ ( set_intersection2 @ SV68 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(815,plain,
! [SV11: $i,SV100: $i,SV69: $i] :
( ( ( subset @ SV69 @ SV100 )
= $false )
| ( ( subset @ SV11 @ SV69 )
= $false )
| ( ( subset @ SV11 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(816,plain,
! [SV101: $i,SV79: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV79 )
= $false )
| ( ( disjoint @ SV79 @ SV101 )
= $false )
| ( ( disjoint @ SV23 @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(817,plain,
! [SV27: $i,SV82: $i,SV102: $i] :
( ( ( subset @ SV102 @ SV82 )
= $false )
| ( ( subset @ SV27 @ SV82 )
= $false )
| ( ( subset @ ( set_union2 @ SV27 @ SV102 ) @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(818,plain,
! [SV140: $i,SV108: $i] :
( ( ( ( set_difference @ SV108 @ SV140 )
= SV108 )
= $false )
| ( ( disjoint @ SV108 @ SV140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(819,plain,
! [SV141: $i,SV109: $i] :
( ( ( disjoint @ SV109 @ SV141 )
= $false )
| ( ( ( set_difference @ SV109 @ SV141 )
= SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(820,plain,
! [SV142: $i,SV110: $i] :
( ( ( ( set_difference @ SV110 @ SV142 )
= empty_set )
= $false )
| ( ( subset @ SV110 @ SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(821,plain,
! [SV143: $i,SV111: $i] :
( ( ( subset @ SV111 @ SV143 )
= $false )
| ( ( ( set_difference @ SV111 @ SV143 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(822,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV144 ) ) )
| ~ ( ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV51 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV144 ) ) ) )
= $true )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(823,plain,
! [SV145: $i,SV51: $i,SV179: $i] :
( ( ( ( SV179
!= ( unordered_pair @ SV51 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SV179 )
| ( SY398 = SV51 )
| ( SY398 = SV145 ) )
| ~ ~ ( ~ ! [SY399: $i] :
( ( SY399 != SV51 )
| ( in @ SY399 @ SV179 ) )
| ~ ! [SY400: $i] :
( ( SY400 != SV145 )
| ( in @ SY400 @ SV179 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(824,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
| ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) ) ) ) )
= $true )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(825,plain,
! [SV147: $i,SV52: $i,SV181: $i] :
( ( ( ( SV181
!= ( set_intersection2 @ SV52 @ SV147 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SV52 )
| ~ ( in @ SY401 @ SV147 )
| ( in @ SY401 @ SV181 ) )
| ~ ~ ( ~ ! [SY402: $i] :
( ~ ( in @ SY402 @ SV181 )
| ( in @ SY402 @ SV52 ) )
| ~ ! [SY403: $i] :
( ~ ( in @ SY403 @ SV181 )
| ( in @ SY403 @ SV147 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(826,plain,
! [SV112: $i,SV148: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
| ~ ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 ) )
| ~ ( ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
| ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 ) ) )
= $false )
| ( ( SV148
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(827,plain,
! [SV113: $i,SV149: $i] :
( ( ( SV149
= ( powerset @ SV113 ) )
= $false )
| ( ( ~ ( ~ ! [SY368: $i] :
( ~ ( in @ SY368 @ SV149 )
| ( subset @ SY368 @ SV113 ) )
| ~ ! [SY369: $i] :
( ~ ( subset @ SY369 @ SV113 )
| ( in @ SY369 @ SV149 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(828,plain,
! [SV150: $i,SV114: $i] :
( ( ( in @ SV114 @ SV150 )
= $false )
| ( ( subset @ ( singleton @ SV114 ) @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(829,plain,
! [SV151: $i,SV115: $i] :
( ( ( subset @ ( singleton @ SV115 ) @ SV151 )
= $false )
| ( ( in @ SV115 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(830,plain,
! [SV152: $i,SV116: $i] :
( ( ( SV116 = SV152 )
= $true )
| ( ( ~ ( subset @ SV116 @ SV152 ) )
= $true )
| ( ( proper_subset @ SV116 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(831,plain,
! [SV192: $i] :
( ( ! [SY419: $i] :
( ~ ( proper_subset @ SV192 @ SY419 )
| ( SV192 != SY419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(832,plain,
! [SV193: $i] :
( ( ! [SY420: $i] :
( ~ ( proper_subset @ SV193 @ SY420 )
| ( subset @ SV193 @ SY420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(833,plain,
! [SV118: $i,SV194: $i] :
( ( ( ~ ( in @ SV194 @ SV118 ) )
= $true )
| ( ( SV118 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(834,plain,
! [SV154: $i,SV120: $i,SV195: $i] :
( ( ( ~ ( in @ SV195 @ ( set_intersection2 @ SV120 @ SV154 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV120 @ SV154 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(835,plain,
! [SV155: $i,SV182: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV182 )
| ~ ( in @ SV155 @ SV182 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV53 @ SV155 ) @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(836,plain,
! [SV53: $i] :
( ( ! [SY256: $i,SY257: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY256 ) @ SY257 )
| ( in @ SV53 @ SY257 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[777]) ).
thf(837,plain,
! [SV53: $i] :
( ( ! [SY258: $i,SY259: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SY258 ) @ SY259 )
| ( in @ SY258 @ SY259 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[778]) ).
thf(838,plain,
! [SV196: $i,SV95: $i,SV183: $i,SV54: $i] :
( ( ~ ( in @ SV54 @ SV183 )
| ~ ( in @ SV95 @ SV196 )
| ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV183 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(839,plain,
! [SV95: $i,SV54: $i] :
( ( ~ ! [SY310: $i] :
( ! [SY311: $i] :
~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY310 @ SY311 ) )
| ( in @ SV54 @ SY310 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[780]) ).
thf(840,plain,
! [SV95: $i,SV54: $i] :
( ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY312 @ SY313 ) )
| ( in @ SV95 @ SY313 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[780]) ).
thf(841,plain,
! [SV156: $i,SV121: $i] :
( ( ( ~ ( subset @ SV121 @ SV156 ) )
= $true )
| ( ( ~ ( subset @ SV156 @ SV121 ) )
= $true )
| ( ( SV121 = SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[781]) ).
thf(842,plain,
! [SV197: $i] :
( ( ! [SY421: $i] :
( ( SV197 != SY421 )
| ( subset @ SV197 @ SY421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(843,plain,
! [SV198: $i] :
( ( ! [SY422: $i] :
( ( SV198 != SY422 )
| ( subset @ SY422 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(844,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) ) ) ) )
= $true )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(845,plain,
! [SV158: $i,SV55: $i,SV185: $i] :
( ( ( ( SV185
!= ( set_difference @ SV55 @ SV158 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SV55 )
| ( in @ SY405 @ SV158 )
| ( in @ SY405 @ SV185 ) )
| ~ ~ ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SV185 )
| ( in @ SY406 @ SV55 ) )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV185 )
| ~ ( in @ SY407 @ SV158 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[785]) ).
thf(846,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) ) )
| ~ ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) ) ) )
= $true )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(847,plain,
! [SV160: $i,SV56: $i,SV187: $i] :
( ( ( ( SV187
!= ( set_union2 @ SV56 @ SV160 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV187 )
| ( in @ SY408 @ SV56 )
| ( in @ SY408 @ SV160 ) )
| ~ ~ ( ~ ! [SY409: $i] :
( ~ ( in @ SY409 @ SV56 )
| ( in @ SY409 @ SV187 ) )
| ~ ! [SY410: $i] :
( ~ ( in @ SY410 @ SV160 )
| ( in @ SY410 @ SV187 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(848,plain,
! [SV161: $i,SV122: $i] :
( ( ( ( set_intersection2 @ SV122 @ SV161 )
= empty_set )
= $false )
| ( ( disjoint @ SV122 @ SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(849,plain,
! [SV162: $i,SV123: $i] :
( ( ( disjoint @ SV123 @ SV162 )
= $false )
| ( ( ( set_intersection2 @ SV123 @ SV162 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(850,plain,
( ( sK1_A = empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(851,plain,
( ( sK1_A
= ( singleton @ sK2_SY183 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(852,plain,
! [SV163: $i,SV124: $i] :
( ( ( subset @ SV124 @ ( singleton @ SV163 ) )
= $false )
| ( ( ( SV124 = empty_set )
| ( SV124
= ( singleton @ SV163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(853,plain,
! [SV199: $i] :
( ( ( SV199 != empty_set )
| ! [SY423: $i] : ( subset @ SV199 @ ( singleton @ SY423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(854,plain,
! [SV200: $i] :
( ( ! [SY424: $i] :
( ( SV200
!= ( singleton @ SY424 ) )
| ( subset @ SV200 @ ( singleton @ SY424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(855,plain,
! [SV164: $i,SV125: $i] :
( ( ( in @ SV125 @ SV164 )
= $false )
| ( ( subset @ ( singleton @ SV125 ) @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(856,plain,
! [SV165: $i,SV126: $i] :
( ( ( subset @ ( singleton @ SV126 ) @ SV165 )
= $false )
| ( ( in @ SV126 @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(857,plain,
! [SV127: $i,SV166: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV166 @ SV127 ) @ SV127 )
| ~ ~ ( in @ ( sK11_C @ SV166 @ SV127 ) @ SV166 ) )
= $false )
| ( ( subset @ SV127 @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(858,plain,
! [SV167: $i,SV128: $i] :
( ( ( subset @ SV128 @ SV167 )
= $false )
| ( ( ! [SY382: $i] :
( ~ ( in @ SY382 @ SV128 )
| ( in @ SY382 @ SV167 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(859,plain,
! [SV188: $i,SV96: $i,SV57: $i] :
( ( ( ! [SY411: $i] :
( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SV188 @ SY411 ) ) )
= $true )
| ( ( SV57 = SV188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(860,plain,
! [SV201: $i,SV189: $i,SV96: $i,SV57: $i] :
( ( ( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SV189 @ SV201 ) )
| ( SV96 = SV201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(861,plain,
! [SV58: $i,SV97: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 ) )
= $true )
| ( ( ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 ) )
= $true )
| ( ( SV58 = SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(862,plain,
! [SV58: $i,SV97: $i] :
( ( ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
= $true )
| ( ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 )
= $true )
| ( ( SV58 = SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(863,plain,
! [SV129: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV168 @ SV129 ) @ SV129 )
| ~ ( in @ ( sK23_C @ SV168 @ SV129 ) @ SV168 ) )
= $false )
| ( ( disjoint @ SV129 @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(864,plain,
! [SV169: $i,SV130: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV130 )
| ~ ( in @ SV202 @ SV169 ) )
= $true )
| ( ( ~ ( disjoint @ SV130 @ SV169 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(865,plain,
! [SV131: $i,SV170: $i] :
( ( ( ~ ( ( ( sK21_C @ SV170 @ SV131 )
!= SV131 )
| ~ ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 ) )
| ~ ( ( ( sK21_C @ SV170 @ SV131 )
= SV131 )
| ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 ) ) )
= $false )
| ( ( SV170
= ( singleton @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(866,plain,
! [SV132: $i,SV171: $i] :
( ( ( SV171
= ( singleton @ SV132 ) )
= $false )
| ( ( ~ ( ~ ! [SY384: $i] :
( ( SY384 != SV132 )
| ( in @ SY384 @ SV171 ) )
| ~ ! [SY385: $i] :
( ~ ( in @ SY385 @ SV171 )
| ( SY385 = SV132 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(867,plain,
! [SV133: $i,SV172: $i] :
( ( ( ~ ( ! [SY386: $i] :
( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SY386 )
| ~ ( in @ SY386 @ SV133 ) )
| ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ ( sK9_SY185 @ SV172 @ SV133 ) )
| ~ ( in @ ( sK9_SY185 @ SV172 @ SV133 ) @ SV133 ) )
| ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) ) )
= $false )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(868,plain,
! [SV134: $i,SV173: $i] :
( ( ( SV173
= ( union @ SV134 ) )
= $false )
| ( ( ~ ( ~ ! [SY387: $i] :
( ! [SY354: $i] :
( ~ ( in @ SY387 @ SY354 )
| ~ ( in @ SY354 @ SV134 ) )
| ( in @ SY387 @ SV173 ) )
| ~ ! [SY389: $i] :
( ~ ( in @ SY389 @ SV173 )
| ~ ( ~ ( in @ SY389 @ ( sK7_D @ SY389 @ SV173 @ SV134 ) )
| ~ ( in @ ( sK7_D @ SY389 @ SV173 @ SV134 ) @ SV134 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(869,plain,
! [SV174: $i,SV135: $i] :
( ( ( ( set_difference @ SV135 @ SV174 )
= empty_set )
= $false )
| ( ( subset @ SV135 @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(870,plain,
! [SV175: $i,SV136: $i] :
( ( ( subset @ SV136 @ SV175 )
= $false )
| ( ( ( set_difference @ SV136 @ SV175 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(871,plain,
! [SV190: $i,SV176: $i,SV59: $i] :
( ( ( ~ ( ~ ( ! [SY413: $i,SY414: $i] :
( ~ ( in @ SY413 @ SV59 )
| ~ ( in @ SY414 @ SV176 )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ SY413 @ SY414 ) ) )
| ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) @ SV176 ) )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) ) ) )
| ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) ) ) )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(872,plain,
! [SV177: $i,SV59: $i,SV191: $i] :
( ( ( ( SV191
!= ( cartesian_product2 @ SV59 @ SV177 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY415: $i] :
( ! [SY395: $i,SY396: $i] :
( ~ ( in @ SY395 @ SV59 )
| ~ ( in @ SY396 @ SV177 )
| ( SY415
!= ( ordered_pair @ SY395 @ SY396 ) ) )
| ( in @ SY415 @ SV191 ) )
| ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV191 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY418 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SY418 @ SV191 @ SV177 @ SV59 ) @ SV177 ) )
| ( SY418
!= ( ordered_pair @ ( sK12_E @ SY418 @ SV191 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SY418 @ SV191 @ SV177 @ SV59 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(873,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV144 ) ) )
| ~ ( ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV51 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV144 ) ) )
= $false )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(874,plain,
! [SV145: $i,SV51: $i,SV179: $i] :
( ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SV179 )
| ( SY398 = SV51 )
| ( SY398 = SV145 ) )
| ~ ~ ( ~ ! [SY399: $i] :
( ( SY399 != SV51 )
| ( in @ SY399 @ SV179 ) )
| ~ ! [SY400: $i] :
( ( SY400 != SV145 )
| ( in @ SY400 @ SV179 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(875,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
| ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) ) ) )
= $false )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(876,plain,
! [SV147: $i,SV52: $i,SV181: $i] :
( ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false )
| ( ( ~ ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SV52 )
| ~ ( in @ SY401 @ SV147 )
| ( in @ SY401 @ SV181 ) )
| ~ ~ ( ~ ! [SY402: $i] :
( ~ ( in @ SY402 @ SV181 )
| ( in @ SY402 @ SV52 ) )
| ~ ! [SY403: $i] :
( ~ ( in @ SY403 @ SV181 )
| ( in @ SY403 @ SV147 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(877,plain,
! [SV112: $i,SV148: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
| ~ ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 ) ) )
= $false )
| ( ( SV148
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[826]) ).
thf(878,plain,
! [SV112: $i,SV148: $i] :
( ( ( ~ ( ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
| ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 ) ) )
= $false )
| ( ( SV148
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[826]) ).
thf(879,plain,
! [SV113: $i,SV149: $i] :
( ( ( ~ ! [SY368: $i] :
( ~ ( in @ SY368 @ SV149 )
| ( subset @ SY368 @ SV113 ) )
| ~ ! [SY369: $i] :
( ~ ( subset @ SY369 @ SV113 )
| ( in @ SY369 @ SV149 ) ) )
= $false )
| ( ( SV149
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(880,plain,
! [SV152: $i,SV116: $i] :
( ( ( subset @ SV116 @ SV152 )
= $false )
| ( ( SV116 = SV152 )
= $true )
| ( ( proper_subset @ SV116 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[830]) ).
thf(881,plain,
! [SV203: $i,SV192: $i] :
( ( ~ ( proper_subset @ SV192 @ SV203 )
| ( SV192 != SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(882,plain,
! [SV204: $i,SV193: $i] :
( ( ~ ( proper_subset @ SV193 @ SV204 )
| ( subset @ SV193 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(883,plain,
! [SV118: $i,SV194: $i] :
( ( ( in @ SV194 @ SV118 )
= $false )
| ( ( SV118 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(884,plain,
! [SV154: $i,SV120: $i,SV195: $i] :
( ( ( in @ SV195 @ ( set_intersection2 @ SV120 @ SV154 ) )
= $false )
| ( ( ~ ( disjoint @ SV120 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(885,plain,
! [SV155: $i,SV182: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV182 ) )
= $true )
| ( ( ~ ( in @ SV155 @ SV182 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV53 @ SV155 ) @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(886,plain,
! [SV205: $i,SV53: $i] :
( ( ! [SY425: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SV205 ) @ SY425 )
| ( in @ SV53 @ SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(887,plain,
! [SV206: $i,SV53: $i] :
( ( ! [SY426: $i] :
( ~ ( subset @ ( unordered_pair @ SV53 @ SV206 ) @ SY426 )
| ( in @ SV206 @ SY426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(888,plain,
! [SV196: $i,SV95: $i,SV183: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV183 )
| ~ ( in @ SV95 @ SV196 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV183 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(889,plain,
! [SV95: $i,SV54: $i] :
( ( ! [SY310: $i] :
( ! [SY311: $i] :
~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY310 @ SY311 ) )
| ( in @ SV54 @ SY310 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(890,plain,
! [SV95: $i,SV54: $i] :
( ( ! [SY312: $i,SY313: $i] :
( ~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SY312 @ SY313 ) )
| ( in @ SV95 @ SY313 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[840]) ).
thf(891,plain,
! [SV156: $i,SV121: $i] :
( ( ( subset @ SV121 @ SV156 )
= $false )
| ( ( ~ ( subset @ SV156 @ SV121 ) )
= $true )
| ( ( SV121 = SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(892,plain,
! [SV207: $i,SV197: $i] :
( ( ( SV197 != SV207 )
| ( subset @ SV197 @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(893,plain,
! [SV208: $i,SV198: $i] :
( ( ( SV198 != SV208 )
| ( subset @ SV208 @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(894,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) ) ) )
= $false )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(895,plain,
! [SV158: $i,SV55: $i,SV185: $i] :
( ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false )
| ( ( ~ ( ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SV55 )
| ( in @ SY405 @ SV158 )
| ( in @ SY405 @ SV185 ) )
| ~ ~ ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SV185 )
| ( in @ SY406 @ SV55 ) )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV185 )
| ~ ( in @ SY407 @ SV158 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(896,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) ) )
| ~ ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) ) )
= $false )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(897,plain,
! [SV160: $i,SV56: $i,SV187: $i] :
( ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false )
| ( ( ~ ( ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV187 )
| ( in @ SY408 @ SV56 )
| ( in @ SY408 @ SV160 ) )
| ~ ~ ( ~ ! [SY409: $i] :
( ~ ( in @ SY409 @ SV56 )
| ( in @ SY409 @ SV187 ) )
| ~ ! [SY410: $i] :
( ~ ( in @ SY410 @ SV160 )
| ( in @ SY410 @ SV187 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(898,plain,
! [SV163: $i,SV124: $i] :
( ( ( SV124 = empty_set )
= $true )
| ( ( SV124
= ( singleton @ SV163 ) )
= $true )
| ( ( subset @ SV124 @ ( singleton @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(899,plain,
! [SV199: $i] :
( ( ( ( SV199 != empty_set ) )
= $true )
| ( ( ! [SY423: $i] : ( subset @ SV199 @ ( singleton @ SY423 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(900,plain,
! [SV209: $i,SV200: $i] :
( ( ( SV200
!= ( singleton @ SV209 ) )
| ( subset @ SV200 @ ( singleton @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(901,plain,
! [SV127: $i,SV166: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV166 @ SV127 ) @ SV127 ) )
= $false )
| ( ( subset @ SV127 @ SV166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(902,plain,
! [SV127: $i,SV166: $i] :
( ( ( ~ ~ ( in @ ( sK11_C @ SV166 @ SV127 ) @ SV166 ) )
= $false )
| ( ( subset @ SV127 @ SV166 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(903,plain,
! [SV167: $i,SV128: $i,SV210: $i] :
( ( ( ~ ( in @ SV210 @ SV128 )
| ( in @ SV210 @ SV167 ) )
= $true )
| ( ( subset @ SV128 @ SV167 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(904,plain,
! [SV211: $i,SV188: $i,SV96: $i,SV57: $i] :
( ( ( ( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SV188 @ SV211 ) ) )
= $true )
| ( ( SV57 = SV188 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(905,plain,
! [SV201: $i,SV189: $i,SV96: $i,SV57: $i] :
( ( ( ( ( ordered_pair @ SV57 @ SV96 )
!= ( ordered_pair @ SV189 @ SV201 ) ) )
= $true )
| ( ( SV96 = SV201 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(906,plain,
! [SV58: $i,SV97: $i] :
( ( ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
= $false )
| ( ( ~ ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 ) )
= $true )
| ( ( SV58 = SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(907,plain,
! [SV129: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV168 @ SV129 ) @ SV129 ) )
= $false )
| ( ( disjoint @ SV129 @ SV168 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(908,plain,
! [SV129: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV168 @ SV129 ) @ SV168 ) )
= $false )
| ( ( disjoint @ SV129 @ SV168 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(909,plain,
! [SV169: $i,SV130: $i,SV202: $i] :
( ( ( ~ ( in @ SV202 @ SV130 ) )
= $true )
| ( ( ~ ( in @ SV202 @ SV169 ) )
= $true )
| ( ( ~ ( disjoint @ SV130 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(910,plain,
! [SV131: $i,SV170: $i] :
( ( ( ~ ( ( ( sK21_C @ SV170 @ SV131 )
!= SV131 )
| ~ ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 ) ) )
= $false )
| ( ( SV170
= ( singleton @ SV131 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(911,plain,
! [SV131: $i,SV170: $i] :
( ( ( ~ ( ( ( sK21_C @ SV170 @ SV131 )
= SV131 )
| ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 ) ) )
= $false )
| ( ( SV170
= ( singleton @ SV131 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[865]) ).
thf(912,plain,
! [SV171: $i,SV132: $i] :
( ( ( ~ ! [SY384: $i] :
( ( SY384 != SV132 )
| ( in @ SY384 @ SV171 ) )
| ~ ! [SY385: $i] :
( ~ ( in @ SY385 @ SV171 )
| ( SY385 = SV132 ) ) )
= $false )
| ( ( SV171
= ( singleton @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(913,plain,
! [SV133: $i,SV172: $i] :
( ( ( ~ ( ! [SY386: $i] :
( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SY386 )
| ~ ( in @ SY386 @ SV133 ) )
| ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) ) )
= $false )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[867]) ).
thf(914,plain,
! [SV133: $i,SV172: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ ( sK9_SY185 @ SV172 @ SV133 ) )
| ~ ( in @ ( sK9_SY185 @ SV172 @ SV133 ) @ SV133 ) )
| ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) ) )
= $false )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[867]) ).
thf(915,plain,
! [SV173: $i,SV134: $i] :
( ( ( ~ ! [SY387: $i] :
( ! [SY354: $i] :
( ~ ( in @ SY387 @ SY354 )
| ~ ( in @ SY354 @ SV134 ) )
| ( in @ SY387 @ SV173 ) )
| ~ ! [SY389: $i] :
( ~ ( in @ SY389 @ SV173 )
| ~ ( ~ ( in @ SY389 @ ( sK7_D @ SY389 @ SV173 @ SV134 ) )
| ~ ( in @ ( sK7_D @ SY389 @ SV173 @ SV134 ) @ SV134 ) ) ) )
= $false )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(916,plain,
! [SV190: $i,SV176: $i,SV59: $i] :
( ( ( ~ ( ! [SY413: $i,SY414: $i] :
( ~ ( in @ SY413 @ SV59 )
| ~ ( in @ SY414 @ SV176 )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ SY413 @ SY414 ) ) )
| ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) @ SV176 ) )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) ) ) )
| ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) ) )
= $false )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(917,plain,
! [SV177: $i,SV59: $i,SV191: $i] :
( ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false )
| ( ( ~ ( ~ ! [SY415: $i] :
( ! [SY395: $i,SY396: $i] :
( ~ ( in @ SY395 @ SV59 )
| ~ ( in @ SY396 @ SV177 )
| ( SY415
!= ( ordered_pair @ SY395 @ SY396 ) ) )
| ( in @ SY415 @ SV191 ) )
| ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV191 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY418 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SY418 @ SV191 @ SV177 @ SV59 ) @ SV177 ) )
| ( SY418
!= ( ordered_pair @ ( sK12_E @ SY418 @ SV191 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SY418 @ SV191 @ SV177 @ SV59 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(918,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV144 ) ) ) )
= $false )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(919,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ~ ( ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV51 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV144 ) ) )
= $false )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(920,plain,
! [SV145: $i,SV51: $i,SV179: $i] :
( ( ( ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SV179 )
| ( SY398 = SV51 )
| ( SY398 = SV145 ) )
| ~ ~ ( ~ ! [SY399: $i] :
( ( SY399 != SV51 )
| ( in @ SY399 @ SV179 ) )
| ~ ! [SY400: $i] :
( ( SY400 != SV145 )
| ( in @ SY400 @ SV179 ) ) ) )
= $false )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(921,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) ) )
= $false )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[875]) ).
thf(922,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
| ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) ) ) )
= $false )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[875]) ).
thf(923,plain,
! [SV181: $i,SV147: $i,SV52: $i] :
( ( ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SV52 )
| ~ ( in @ SY401 @ SV147 )
| ( in @ SY401 @ SV181 ) )
| ~ ~ ( ~ ! [SY402: $i] :
( ~ ( in @ SY402 @ SV181 )
| ( in @ SY402 @ SV52 ) )
| ~ ! [SY403: $i] :
( ~ ( in @ SY403 @ SV181 )
| ( in @ SY403 @ SV147 ) ) ) )
= $false )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(924,plain,
! [SV112: $i,SV148: $i] :
( ( ( ~ ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
| ~ ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 ) )
= $true )
| ( ( SV148
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(925,plain,
! [SV112: $i,SV148: $i] :
( ( ( ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
| ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 ) )
= $true )
| ( ( SV148
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(926,plain,
! [SV113: $i,SV149: $i] :
( ( ( ~ ! [SY368: $i] :
( ~ ( in @ SY368 @ SV149 )
| ( subset @ SY368 @ SV113 ) ) )
= $false )
| ( ( SV149
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[879]) ).
thf(927,plain,
! [SV149: $i,SV113: $i] :
( ( ( ~ ! [SY369: $i] :
( ~ ( subset @ SY369 @ SV113 )
| ( in @ SY369 @ SV149 ) ) )
= $false )
| ( ( SV149
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[879]) ).
thf(928,plain,
! [SV203: $i,SV192: $i] :
( ( ( ~ ( proper_subset @ SV192 @ SV203 ) )
= $true )
| ( ( ( SV192 != SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(929,plain,
! [SV204: $i,SV193: $i] :
( ( ( ~ ( proper_subset @ SV193 @ SV204 ) )
= $true )
| ( ( subset @ SV193 @ SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(930,plain,
! [SV195: $i,SV154: $i,SV120: $i] :
( ( ( disjoint @ SV120 @ SV154 )
= $false )
| ( ( in @ SV195 @ ( set_intersection2 @ SV120 @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(931,plain,
! [SV155: $i,SV182: $i,SV53: $i] :
( ( ( in @ SV53 @ SV182 )
= $false )
| ( ( ~ ( in @ SV155 @ SV182 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV53 @ SV155 ) @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(932,plain,
! [SV212: $i,SV205: $i,SV53: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV53 @ SV205 ) @ SV212 )
| ( in @ SV53 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(933,plain,
! [SV213: $i,SV206: $i,SV53: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV53 @ SV206 ) @ SV213 )
| ( in @ SV206 @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(934,plain,
! [SV196: $i,SV95: $i,SV183: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV183 ) )
= $true )
| ( ( ~ ( in @ SV95 @ SV196 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV183 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(935,plain,
! [SV214: $i,SV95: $i,SV54: $i] :
( ( ! [SY427: $i] :
~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV214 @ SY427 ) )
| ( in @ SV54 @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(936,plain,
! [SV215: $i,SV95: $i,SV54: $i] :
( ( ! [SY428: $i] :
( ~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV215 @ SY428 ) )
| ( in @ SV95 @ SY428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(937,plain,
! [SV121: $i,SV156: $i] :
( ( ( subset @ SV156 @ SV121 )
= $false )
| ( ( subset @ SV121 @ SV156 )
= $false )
| ( ( SV121 = SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(938,plain,
! [SV207: $i,SV197: $i] :
( ( ( ( SV197 != SV207 ) )
= $true )
| ( ( subset @ SV197 @ SV207 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(939,plain,
! [SV208: $i,SV198: $i] :
( ( ( ( SV198 != SV208 ) )
= $true )
| ( ( subset @ SV208 @ SV198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[893]) ).
thf(940,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) ) )
= $false )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[894]) ).
thf(941,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) ) ) )
= $false )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[894]) ).
thf(942,plain,
! [SV185: $i,SV158: $i,SV55: $i] :
( ( ( ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SV55 )
| ( in @ SY405 @ SV158 )
| ( in @ SY405 @ SV185 ) )
| ~ ~ ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SV185 )
| ( in @ SY406 @ SV55 ) )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV185 )
| ~ ( in @ SY407 @ SV158 ) ) ) )
= $false )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(943,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) ) ) )
= $false )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(944,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ~ ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) ) )
= $false )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(945,plain,
! [SV160: $i,SV56: $i,SV187: $i] :
( ( ( ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV187 )
| ( in @ SY408 @ SV56 )
| ( in @ SY408 @ SV160 ) )
| ~ ~ ( ~ ! [SY409: $i] :
( ~ ( in @ SY409 @ SV56 )
| ( in @ SY409 @ SV187 ) )
| ~ ! [SY410: $i] :
( ~ ( in @ SY410 @ SV160 )
| ( in @ SY410 @ SV187 ) ) ) )
= $false )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(946,plain,
! [SV199: $i] :
( ( ( SV199 = empty_set )
= $false )
| ( ( ! [SY423: $i] : ( subset @ SV199 @ ( singleton @ SY423 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(947,plain,
! [SV209: $i,SV200: $i] :
( ( ( ( SV200
!= ( singleton @ SV209 ) ) )
= $true )
| ( ( subset @ SV200 @ ( singleton @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(948,plain,
! [SV127: $i,SV166: $i] :
( ( ( in @ ( sK11_C @ SV166 @ SV127 ) @ SV127 )
= $true )
| ( ( subset @ SV127 @ SV166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[901]) ).
thf(949,plain,
! [SV127: $i,SV166: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV166 @ SV127 ) @ SV166 ) )
= $true )
| ( ( subset @ SV127 @ SV166 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[902]) ).
thf(950,plain,
! [SV167: $i,SV128: $i,SV210: $i] :
( ( ( ~ ( in @ SV210 @ SV128 ) )
= $true )
| ( ( in @ SV210 @ SV167 )
= $true )
| ( ( subset @ SV128 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(951,plain,
! [SV211: $i,SV188: $i,SV96: $i,SV57: $i] :
( ( ( ( ordered_pair @ SV57 @ SV96 )
= ( ordered_pair @ SV188 @ SV211 ) )
= $false )
| ( ( SV57 = SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(952,plain,
! [SV201: $i,SV189: $i,SV96: $i,SV57: $i] :
( ( ( ( ordered_pair @ SV57 @ SV96 )
= ( ordered_pair @ SV189 @ SV201 ) )
= $false )
| ( ( SV96 = SV201 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(953,plain,
! [SV58: $i,SV97: $i] :
( ( ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV97 )
= $false )
| ( ( in @ ( sK3_C @ SV97 @ SV58 ) @ SV58 )
= $false )
| ( ( SV58 = SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(954,plain,
! [SV129: $i,SV168: $i] :
( ( ( in @ ( sK23_C @ SV168 @ SV129 ) @ SV129 )
= $true )
| ( ( disjoint @ SV129 @ SV168 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(955,plain,
! [SV129: $i,SV168: $i] :
( ( ( in @ ( sK23_C @ SV168 @ SV129 ) @ SV168 )
= $true )
| ( ( disjoint @ SV129 @ SV168 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[908]) ).
thf(956,plain,
! [SV169: $i,SV130: $i,SV202: $i] :
( ( ( in @ SV202 @ SV130 )
= $false )
| ( ( ~ ( in @ SV202 @ SV169 ) )
= $true )
| ( ( ~ ( disjoint @ SV130 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(957,plain,
! [SV131: $i,SV170: $i] :
( ( ( ( ( sK21_C @ SV170 @ SV131 )
!= SV131 )
| ~ ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 ) )
= $true )
| ( ( SV170
= ( singleton @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[910]) ).
thf(958,plain,
! [SV131: $i,SV170: $i] :
( ( ( ( ( sK21_C @ SV170 @ SV131 )
= SV131 )
| ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 ) )
= $true )
| ( ( SV170
= ( singleton @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[911]) ).
thf(959,plain,
! [SV171: $i,SV132: $i] :
( ( ( ~ ! [SY384: $i] :
( ( SY384 != SV132 )
| ( in @ SY384 @ SV171 ) ) )
= $false )
| ( ( SV171
= ( singleton @ SV132 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[912]) ).
thf(960,plain,
! [SV132: $i,SV171: $i] :
( ( ( ~ ! [SY385: $i] :
( ~ ( in @ SY385 @ SV171 )
| ( SY385 = SV132 ) ) )
= $false )
| ( ( SV171
= ( singleton @ SV132 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[912]) ).
thf(961,plain,
! [SV133: $i,SV172: $i] :
( ( ( ! [SY386: $i] :
( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SY386 )
| ~ ( in @ SY386 @ SV133 ) )
| ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(962,plain,
! [SV133: $i,SV172: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ ( sK9_SY185 @ SV172 @ SV133 ) )
| ~ ( in @ ( sK9_SY185 @ SV172 @ SV133 ) @ SV133 ) )
| ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[914]) ).
thf(963,plain,
! [SV173: $i,SV134: $i] :
( ( ( ~ ! [SY387: $i] :
( ! [SY354: $i] :
( ~ ( in @ SY387 @ SY354 )
| ~ ( in @ SY354 @ SV134 ) )
| ( in @ SY387 @ SV173 ) ) )
= $false )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(964,plain,
! [SV134: $i,SV173: $i] :
( ( ( ~ ! [SY389: $i] :
( ~ ( in @ SY389 @ SV173 )
| ~ ( ~ ( in @ SY389 @ ( sK7_D @ SY389 @ SV173 @ SV134 ) )
| ~ ( in @ ( sK7_D @ SY389 @ SV173 @ SV134 ) @ SV134 ) ) ) )
= $false )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[915]) ).
thf(965,plain,
! [SV190: $i,SV176: $i,SV59: $i] :
( ( ( ~ ( ! [SY413: $i,SY414: $i] :
( ~ ( in @ SY413 @ SV59 )
| ~ ( in @ SY414 @ SV176 )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ SY413 @ SY414 ) ) )
| ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) ) )
= $false )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(966,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) @ SV176 ) )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) ) ) )
| ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) ) )
= $false )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[916]) ).
thf(967,plain,
! [SV191: $i,SV177: $i,SV59: $i] :
( ( ( ~ ! [SY415: $i] :
( ! [SY395: $i,SY396: $i] :
( ~ ( in @ SY395 @ SV59 )
| ~ ( in @ SY396 @ SV177 )
| ( SY415
!= ( ordered_pair @ SY395 @ SY396 ) ) )
| ( in @ SY415 @ SV191 ) )
| ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV191 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY418 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SY418 @ SV191 @ SV177 @ SV59 ) @ SV177 ) )
| ( SY418
!= ( ordered_pair @ ( sK12_E @ SY418 @ SV191 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SY418 @ SV191 @ SV177 @ SV59 ) ) ) ) ) )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(968,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV144 ) ) ) )
= $true )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[918]) ).
thf(969,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV51 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV144 ) )
= $true )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[919]) ).
thf(970,plain,
! [SV145: $i,SV51: $i,SV179: $i] :
( ( ( ~ ! [SY398: $i] :
( ~ ( in @ SY398 @ SV179 )
| ( SY398 = SV51 )
| ( SY398 = SV145 ) ) )
= $false )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[920]) ).
thf(971,plain,
! [SV145: $i,SV179: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ! [SY399: $i] :
( ( SY399 != SV51 )
| ( in @ SY399 @ SV179 ) )
| ~ ! [SY400: $i] :
( ( SY400 != SV145 )
| ( in @ SY400 @ SV179 ) ) ) )
= $false )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[920]) ).
thf(972,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
= $true )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[921]) ).
thf(973,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
| ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) ) ) )
= $true )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(974,plain,
! [SV181: $i,SV147: $i,SV52: $i] :
( ( ( ~ ! [SY401: $i] :
( ~ ( in @ SY401 @ SV52 )
| ~ ( in @ SY401 @ SV147 )
| ( in @ SY401 @ SV181 ) ) )
= $false )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[923]) ).
thf(975,plain,
! [SV147: $i,SV52: $i,SV181: $i] :
( ( ( ~ ~ ( ~ ! [SY402: $i] :
( ~ ( in @ SY402 @ SV181 )
| ( in @ SY402 @ SV52 ) )
| ~ ! [SY403: $i] :
( ~ ( in @ SY403 @ SV181 )
| ( in @ SY403 @ SV147 ) ) ) )
= $false )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[923]) ).
thf(976,plain,
! [SV112: $i,SV148: $i] :
( ( ( ~ ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 ) )
= $true )
| ( ( ~ ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 ) )
= $true )
| ( ( SV148
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(977,plain,
! [SV112: $i,SV148: $i] :
( ( ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
= $true )
| ( ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 )
= $true )
| ( ( SV148
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(978,plain,
! [SV113: $i,SV149: $i] :
( ( ( ! [SY368: $i] :
( ~ ( in @ SY368 @ SV149 )
| ( subset @ SY368 @ SV113 ) ) )
= $true )
| ( ( SV149
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[926]) ).
thf(979,plain,
! [SV149: $i,SV113: $i] :
( ( ( ! [SY369: $i] :
( ~ ( subset @ SY369 @ SV113 )
| ( in @ SY369 @ SV149 ) ) )
= $true )
| ( ( SV149
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[927]) ).
thf(980,plain,
! [SV203: $i,SV192: $i] :
( ( ( proper_subset @ SV192 @ SV203 )
= $false )
| ( ( ( SV192 != SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(981,plain,
! [SV204: $i,SV193: $i] :
( ( ( proper_subset @ SV193 @ SV204 )
= $false )
| ( ( subset @ SV193 @ SV204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(982,plain,
! [SV53: $i,SV182: $i,SV155: $i] :
( ( ( in @ SV155 @ SV182 )
= $false )
| ( ( in @ SV53 @ SV182 )
= $false )
| ( ( subset @ ( unordered_pair @ SV53 @ SV155 ) @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(983,plain,
! [SV212: $i,SV205: $i,SV53: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV53 @ SV205 ) @ SV212 ) )
= $true )
| ( ( in @ SV53 @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(984,plain,
! [SV213: $i,SV206: $i,SV53: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV53 @ SV206 ) @ SV213 ) )
= $true )
| ( ( in @ SV206 @ SV213 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(985,plain,
! [SV196: $i,SV95: $i,SV183: $i,SV54: $i] :
( ( ( in @ SV54 @ SV183 )
= $false )
| ( ( ~ ( in @ SV95 @ SV196 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV183 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(986,plain,
! [SV214: $i,SV95: $i,SV54: $i] :
( ( ( ! [SY427: $i] :
~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV214 @ SY427 ) ) )
= $true )
| ( ( in @ SV54 @ SV214 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(987,plain,
! [SV216: $i,SV215: $i,SV95: $i,SV54: $i] :
( ( ~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV215 @ SV216 ) )
| ( in @ SV95 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(988,plain,
! [SV207: $i,SV197: $i] :
( ( ( SV197 = SV207 )
= $false )
| ( ( subset @ SV197 @ SV207 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(989,plain,
! [SV208: $i,SV198: $i] :
( ( ( SV198 = SV208 )
= $false )
| ( ( subset @ SV208 @ SV198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(990,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
= $true )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[940]) ).
thf(991,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) ) ) )
= $true )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(992,plain,
! [SV185: $i,SV158: $i,SV55: $i] :
( ( ( ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SV55 )
| ( in @ SY405 @ SV158 )
| ( in @ SY405 @ SV185 ) ) )
= $false )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(993,plain,
! [SV158: $i,SV55: $i,SV185: $i] :
( ( ( ~ ~ ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SV185 )
| ( in @ SY406 @ SV55 ) )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV185 )
| ~ ( in @ SY407 @ SV158 ) ) ) )
= $false )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(994,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) ) ) )
= $true )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[943]) ).
thf(995,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) )
= $true )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[944]) ).
thf(996,plain,
! [SV160: $i,SV56: $i,SV187: $i] :
( ( ( ~ ! [SY408: $i] :
( ~ ( in @ SY408 @ SV187 )
| ( in @ SY408 @ SV56 )
| ( in @ SY408 @ SV160 ) ) )
= $false )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(997,plain,
! [SV160: $i,SV187: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ! [SY409: $i] :
( ~ ( in @ SY409 @ SV56 )
| ( in @ SY409 @ SV187 ) )
| ~ ! [SY410: $i] :
( ~ ( in @ SY410 @ SV160 )
| ( in @ SY410 @ SV187 ) ) ) )
= $false )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[945]) ).
thf(998,plain,
! [SV217: $i,SV199: $i] :
( ( ( subset @ SV199 @ ( singleton @ SV217 ) )
= $true )
| ( ( SV199 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(999,plain,
! [SV209: $i,SV200: $i] :
( ( ( SV200
= ( singleton @ SV209 ) )
= $false )
| ( ( subset @ SV200 @ ( singleton @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(1000,plain,
! [SV127: $i,SV166: $i] :
( ( ( in @ ( sK11_C @ SV166 @ SV127 ) @ SV166 )
= $false )
| ( ( subset @ SV127 @ SV166 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(1001,plain,
! [SV167: $i,SV128: $i,SV210: $i] :
( ( ( in @ SV210 @ SV128 )
= $false )
| ( ( in @ SV210 @ SV167 )
= $true )
| ( ( subset @ SV128 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(1002,plain,
! [SV130: $i,SV169: $i,SV202: $i] :
( ( ( in @ SV202 @ SV169 )
= $false )
| ( ( in @ SV202 @ SV130 )
= $false )
| ( ( ~ ( disjoint @ SV130 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1003,plain,
! [SV131: $i,SV170: $i] :
( ( ( ( ( sK21_C @ SV170 @ SV131 )
!= SV131 ) )
= $true )
| ( ( ~ ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 ) )
= $true )
| ( ( SV170
= ( singleton @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1004,plain,
! [SV131: $i,SV170: $i] :
( ( ( ( sK21_C @ SV170 @ SV131 )
= SV131 )
= $true )
| ( ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 )
= $true )
| ( ( SV170
= ( singleton @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1005,plain,
! [SV171: $i,SV132: $i] :
( ( ( ! [SY384: $i] :
( ( SY384 != SV132 )
| ( in @ SY384 @ SV171 ) ) )
= $true )
| ( ( SV171
= ( singleton @ SV132 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[959]) ).
thf(1006,plain,
! [SV132: $i,SV171: $i] :
( ( ( ! [SY385: $i] :
( ~ ( in @ SY385 @ SV171 )
| ( SY385 = SV132 ) ) )
= $true )
| ( ( SV171
= ( singleton @ SV132 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[960]) ).
thf(1007,plain,
! [SV133: $i,SV172: $i] :
( ( ( ! [SY386: $i] :
( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SY386 )
| ~ ( in @ SY386 @ SV133 ) ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(1008,plain,
! [SV133: $i,SV172: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ ( sK9_SY185 @ SV172 @ SV133 ) )
| ~ ( in @ ( sK9_SY185 @ SV172 @ SV133 ) @ SV133 ) ) )
= $true )
| ( ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(1009,plain,
! [SV173: $i,SV134: $i] :
( ( ( ! [SY387: $i] :
( ! [SY354: $i] :
( ~ ( in @ SY387 @ SY354 )
| ~ ( in @ SY354 @ SV134 ) )
| ( in @ SY387 @ SV173 ) ) )
= $true )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[963]) ).
thf(1010,plain,
! [SV134: $i,SV173: $i] :
( ( ( ! [SY389: $i] :
( ~ ( in @ SY389 @ SV173 )
| ~ ( ~ ( in @ SY389 @ ( sK7_D @ SY389 @ SV173 @ SV134 ) )
| ~ ( in @ ( sK7_D @ SY389 @ SV173 @ SV134 ) @ SV134 ) ) ) )
= $true )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[964]) ).
thf(1011,plain,
! [SV190: $i,SV176: $i,SV59: $i] :
( ( ( ! [SY413: $i,SY414: $i] :
( ~ ( in @ SY413 @ SV59 )
| ~ ( in @ SY414 @ SV176 )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ SY413 @ SY414 ) ) )
| ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(1012,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) @ SV176 ) )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) ) ) )
| ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(1013,plain,
! [SV191: $i,SV177: $i,SV59: $i] :
( ( ( ~ ! [SY415: $i] :
( ! [SY395: $i,SY396: $i] :
( ~ ( in @ SY395 @ SV59 )
| ~ ( in @ SY396 @ SV177 )
| ( SY415
!= ( ordered_pair @ SY395 @ SY396 ) ) )
| ( in @ SY415 @ SV191 ) ) )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[967]) ).
thf(1014,plain,
! [SV59: $i,SV177: $i,SV191: $i] :
( ( ( ~ ! [SY418: $i] :
( ~ ( in @ SY418 @ SV191 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY418 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SY418 @ SV191 @ SV177 @ SV59 ) @ SV177 ) )
| ( SY418
!= ( ordered_pair @ ( sK12_E @ SY418 @ SV191 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SY418 @ SV191 @ SV177 @ SV59 ) ) ) ) ) )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[967]) ).
thf(1015,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV144 ) ) )
= $false )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1016,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
= $true )
| ( ( ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV51 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV144 ) )
= $true )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1017,plain,
! [SV145: $i,SV51: $i,SV179: $i] :
( ( ( ! [SY398: $i] :
( ~ ( in @ SY398 @ SV179 )
| ( SY398 = SV51 )
| ( SY398 = SV145 ) ) )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1018,plain,
! [SV145: $i,SV179: $i,SV51: $i] :
( ( ( ~ ( ~ ! [SY399: $i] :
( ( SY399 != SV51 )
| ( in @ SY399 @ SV179 ) )
| ~ ! [SY400: $i] :
( ( SY400 != SV145 )
| ( in @ SY400 @ SV179 ) ) ) )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[971]) ).
thf(1019,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
= $true )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1020,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
| ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) ) )
= $false )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1021,plain,
! [SV181: $i,SV147: $i,SV52: $i] :
( ( ( ! [SY401: $i] :
( ~ ( in @ SY401 @ SV52 )
| ~ ( in @ SY401 @ SV147 )
| ( in @ SY401 @ SV181 ) ) )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(1022,plain,
! [SV147: $i,SV52: $i,SV181: $i] :
( ( ( ~ ( ~ ! [SY402: $i] :
( ~ ( in @ SY402 @ SV181 )
| ( in @ SY402 @ SV52 ) )
| ~ ! [SY403: $i] :
( ~ ( in @ SY403 @ SV181 )
| ( in @ SY403 @ SV147 ) ) ) )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(1023,plain,
! [SV112: $i,SV148: $i] :
( ( ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
= $false )
| ( ( ~ ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 ) )
= $true )
| ( ( SV148
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1024,plain,
! [SV113: $i,SV149: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ SV149 )
| ( subset @ SV218 @ SV113 ) )
= $true )
| ( ( SV149
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1025,plain,
! [SV149: $i,SV113: $i,SV219: $i] :
( ( ( ~ ( subset @ SV219 @ SV113 )
| ( in @ SV219 @ SV149 ) )
= $true )
| ( ( SV149
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1026,plain,
! [SV203: $i,SV192: $i] :
( ( ( SV192 = SV203 )
= $false )
| ( ( proper_subset @ SV192 @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1027,plain,
! [SV212: $i,SV205: $i,SV53: $i] :
( ( ( subset @ ( unordered_pair @ SV53 @ SV205 ) @ SV212 )
= $false )
| ( ( in @ SV53 @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1028,plain,
! [SV213: $i,SV206: $i,SV53: $i] :
( ( ( subset @ ( unordered_pair @ SV53 @ SV206 ) @ SV213 )
= $false )
| ( ( in @ SV206 @ SV213 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1029,plain,
! [SV183: $i,SV54: $i,SV196: $i,SV95: $i] :
( ( ( in @ SV95 @ SV196 )
= $false )
| ( ( in @ SV54 @ SV183 )
= $false )
| ( ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV183 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1030,plain,
! [SV220: $i,SV214: $i,SV95: $i,SV54: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV214 @ SV220 ) ) )
= $true )
| ( ( in @ SV54 @ SV214 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1031,plain,
! [SV216: $i,SV215: $i,SV95: $i,SV54: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV215 @ SV216 ) ) )
= $true )
| ( ( in @ SV95 @ SV216 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1032,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
= $true )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1033,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) ) )
= $false )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1034,plain,
! [SV185: $i,SV158: $i,SV55: $i] :
( ( ( ! [SY405: $i] :
( ~ ( in @ SY405 @ SV55 )
| ( in @ SY405 @ SV158 )
| ( in @ SY405 @ SV185 ) ) )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1035,plain,
! [SV158: $i,SV55: $i,SV185: $i] :
( ( ( ~ ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SV185 )
| ( in @ SY406 @ SV55 ) )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV185 )
| ~ ( in @ SY407 @ SV158 ) ) ) )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1036,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) ) )
= $false )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1037,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
= $true )
| ( ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 )
| ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) )
= $true )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1038,plain,
! [SV160: $i,SV56: $i,SV187: $i] :
( ( ( ! [SY408: $i] :
( ~ ( in @ SY408 @ SV187 )
| ( in @ SY408 @ SV56 )
| ( in @ SY408 @ SV160 ) ) )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(1039,plain,
! [SV160: $i,SV187: $i,SV56: $i] :
( ( ( ~ ( ~ ! [SY409: $i] :
( ~ ( in @ SY409 @ SV56 )
| ( in @ SY409 @ SV187 ) )
| ~ ! [SY410: $i] :
( ~ ( in @ SY410 @ SV160 )
| ( in @ SY410 @ SV187 ) ) ) )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[997]) ).
thf(1040,plain,
! [SV202: $i,SV169: $i,SV130: $i] :
( ( ( disjoint @ SV130 @ SV169 )
= $false )
| ( ( in @ SV202 @ SV130 )
= $false )
| ( ( in @ SV202 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1041,plain,
! [SV131: $i,SV170: $i] :
( ( ( ( sK21_C @ SV170 @ SV131 )
= SV131 )
= $false )
| ( ( ~ ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 ) )
= $true )
| ( ( SV170
= ( singleton @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1042,plain,
! [SV171: $i,SV132: $i,SV221: $i] :
( ( ( ( SV221 != SV132 )
| ( in @ SV221 @ SV171 ) )
= $true )
| ( ( SV171
= ( singleton @ SV132 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1043,plain,
! [SV132: $i,SV171: $i,SV222: $i] :
( ( ( ~ ( in @ SV222 @ SV171 )
| ( SV222 = SV132 ) )
= $true )
| ( ( SV171
= ( singleton @ SV132 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1044,plain,
! [SV223: $i,SV133: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV223 )
| ~ ( in @ SV223 @ SV133 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1045,plain,
! [SV133: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ ( sK9_SY185 @ SV172 @ SV133 ) )
| ~ ( in @ ( sK9_SY185 @ SV172 @ SV133 ) @ SV133 ) )
= $false )
| ( ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1046,plain,
! [SV173: $i,SV134: $i,SV224: $i] :
( ( ( ! [SY429: $i] :
( ~ ( in @ SV224 @ SY429 )
| ~ ( in @ SY429 @ SV134 ) )
| ( in @ SV224 @ SV173 ) )
= $true )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1047,plain,
! [SV134: $i,SV173: $i,SV225: $i] :
( ( ( ~ ( in @ SV225 @ SV173 )
| ~ ( ~ ( in @ SV225 @ ( sK7_D @ SV225 @ SV173 @ SV134 ) )
| ~ ( in @ ( sK7_D @ SV225 @ SV173 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1048,plain,
! [SV190: $i,SV176: $i,SV59: $i] :
( ( ( ! [SY413: $i,SY414: $i] :
( ~ ( in @ SY413 @ SV59 )
| ~ ( in @ SY414 @ SV176 )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ SY413 @ SY414 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1049,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) @ SV176 ) )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) ) ) ) )
= $true )
| ( ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1050,plain,
! [SV191: $i,SV177: $i,SV59: $i] :
( ( ( ! [SY415: $i] :
( ! [SY395: $i,SY396: $i] :
( ~ ( in @ SY395 @ SV59 )
| ~ ( in @ SY396 @ SV177 )
| ( SY415
!= ( ordered_pair @ SY395 @ SY396 ) ) )
| ( in @ SY415 @ SV191 ) ) )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1013]) ).
thf(1051,plain,
! [SV59: $i,SV177: $i,SV191: $i] :
( ( ( ! [SY418: $i] :
( ~ ( in @ SY418 @ SV191 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY418 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SY418 @ SV191 @ SV177 @ SV59 ) @ SV177 ) )
| ( SY418
!= ( ordered_pair @ ( sK12_E @ SY418 @ SV191 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SY418 @ SV191 @ SV177 @ SV59 ) ) ) ) ) )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1052,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV51 ) ) )
= $false )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1053,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV144 ) ) )
= $false )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1054,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV51 )
= $true )
| ( ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV144 )
= $true )
| ( ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
= $true )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1055,plain,
! [SV145: $i,SV51: $i,SV179: $i,SV226: $i] :
( ( ( ~ ( in @ SV226 @ SV179 )
| ( SV226 = SV51 )
| ( SV226 = SV145 ) )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1056,plain,
! [SV145: $i,SV179: $i,SV51: $i] :
( ( ( ~ ! [SY399: $i] :
( ( SY399 != SV51 )
| ( in @ SY399 @ SV179 ) )
| ~ ! [SY400: $i] :
( ( SY400 != SV145 )
| ( in @ SY400 @ SV179 ) ) )
= $false )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1057,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
= $true )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1058,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) ) )
= $false )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1059,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) ) )
= $false )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1060,plain,
! [SV181: $i,SV147: $i,SV52: $i,SV227: $i] :
( ( ( ~ ( in @ SV227 @ SV52 )
| ~ ( in @ SV227 @ SV147 )
| ( in @ SV227 @ SV181 ) )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1061,plain,
! [SV147: $i,SV52: $i,SV181: $i] :
( ( ( ~ ! [SY402: $i] :
( ~ ( in @ SY402 @ SV181 )
| ( in @ SY402 @ SV52 ) )
| ~ ! [SY403: $i] :
( ~ ( in @ SY403 @ SV181 )
| ( in @ SY403 @ SV147 ) ) )
= $false )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1062,plain,
! [SV112: $i,SV148: $i] :
( ( ( subset @ ( sK19_C @ SV148 @ SV112 ) @ SV112 )
= $false )
| ( ( in @ ( sK19_C @ SV148 @ SV112 ) @ SV148 )
= $false )
| ( ( SV148
= ( powerset @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1063,plain,
! [SV113: $i,SV149: $i,SV218: $i] :
( ( ( ~ ( in @ SV218 @ SV149 ) )
= $true )
| ( ( subset @ SV218 @ SV113 )
= $true )
| ( ( SV149
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1064,plain,
! [SV149: $i,SV113: $i,SV219: $i] :
( ( ( ~ ( subset @ SV219 @ SV113 ) )
= $true )
| ( ( in @ SV219 @ SV149 )
= $true )
| ( ( SV149
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1065,plain,
! [SV220: $i,SV214: $i,SV95: $i,SV54: $i] :
( ( ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV214 @ SV220 ) )
= $false )
| ( ( in @ SV54 @ SV214 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1066,plain,
! [SV216: $i,SV215: $i,SV95: $i,SV54: $i] :
( ( ( in @ ( ordered_pair @ SV54 @ SV95 ) @ ( cartesian_product2 @ SV215 @ SV216 ) )
= $false )
| ( ( in @ SV95 @ SV216 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1067,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 ) )
= $true )
| ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
= $true )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1068,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) ) )
= $false )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1033]) ).
thf(1069,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) ) )
= $false )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1033]) ).
thf(1070,plain,
! [SV185: $i,SV158: $i,SV55: $i,SV228: $i] :
( ( ( ~ ( in @ SV228 @ SV55 )
| ( in @ SV228 @ SV158 )
| ( in @ SV228 @ SV185 ) )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1071,plain,
! [SV158: $i,SV55: $i,SV185: $i] :
( ( ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SV185 )
| ( in @ SY406 @ SV55 ) )
| ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV185 )
| ~ ( in @ SY407 @ SV158 ) ) )
= $false )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1072,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 ) ) )
= $false )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1073,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) ) )
= $false )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1036]) ).
thf(1074,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 )
= $true )
| ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 )
= $true )
| ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
= $true )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1075,plain,
! [SV160: $i,SV56: $i,SV187: $i,SV229: $i] :
( ( ( ~ ( in @ SV229 @ SV187 )
| ( in @ SV229 @ SV56 )
| ( in @ SV229 @ SV160 ) )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1076,plain,
! [SV160: $i,SV187: $i,SV56: $i] :
( ( ( ~ ! [SY409: $i] :
( ~ ( in @ SY409 @ SV56 )
| ( in @ SY409 @ SV187 ) )
| ~ ! [SY410: $i] :
( ~ ( in @ SY410 @ SV160 )
| ( in @ SY410 @ SV187 ) ) )
= $false )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1077,plain,
! [SV131: $i,SV170: $i] :
( ( ( in @ ( sK21_C @ SV170 @ SV131 ) @ SV170 )
= $false )
| ( ( ( sK21_C @ SV170 @ SV131 )
= SV131 )
= $false )
| ( ( SV170
= ( singleton @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1078,plain,
! [SV171: $i,SV132: $i,SV221: $i] :
( ( ( ( SV221 != SV132 ) )
= $true )
| ( ( in @ SV221 @ SV171 )
= $true )
| ( ( SV171
= ( singleton @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1042]) ).
thf(1079,plain,
! [SV132: $i,SV171: $i,SV222: $i] :
( ( ( ~ ( in @ SV222 @ SV171 ) )
= $true )
| ( ( SV222 = SV132 )
= $true )
| ( ( SV171
= ( singleton @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1080,plain,
! [SV223: $i,SV133: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV223 ) )
= $true )
| ( ( ~ ( in @ SV223 @ SV133 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1081,plain,
! [SV133: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ ( sK9_SY185 @ SV172 @ SV133 ) ) )
= $false )
| ( ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1045]) ).
thf(1082,plain,
! [SV133: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK9_SY185 @ SV172 @ SV133 ) @ SV133 ) )
= $false )
| ( ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1045]) ).
thf(1083,plain,
! [SV173: $i,SV134: $i,SV224: $i] :
( ( ( ! [SY429: $i] :
( ~ ( in @ SV224 @ SY429 )
| ~ ( in @ SY429 @ SV134 ) ) )
= $true )
| ( ( in @ SV224 @ SV173 )
= $true )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1084,plain,
! [SV134: $i,SV173: $i,SV225: $i] :
( ( ( ~ ( in @ SV225 @ SV173 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV225 @ ( sK7_D @ SV225 @ SV173 @ SV134 ) )
| ~ ( in @ ( sK7_D @ SV225 @ SV173 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1085,plain,
! [SV190: $i,SV176: $i,SV59: $i,SV230: $i] :
( ( ( ! [SY430: $i] :
( ~ ( in @ SV230 @ SV59 )
| ~ ( in @ SY430 @ SV176 )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ SV230 @ SY430 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1086,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) @ SV176 ) )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) ) ) )
= $false )
| ( ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1087,plain,
! [SV191: $i,SV231: $i,SV177: $i,SV59: $i] :
( ( ( ! [SY431: $i,SY432: $i] :
( ~ ( in @ SY431 @ SV59 )
| ~ ( in @ SY432 @ SV177 )
| ( SV231
!= ( ordered_pair @ SY431 @ SY432 ) ) )
| ( in @ SV231 @ SV191 ) )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1088,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( ~ ( in @ SV232 @ SV191 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV177 ) )
| ( SV232
!= ( ordered_pair @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) ) ) ) )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1089,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV51 ) )
= $true )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1090,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
| ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV144 ) )
= $true )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1053]) ).
thf(1091,plain,
! [SV145: $i,SV51: $i,SV179: $i,SV226: $i] :
( ( ( ~ ( in @ SV226 @ SV179 ) )
= $true )
| ( ( ( SV226 = SV51 )
| ( SV226 = SV145 ) )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1092,plain,
! [SV145: $i,SV179: $i,SV51: $i] :
( ( ( ~ ! [SY399: $i] :
( ( SY399 != SV51 )
| ( in @ SY399 @ SV179 ) ) )
= $false )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1093,plain,
! [SV51: $i,SV179: $i,SV145: $i] :
( ( ( ~ ! [SY400: $i] :
( ( SY400 != SV145 )
| ( in @ SY400 @ SV179 ) ) )
= $false )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1094,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
= $false )
| ( ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
= $true )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1095,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
= $true )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1058]) ).
thf(1096,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
| ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
= $true )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1059]) ).
thf(1097,plain,
! [SV181: $i,SV147: $i,SV52: $i,SV227: $i] :
( ( ( ~ ( in @ SV227 @ SV52 )
| ~ ( in @ SV227 @ SV147 ) )
= $true )
| ( ( in @ SV227 @ SV181 )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1098,plain,
! [SV147: $i,SV52: $i,SV181: $i] :
( ( ( ~ ! [SY402: $i] :
( ~ ( in @ SY402 @ SV181 )
| ( in @ SY402 @ SV52 ) ) )
= $false )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1099,plain,
! [SV52: $i,SV147: $i,SV181: $i] :
( ( ( ~ ! [SY403: $i] :
( ~ ( in @ SY403 @ SV181 )
| ( in @ SY403 @ SV147 ) ) )
= $false )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1100,plain,
! [SV113: $i,SV149: $i,SV218: $i] :
( ( ( in @ SV218 @ SV149 )
= $false )
| ( ( subset @ SV218 @ SV113 )
= $true )
| ( ( SV149
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1101,plain,
! [SV149: $i,SV113: $i,SV219: $i] :
( ( ( subset @ SV219 @ SV113 )
= $false )
| ( ( in @ SV219 @ SV149 )
= $true )
| ( ( SV149
= ( powerset @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1102,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
= $false )
| ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
= $true )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1067]) ).
thf(1103,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
= $true )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1104,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
| ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 ) )
= $true )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1069]) ).
thf(1105,plain,
! [SV185: $i,SV158: $i,SV55: $i,SV228: $i] :
( ( ( ~ ( in @ SV228 @ SV55 )
| ( in @ SV228 @ SV158 ) )
= $true )
| ( ( in @ SV228 @ SV185 )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1106,plain,
! [SV158: $i,SV55: $i,SV185: $i] :
( ( ( ~ ! [SY406: $i] :
( ~ ( in @ SY406 @ SV185 )
| ( in @ SY406 @ SV55 ) ) )
= $false )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1071]) ).
thf(1107,plain,
! [SV55: $i,SV158: $i,SV185: $i] :
( ( ( ~ ! [SY407: $i] :
( ~ ( in @ SY407 @ SV185 )
| ~ ( in @ SY407 @ SV158 ) ) )
= $false )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1071]) ).
thf(1108,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 ) )
= $true )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1109,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
| ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) )
= $true )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1110,plain,
! [SV160: $i,SV56: $i,SV187: $i,SV229: $i] :
( ( ( ~ ( in @ SV229 @ SV187 ) )
= $true )
| ( ( ( in @ SV229 @ SV56 )
| ( in @ SV229 @ SV160 ) )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1111,plain,
! [SV160: $i,SV187: $i,SV56: $i] :
( ( ( ~ ! [SY409: $i] :
( ~ ( in @ SY409 @ SV56 )
| ( in @ SY409 @ SV187 ) ) )
= $false )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1112,plain,
! [SV56: $i,SV187: $i,SV160: $i] :
( ( ( ~ ! [SY410: $i] :
( ~ ( in @ SY410 @ SV160 )
| ( in @ SY410 @ SV187 ) ) )
= $false )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1113,plain,
! [SV171: $i,SV132: $i,SV221: $i] :
( ( ( SV221 = SV132 )
= $false )
| ( ( in @ SV221 @ SV171 )
= $true )
| ( ( SV171
= ( singleton @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1114,plain,
! [SV132: $i,SV171: $i,SV222: $i] :
( ( ( in @ SV222 @ SV171 )
= $false )
| ( ( SV222 = SV132 )
= $true )
| ( ( SV171
= ( singleton @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1115,plain,
! [SV223: $i,SV133: $i,SV172: $i] :
( ( ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV223 )
= $false )
| ( ( ~ ( in @ SV223 @ SV133 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1116,plain,
! [SV133: $i,SV172: $i] :
( ( ( in @ ( sK8_C @ SV172 @ SV133 ) @ ( sK9_SY185 @ SV172 @ SV133 ) )
= $true )
| ( ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1081]) ).
thf(1117,plain,
! [SV133: $i,SV172: $i] :
( ( ( in @ ( sK9_SY185 @ SV172 @ SV133 ) @ SV133 )
= $true )
| ( ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1118,plain,
! [SV173: $i,SV134: $i,SV233: $i,SV224: $i] :
( ( ( ~ ( in @ SV224 @ SV233 )
| ~ ( in @ SV233 @ SV134 ) )
= $true )
| ( ( in @ SV224 @ SV173 )
= $true )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1119,plain,
! [SV134: $i,SV173: $i,SV225: $i] :
( ( ( in @ SV225 @ SV173 )
= $false )
| ( ( ~ ( ~ ( in @ SV225 @ ( sK7_D @ SV225 @ SV173 @ SV134 ) )
| ~ ( in @ ( sK7_D @ SV225 @ SV173 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1120,plain,
! [SV190: $i,SV176: $i,SV234: $i,SV59: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ SV59 )
| ~ ( in @ SV234 @ SV176 )
| ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ SV230 @ SV234 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1121,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) @ SV176 ) ) )
= $false )
| ( ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1086]) ).
thf(1122,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) ) ) )
= $false )
| ( ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1086]) ).
thf(1123,plain,
! [SV191: $i,SV231: $i,SV177: $i,SV59: $i] :
( ( ( ! [SY431: $i,SY432: $i] :
( ~ ( in @ SY431 @ SV59 )
| ~ ( in @ SY432 @ SV177 )
| ( SV231
!= ( ordered_pair @ SY431 @ SY432 ) ) ) )
= $true )
| ( ( in @ SV231 @ SV191 )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1124,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( ~ ( in @ SV232 @ SV191 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV177 ) )
| ( SV232
!= ( ordered_pair @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) ) ) ) )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1125,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 ) )
= $true )
| ( ( ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV51 ) )
= $true )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1126,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 ) )
= $true )
| ( ( ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV144 ) )
= $true )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1127,plain,
! [SV145: $i,SV51: $i,SV179: $i,SV226: $i] :
( ( ( in @ SV226 @ SV179 )
= $false )
| ( ( ( SV226 = SV51 )
| ( SV226 = SV145 ) )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1128,plain,
! [SV145: $i,SV179: $i,SV51: $i] :
( ( ( ! [SY399: $i] :
( ( SY399 != SV51 )
| ( in @ SY399 @ SV179 ) ) )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1092]) ).
thf(1129,plain,
! [SV51: $i,SV179: $i,SV145: $i] :
( ( ( ! [SY400: $i] :
( ( SY400 != SV145 )
| ( in @ SY400 @ SV179 ) ) )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1130,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
= $false )
| ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
= $false )
| ( ( ~ ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 ) )
= $true )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1131,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
= $true )
| ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 )
= $true )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1132,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
= $true )
| ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 )
= $true )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1133,plain,
! [SV181: $i,SV147: $i,SV52: $i,SV227: $i] :
( ( ( ~ ( in @ SV227 @ SV52 ) )
= $true )
| ( ( ~ ( in @ SV227 @ SV147 ) )
= $true )
| ( ( in @ SV227 @ SV181 )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1134,plain,
! [SV147: $i,SV52: $i,SV181: $i] :
( ( ( ! [SY402: $i] :
( ~ ( in @ SY402 @ SV181 )
| ( in @ SY402 @ SV52 ) ) )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1135,plain,
! [SV52: $i,SV147: $i,SV181: $i] :
( ( ( ! [SY403: $i] :
( ~ ( in @ SY403 @ SV181 )
| ( in @ SY403 @ SV147 ) ) )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1099]) ).
thf(1136,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 )
= $false )
| ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
= $true )
| ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
= $false )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1137,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV55 )
= $true )
| ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 )
= $true )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1138,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 ) )
= $true )
| ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 )
= $true )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1139,plain,
! [SV185: $i,SV158: $i,SV55: $i,SV228: $i] :
( ( ( ~ ( in @ SV228 @ SV55 ) )
= $true )
| ( ( in @ SV228 @ SV158 )
= $true )
| ( ( in @ SV228 @ SV185 )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1140,plain,
! [SV158: $i,SV55: $i,SV185: $i] :
( ( ( ! [SY406: $i] :
( ~ ( in @ SY406 @ SV185 )
| ( in @ SY406 @ SV55 ) ) )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1141,plain,
! [SV55: $i,SV158: $i,SV185: $i] :
( ( ( ! [SY407: $i] :
( ~ ( in @ SY407 @ SV185 )
| ~ ( in @ SY407 @ SV158 ) ) )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1142,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 ) )
= $true )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1143,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) )
= $true )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1144,plain,
! [SV160: $i,SV56: $i,SV187: $i,SV229: $i] :
( ( ( in @ SV229 @ SV187 )
= $false )
| ( ( ( in @ SV229 @ SV56 )
| ( in @ SV229 @ SV160 ) )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1145,plain,
! [SV160: $i,SV187: $i,SV56: $i] :
( ( ( ! [SY409: $i] :
( ~ ( in @ SY409 @ SV56 )
| ( in @ SY409 @ SV187 ) ) )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1146,plain,
! [SV56: $i,SV187: $i,SV160: $i] :
( ( ( ! [SY410: $i] :
( ~ ( in @ SY410 @ SV160 )
| ( in @ SY410 @ SV187 ) ) )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1147,plain,
! [SV172: $i,SV133: $i,SV223: $i] :
( ( ( in @ SV223 @ SV133 )
= $false )
| ( ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV223 )
= $false )
| ( ( ~ ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 ) )
= $true )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1115]) ).
thf(1148,plain,
! [SV173: $i,SV134: $i,SV233: $i,SV224: $i] :
( ( ( ~ ( in @ SV224 @ SV233 ) )
= $true )
| ( ( ~ ( in @ SV233 @ SV134 ) )
= $true )
| ( ( in @ SV224 @ SV173 )
= $true )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1149,plain,
! [SV134: $i,SV173: $i,SV225: $i] :
( ( ( ~ ( in @ SV225 @ ( sK7_D @ SV225 @ SV173 @ SV134 ) )
| ~ ( in @ ( sK7_D @ SV225 @ SV173 @ SV134 ) @ SV134 ) )
= $false )
| ( ( in @ SV225 @ SV173 )
= $false )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1150,plain,
! [SV190: $i,SV176: $i,SV234: $i,SV59: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ SV59 )
| ~ ( in @ SV234 @ SV176 ) )
= $true )
| ( ( ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ SV230 @ SV234 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1151,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) @ SV176 ) ) )
= $true )
| ( ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1152,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( ( sK14_D @ SV190 @ SV176 @ SV59 )
= ( ordered_pair @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) ) )
= $true )
| ( ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1153,plain,
! [SV191: $i,SV231: $i,SV177: $i,SV59: $i,SV235: $i] :
( ( ( ! [SY433: $i] :
( ~ ( in @ SV235 @ SV59 )
| ~ ( in @ SY433 @ SV177 )
| ( SV231
!= ( ordered_pair @ SV235 @ SY433 ) ) ) )
= $true )
| ( ( in @ SV231 @ SV191 )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1154,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( in @ SV232 @ SV191 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV177 ) )
| ( SV232
!= ( ordered_pair @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) ) ) ) )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1155,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
= $false )
| ( ( ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV51 ) )
= $true )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1156,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
= $false )
| ( ( ( ( sK18_D @ SV178 @ SV144 @ SV51 )
!= SV144 ) )
= $true )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1157,plain,
! [SV179: $i,SV145: $i,SV51: $i,SV226: $i] :
( ( ( SV226 = SV51 )
= $true )
| ( ( SV226 = SV145 )
= $true )
| ( ( in @ SV226 @ SV179 )
= $false )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1158,plain,
! [SV145: $i,SV179: $i,SV51: $i,SV236: $i] :
( ( ( ( SV236 != SV51 )
| ( in @ SV236 @ SV179 ) )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1159,plain,
! [SV51: $i,SV179: $i,SV145: $i,SV237: $i] :
( ( ( ( SV237 != SV145 )
| ( in @ SV237 @ SV179 ) )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1160,plain,
! [SV52: $i,SV146: $i,SV180: $i] :
( ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV180 )
= $false )
| ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV52 )
= $false )
| ( ( in @ ( sK10_D @ SV180 @ SV146 @ SV52 ) @ SV146 )
= $false )
| ( ( SV180
= ( set_intersection2 @ SV52 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1161,plain,
! [SV181: $i,SV147: $i,SV52: $i,SV227: $i] :
( ( ( in @ SV227 @ SV52 )
= $false )
| ( ( ~ ( in @ SV227 @ SV147 ) )
= $true )
| ( ( in @ SV227 @ SV181 )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1162,plain,
! [SV147: $i,SV52: $i,SV181: $i,SV238: $i] :
( ( ( ~ ( in @ SV238 @ SV181 )
| ( in @ SV238 @ SV52 ) )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1163,plain,
! [SV52: $i,SV147: $i,SV181: $i,SV239: $i] :
( ( ( ~ ( in @ SV239 @ SV181 )
| ( in @ SV239 @ SV147 ) )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1164,plain,
! [SV55: $i,SV157: $i,SV184: $i] :
( ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV157 )
= $false )
| ( ( in @ ( sK6_D @ SV184 @ SV157 @ SV55 ) @ SV184 )
= $true )
| ( ( SV184
= ( set_difference @ SV55 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1165,plain,
! [SV185: $i,SV158: $i,SV55: $i,SV228: $i] :
( ( ( in @ SV228 @ SV55 )
= $false )
| ( ( in @ SV228 @ SV158 )
= $true )
| ( ( in @ SV228 @ SV185 )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1166,plain,
! [SV158: $i,SV55: $i,SV185: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ SV185 )
| ( in @ SV240 @ SV55 ) )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1167,plain,
! [SV55: $i,SV158: $i,SV185: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV185 )
| ~ ( in @ SV241 @ SV158 ) )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1168,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
= $false )
| ( ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 ) )
= $true )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1169,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
= $false )
| ( ( ~ ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 ) )
= $true )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1170,plain,
! [SV187: $i,SV160: $i,SV56: $i,SV229: $i] :
( ( ( in @ SV229 @ SV56 )
= $true )
| ( ( in @ SV229 @ SV160 )
= $true )
| ( ( in @ SV229 @ SV187 )
= $false )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1171,plain,
! [SV160: $i,SV187: $i,SV56: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV56 )
| ( in @ SV242 @ SV187 ) )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1172,plain,
! [SV56: $i,SV187: $i,SV160: $i,SV243: $i] :
( ( ( ~ ( in @ SV243 @ SV160 )
| ( in @ SV243 @ SV187 ) )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1173,plain,
! [SV223: $i,SV133: $i,SV172: $i] :
( ( ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV172 )
= $false )
| ( ( in @ ( sK8_C @ SV172 @ SV133 ) @ SV223 )
= $false )
| ( ( in @ SV223 @ SV133 )
= $false )
| ( ( SV172
= ( union @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1174,plain,
! [SV173: $i,SV134: $i,SV233: $i,SV224: $i] :
( ( ( in @ SV224 @ SV233 )
= $false )
| ( ( ~ ( in @ SV233 @ SV134 ) )
= $true )
| ( ( in @ SV224 @ SV173 )
= $true )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1175,plain,
! [SV134: $i,SV173: $i,SV225: $i] :
( ( ( ~ ( in @ SV225 @ ( sK7_D @ SV225 @ SV173 @ SV134 ) ) )
= $false )
| ( ( in @ SV225 @ SV173 )
= $false )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1149]) ).
thf(1176,plain,
! [SV134: $i,SV173: $i,SV225: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV225 @ SV173 @ SV134 ) @ SV134 ) )
= $false )
| ( ( in @ SV225 @ SV173 )
= $false )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1149]) ).
thf(1177,plain,
! [SV190: $i,SV176: $i,SV234: $i,SV59: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ SV59 ) )
= $true )
| ( ( ~ ( in @ SV234 @ SV176 ) )
= $true )
| ( ( ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ SV230 @ SV234 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1178,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) @ SV176 ) )
= $false )
| ( ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1179,plain,
! [SV191: $i,SV231: $i,SV177: $i,SV244: $i,SV59: $i,SV235: $i] :
( ( ( ~ ( in @ SV235 @ SV59 )
| ~ ( in @ SV244 @ SV177 )
| ( SV231
!= ( ordered_pair @ SV235 @ SV244 ) ) )
= $true )
| ( ( in @ SV231 @ SV191 )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1180,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV177 ) )
| ( SV232
!= ( ordered_pair @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) ) ) )
= $false )
| ( ( in @ SV232 @ SV191 )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1154]) ).
thf(1181,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV51 )
= $false )
| ( ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
= $false )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1155]) ).
thf(1182,plain,
! [SV51: $i,SV144: $i,SV178: $i] :
( ( ( ( sK18_D @ SV178 @ SV144 @ SV51 )
= SV144 )
= $false )
| ( ( in @ ( sK18_D @ SV178 @ SV144 @ SV51 ) @ SV178 )
= $false )
| ( ( SV178
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1183,plain,
! [SV145: $i,SV179: $i,SV51: $i,SV236: $i] :
( ( ( ( SV236 != SV51 ) )
= $true )
| ( ( in @ SV236 @ SV179 )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1184,plain,
! [SV51: $i,SV179: $i,SV145: $i,SV237: $i] :
( ( ( ( SV237 != SV145 ) )
= $true )
| ( ( in @ SV237 @ SV179 )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1185,plain,
! [SV181: $i,SV52: $i,SV147: $i,SV227: $i] :
( ( ( in @ SV227 @ SV147 )
= $false )
| ( ( in @ SV227 @ SV52 )
= $false )
| ( ( in @ SV227 @ SV181 )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1186,plain,
! [SV147: $i,SV52: $i,SV181: $i,SV238: $i] :
( ( ( ~ ( in @ SV238 @ SV181 ) )
= $true )
| ( ( in @ SV238 @ SV52 )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1162]) ).
thf(1187,plain,
! [SV52: $i,SV147: $i,SV181: $i,SV239: $i] :
( ( ( ~ ( in @ SV239 @ SV181 ) )
= $true )
| ( ( in @ SV239 @ SV147 )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1163]) ).
thf(1188,plain,
! [SV158: $i,SV55: $i,SV185: $i,SV240: $i] :
( ( ( ~ ( in @ SV240 @ SV185 ) )
= $true )
| ( ( in @ SV240 @ SV55 )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1189,plain,
! [SV55: $i,SV158: $i,SV185: $i,SV241: $i] :
( ( ( ~ ( in @ SV241 @ SV185 ) )
= $true )
| ( ( ~ ( in @ SV241 @ SV158 ) )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1190,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV56 )
= $false )
| ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
= $false )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1191,plain,
! [SV56: $i,SV159: $i,SV186: $i] :
( ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV159 )
= $false )
| ( ( in @ ( sK17_D @ SV186 @ SV159 @ SV56 ) @ SV186 )
= $false )
| ( ( SV186
= ( set_union2 @ SV56 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1169]) ).
thf(1192,plain,
! [SV160: $i,SV187: $i,SV56: $i,SV242: $i] :
( ( ( ~ ( in @ SV242 @ SV56 ) )
= $true )
| ( ( in @ SV242 @ SV187 )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1193,plain,
! [SV56: $i,SV187: $i,SV160: $i,SV243: $i] :
( ( ( ~ ( in @ SV243 @ SV160 ) )
= $true )
| ( ( in @ SV243 @ SV187 )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1194,plain,
! [SV173: $i,SV224: $i,SV134: $i,SV233: $i] :
( ( ( in @ SV233 @ SV134 )
= $false )
| ( ( in @ SV224 @ SV233 )
= $false )
| ( ( in @ SV224 @ SV173 )
= $true )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1195,plain,
! [SV134: $i,SV173: $i,SV225: $i] :
( ( ( in @ SV225 @ ( sK7_D @ SV225 @ SV173 @ SV134 ) )
= $true )
| ( ( in @ SV225 @ SV173 )
= $false )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1175]) ).
thf(1196,plain,
! [SV134: $i,SV173: $i,SV225: $i] :
( ( ( in @ ( sK7_D @ SV225 @ SV173 @ SV134 ) @ SV134 )
= $true )
| ( ( in @ SV225 @ SV173 )
= $false )
| ( ( SV173
= ( union @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1176]) ).
thf(1197,plain,
! [SV190: $i,SV176: $i,SV234: $i,SV59: $i,SV230: $i] :
( ( ( in @ SV230 @ SV59 )
= $false )
| ( ( ~ ( in @ SV234 @ SV176 ) )
= $true )
| ( ( ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ SV230 @ SV234 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1177]) ).
thf(1198,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ SV59 ) )
= $false )
| ( ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1199,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) @ SV176 ) )
= $false )
| ( ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1178]) ).
thf(1200,plain,
! [SV191: $i,SV231: $i,SV177: $i,SV244: $i,SV59: $i,SV235: $i] :
( ( ( ~ ( in @ SV235 @ SV59 )
| ~ ( in @ SV244 @ SV177 ) )
= $true )
| ( ( ( SV231
!= ( ordered_pair @ SV235 @ SV244 ) ) )
= $true )
| ( ( in @ SV231 @ SV191 )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1201,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV177 ) ) )
= $false )
| ( ( in @ SV232 @ SV191 )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1202,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( ( SV232
!= ( ordered_pair @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) ) ) )
= $false )
| ( ( in @ SV232 @ SV191 )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1203,plain,
! [SV145: $i,SV179: $i,SV51: $i,SV236: $i] :
( ( ( SV236 = SV51 )
= $false )
| ( ( in @ SV236 @ SV179 )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1204,plain,
! [SV51: $i,SV179: $i,SV145: $i,SV237: $i] :
( ( ( SV237 = SV145 )
= $false )
| ( ( in @ SV237 @ SV179 )
= $true )
| ( ( SV179
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1205,plain,
! [SV147: $i,SV52: $i,SV181: $i,SV238: $i] :
( ( ( in @ SV238 @ SV181 )
= $false )
| ( ( in @ SV238 @ SV52 )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1186]) ).
thf(1206,plain,
! [SV52: $i,SV147: $i,SV181: $i,SV239: $i] :
( ( ( in @ SV239 @ SV181 )
= $false )
| ( ( in @ SV239 @ SV147 )
= $true )
| ( ( SV181
= ( set_intersection2 @ SV52 @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1187]) ).
thf(1207,plain,
! [SV158: $i,SV55: $i,SV185: $i,SV240: $i] :
( ( ( in @ SV240 @ SV185 )
= $false )
| ( ( in @ SV240 @ SV55 )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1208,plain,
! [SV55: $i,SV158: $i,SV185: $i,SV241: $i] :
( ( ( in @ SV241 @ SV185 )
= $false )
| ( ( ~ ( in @ SV241 @ SV158 ) )
= $true )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1209,plain,
! [SV160: $i,SV187: $i,SV56: $i,SV242: $i] :
( ( ( in @ SV242 @ SV56 )
= $false )
| ( ( in @ SV242 @ SV187 )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1210,plain,
! [SV56: $i,SV187: $i,SV160: $i,SV243: $i] :
( ( ( in @ SV243 @ SV160 )
= $false )
| ( ( in @ SV243 @ SV187 )
= $true )
| ( ( SV187
= ( set_union2 @ SV56 @ SV160 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1193]) ).
thf(1211,plain,
! [SV190: $i,SV59: $i,SV230: $i,SV176: $i,SV234: $i] :
( ( ( in @ SV234 @ SV176 )
= $false )
| ( ( in @ SV230 @ SV59 )
= $false )
| ( ( ( ( sK14_D @ SV190 @ SV176 @ SV59 )
!= ( ordered_pair @ SV230 @ SV234 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1212,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( in @ ( sK15_SY189 @ SV190 @ SV176 @ SV59 ) @ SV59 )
= $true )
| ( ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1198]) ).
thf(1213,plain,
! [SV59: $i,SV176: $i,SV190: $i] :
( ( ( in @ ( sK16_SY191 @ SV190 @ SV176 @ SV59 ) @ SV176 )
= $true )
| ( ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1214,plain,
! [SV191: $i,SV231: $i,SV177: $i,SV244: $i,SV59: $i,SV235: $i] :
( ( ( ~ ( in @ SV235 @ SV59 ) )
= $true )
| ( ( ~ ( in @ SV244 @ SV177 ) )
= $true )
| ( ( ( SV231
!= ( ordered_pair @ SV235 @ SV244 ) ) )
= $true )
| ( ( in @ SV231 @ SV191 )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1215,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV177 ) ) )
= $true )
| ( ( in @ SV232 @ SV191 )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1201]) ).
thf(1216,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( SV232
= ( ordered_pair @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) ) )
= $true )
| ( ( in @ SV232 @ SV191 )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1202]) ).
thf(1217,plain,
! [SV55: $i,SV185: $i,SV158: $i,SV241: $i] :
( ( ( in @ SV241 @ SV158 )
= $false )
| ( ( in @ SV241 @ SV185 )
= $false )
| ( ( SV185
= ( set_difference @ SV55 @ SV158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1218,plain,
! [SV234: $i,SV230: $i,SV59: $i,SV176: $i,SV190: $i] :
( ( ( ( sK14_D @ SV190 @ SV176 @ SV59 )
= ( ordered_pair @ SV230 @ SV234 ) )
= $false )
| ( ( in @ SV230 @ SV59 )
= $false )
| ( ( in @ SV234 @ SV176 )
= $false )
| ( ( ~ ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 ) )
= $true )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1219,plain,
! [SV191: $i,SV231: $i,SV177: $i,SV244: $i,SV59: $i,SV235: $i] :
( ( ( in @ SV235 @ SV59 )
= $false )
| ( ( ~ ( in @ SV244 @ SV177 ) )
= $true )
| ( ( ( SV231
!= ( ordered_pair @ SV235 @ SV244 ) ) )
= $true )
| ( ( in @ SV231 @ SV191 )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1220,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( ~ ( in @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV59 )
| ~ ( in @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV177 ) )
= $false )
| ( ( in @ SV232 @ SV191 )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1221,plain,
! [SV230: $i,SV234: $i,SV59: $i,SV176: $i,SV190: $i] :
( ( ( in @ ( sK14_D @ SV190 @ SV176 @ SV59 ) @ SV190 )
= $false )
| ( ( in @ SV234 @ SV176 )
= $false )
| ( ( in @ SV230 @ SV59 )
= $false )
| ( ( ( sK14_D @ SV190 @ SV176 @ SV59 )
= ( ordered_pair @ SV230 @ SV234 ) )
= $false )
| ( ( SV190
= ( cartesian_product2 @ SV59 @ SV176 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1222,plain,
! [SV191: $i,SV231: $i,SV59: $i,SV235: $i,SV177: $i,SV244: $i] :
( ( ( in @ SV244 @ SV177 )
= $false )
| ( ( in @ SV235 @ SV59 )
= $false )
| ( ( ( SV231
!= ( ordered_pair @ SV235 @ SV244 ) ) )
= $true )
| ( ( in @ SV231 @ SV191 )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1223,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( ~ ( in @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV59 ) )
= $false )
| ( ( in @ SV232 @ SV191 )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1220]) ).
thf(1224,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( ~ ( in @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV177 ) )
= $false )
| ( ( in @ SV232 @ SV191 )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1220]) ).
thf(1225,plain,
! [SV191: $i,SV177: $i,SV59: $i,SV244: $i,SV235: $i,SV231: $i] :
( ( ( SV231
= ( ordered_pair @ SV235 @ SV244 ) )
= $false )
| ( ( in @ SV235 @ SV59 )
= $false )
| ( ( in @ SV244 @ SV177 )
= $false )
| ( ( in @ SV231 @ SV191 )
= $true )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1226,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( in @ ( sK12_E @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV59 )
= $true )
| ( ( in @ SV232 @ SV191 )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1223]) ).
thf(1227,plain,
! [SV59: $i,SV177: $i,SV191: $i,SV232: $i] :
( ( ( in @ ( sK13_SY186 @ SV232 @ SV191 @ SV177 @ SV59 ) @ SV177 )
= $true )
| ( ( in @ SV232 @ SV191 )
= $false )
| ( ( SV191
= ( cartesian_product2 @ SV59 @ SV177 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1228,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[265,1227,1226,1225,1221,1217,1216,1213,1212,1210,1209,1207,1206,1205,1204,1203,1196,1195,1194,1191,1190,1185,1182,1181,1173,1170,1165,1164,1160,1157,1152,1137,1136,1132,1131,1117,1116,1114,1113,1101,1100,1077,1074,1066,1065,1062,1054,1040,1029,1028,1027,1026,1004,1001,1000,999,998,989,988,982,981,977,955,954,953,952,951,948,937,930,898,883,880,870,869,862,856,855,851,850,849,848,829,828,821,820,819,818,817,816,815,814,813,774,757,751,711,694,693,692,691,690,687,686,685,680,627,626,625,619,616,614,610,608,605,585,553,549,539,529,479,475,474,473,472,466,462,460,458,457,451,443,413,412,411,410,408,407,405,404,389,379,327,320,319,318,317,316,315,314,313,312,311,310]) ).
thf(1229,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(1230,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(1231,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(1232,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(1233,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)],[245]) ).
thf(1234,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)],[244]) ).
thf(1235,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)],[243]) ).
thf(1236,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)],[242]) ).
thf(1237,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(1238,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)],[240]) ).
thf(1239,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)],[239]) ).
thf(1240,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(1241,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(1242,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(1243,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(1244,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(1245,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(1246,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(1247,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(1248,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(1249,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)],[232]) ).
thf(1250,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(1251,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)],[231]) ).
thf(1252,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)],[230]) ).
thf(1253,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)],[229]) ).
thf(1254,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(1255,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)],[228]) ).
thf(1256,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(1257,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(1258,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(1259,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(1260,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)],[225]) ).
thf(1261,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(1262,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(1263,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(1264,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(1265,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(1266,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)],[221]) ).
thf(1267,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(1268,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(1269,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(1270,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(1271,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(1272,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(1273,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(1274,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(1275,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)],[215]) ).
thf(1276,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)],[214]) ).
thf(1277,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)],[213]) ).
thf(1278,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)],[212]) ).
thf(1279,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)],[211]) ).
thf(1280,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)],[210]) ).
thf(1281,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY187: $i,SY188: $i] :
( ~ ( in @ SY187 @ A )
| ~ ( in @ SY188 @ B )
| ( ( sK14_D @ C @ B @ A )
!= ( ordered_pair @ SY187 @ SY188 ) ) )
| ~ ( in @ ( sK14_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK15_SY189 @ C @ B @ A ) @ A )
& ( in @ ( sK16_SY191 @ C @ B @ A ) @ B )
& ( ( sK14_D @ C @ B @ A )
= ( ordered_pair @ ( sK15_SY189 @ C @ B @ A ) @ ( sK16_SY191 @ 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_SY186 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK12_E @ D @ C @ B @ A ) @ ( sK13_SY186 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(1282,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)],[208]) ).
thf(1283,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)],[207]) ).
thf(1284,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY184: $i] :
( ~ ( in @ ( sK8_C @ B @ A ) @ SY184 )
| ~ ( in @ SY184 @ A ) )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK8_C @ B @ A ) @ ( sK9_SY185 @ B @ A ) )
& ( in @ ( sK9_SY185 @ 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)],[206]) ).
thf(1285,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)],[205]) ).
thf(1286,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(1287,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)],[204]) ).
thf(1288,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)],[203]) ).
thf(1289,plain,
$true = $true,
inference(copy,[status(thm)],[121]) ).
thf(1290,plain,
$true = $true,
inference(copy,[status(thm)],[120]) ).
thf(1291,plain,
$true = $true,
inference(copy,[status(thm)],[119]) ).
thf(1292,plain,
$true = $true,
inference(copy,[status(thm)],[118]) ).
thf(1293,plain,
$true = $true,
inference(copy,[status(thm)],[117]) ).
thf(1294,plain,
$true = $true,
inference(copy,[status(thm)],[116]) ).
thf(1295,plain,
$true = $true,
inference(copy,[status(thm)],[115]) ).
thf(1296,plain,
$true = $true,
inference(copy,[status(thm)],[114]) ).
thf(1297,plain,
$true = $true,
inference(copy,[status(thm)],[113]) ).
thf(1298,plain,
$true = $true,
inference(copy,[status(thm)],[112]) ).
thf(1299,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(1300,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(1301,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(1302,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(1303,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(1304,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(1305,plain,
( ( ! [A: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(1306,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(1307,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(1308,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(1309,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(1310,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(1311,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(1312,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)],[193]) ).
thf(1313,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(1314,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(1315,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(1316,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(1317,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(1318,plain,
( ( ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY183 ) ) )
& ~ ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(1319,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)],[1253]) ).
thf(1320,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)],[1251]) ).
thf(1321,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)],[1266]) ).
thf(1322,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)],[1252]) ).
thf(1323,plain,
( ( ~ ( ~ ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY183 ) ) )
| ~ ~ ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1318]) ).
thf(1324,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)],[1234]) ).
thf(1325,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_SY189 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK16_SY191 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK14_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK15_SY189 @ SX2 @ SX1 @ SX0 ) @ ( sK16_SY191 @ 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_SY186 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK12_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK13_SY186 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1281]) ).
thf(1326,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)],[1236]) ).
thf(1327,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)],[1276]) ).
thf(1328,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)],[1283]) ).
thf(1329,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)],[1312]) ).
thf(1330,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)],[1238]) ).
thf(1331,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)],[1288]) ).
thf(1332,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)],[1287]) ).
thf(1333,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)],[1279]) ).
thf(1334,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)],[1260]) ).
thf(1335,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)],[1278]) ).
thf(1336,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)],[1249]) ).
thf(1337,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)],[1280]) ).
thf(1338,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_SY185 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_SY185 @ 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)],[1284]) ).
thf(1339,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)],[1285]) ).
thf(1340,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)],[1277]) ).
thf(1341,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)],[1233]) ).
thf(1342,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)],[1255]) ).
thf(1343,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)],[1275]) ).
thf(1344,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)],[1282]) ).
thf(1345,plain,
! [SV245: $i] :
( ( ( ( singleton @ SV245 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1346,plain,
! [SV246: $i] :
( ( ! [SY434: $i] :
( ~ ( in @ SV246 @ SY434 )
| ( ( set_union2 @ ( singleton @ SV246 ) @ SY434 )
= SY434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1347,plain,
! [SV247: $i] :
( ( ! [SY435: $i] :
( ~ ( disjoint @ ( singleton @ SV247 ) @ SY435 )
| ~ ( in @ SV247 @ SY435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1348,plain,
! [SV248: $i] :
( ( ! [SY436: $i] :
( ( in @ SV248 @ SY436 )
| ( disjoint @ ( singleton @ SV248 ) @ SY436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1349,plain,
! [SV249: $i] :
( ( ! [SY437: $i] :
( ~ ( subset @ SV249 @ SY437 )
| ! [SY438: $i] :
( ( in @ SY438 @ SV249 )
| ( subset @ SV249 @ ( set_difference @ SY437 @ ( singleton @ SY438 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1350,plain,
! [SV250: $i] :
( ( ! [SY439: $i] :
( ~ ( in @ SV250 @ SY439 )
| ( subset @ SV250 @ ( union @ SY439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1351,plain,
! [SV251: $i] :
( ( ! [SY440: $i,SY441: $i,SY442: $i] :
( ( SV251 = SY442 )
| ( SV251 = SY441 )
| ( ( unordered_pair @ SV251 @ SY440 )
!= ( unordered_pair @ SY441 @ SY442 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1352,plain,
! [SV252: $i] :
( ( ! [SY443: $i] :
( ~ ( subset @ SV252 @ SY443 )
| ( ( set_union2 @ SV252 @ SY443 )
= SY443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1353,plain,
! [SV253: $i] :
( ( ! [SY444: $i] : ( subset @ ( set_intersection2 @ SV253 @ SY444 ) @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1354,plain,
! [SV254: $i] :
( ( ! [SY445: $i,SY446: $i] :
( ~ ( subset @ SV254 @ SY445 )
| ~ ( subset @ SV254 @ SY446 )
| ( subset @ SV254 @ ( set_intersection2 @ SY445 @ SY446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1355,plain,
! [SV255: $i] :
( ( ! [SY447: $i,SY448: $i] :
( ~ ( subset @ SV255 @ SY447 )
| ~ ( subset @ SY447 @ SY448 )
| ( subset @ SV255 @ SY448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1356,plain,
! [SV256: $i] :
( ( ! [SY449: $i] :
( ~ ( subset @ SV256 @ SY449 )
| ! [SY450: $i] : ( subset @ ( set_intersection2 @ SV256 @ SY450 ) @ ( set_intersection2 @ SY449 @ SY450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1357,plain,
! [SV257: $i] :
( ( ! [SY451: $i] :
( ~ ( subset @ SV257 @ SY451 )
| ( ( set_intersection2 @ SV257 @ SY451 )
= SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1358,plain,
! [SV258: $i] :
( ( subset @ empty_set @ SV258 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1359,plain,
! [SV259: $i] :
( ( ! [SY452: $i] :
( ~ ( subset @ SV259 @ SY452 )
| ! [SY453: $i] : ( subset @ ( set_difference @ SV259 @ SY453 ) @ ( set_difference @ SY452 @ SY453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1360,plain,
! [SV260: $i] :
( ( ! [SY454: $i] : ( subset @ ( set_difference @ SV260 @ SY454 ) @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1361,plain,
! [SV261: $i] :
( ( ! [SY455: $i] :
( ( set_union2 @ SV261 @ ( set_difference @ SY455 @ SV261 ) )
= ( set_union2 @ SV261 @ SY455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1362,plain,
! [SV262: $i] :
( ( ~ ( subset @ SV262 @ empty_set )
| ( SV262 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1363,plain,
! [SV263: $i] :
( ( ! [SY456: $i] :
( ( set_difference @ ( set_union2 @ SV263 @ SY456 ) @ SY456 )
= ( set_difference @ SV263 @ SY456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1364,plain,
! [SV264: $i] :
( ( ! [SY457: $i] :
( ~ ( subset @ SV264 @ SY457 )
| ( SY457
= ( set_union2 @ SV264 @ ( set_difference @ SY457 @ SV264 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1365,plain,
! [SV265: $i] :
( ( ! [SY458: $i] :
( ( set_difference @ SV265 @ ( set_difference @ SV265 @ SY458 ) )
= ( set_intersection2 @ SV265 @ SY458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1366,plain,
! [SV266: $i] :
( ( ! [SY459: $i] :
( ~ ( proper_subset @ SY459 @ SV266 )
| ~ ( subset @ SV266 @ SY459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1367,plain,
! [SV267: $i] :
( ( ! [SY460: $i,SY461: $i] :
( ~ ( disjoint @ SY460 @ SY461 )
| ~ ( subset @ SV267 @ SY460 )
| ( disjoint @ SV267 @ SY461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1368,plain,
! [SV268: $i] :
( ( ( unordered_pair @ SV268 @ SV268 )
= ( singleton @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1369,plain,
! [SV269: $i] :
( ( ! [SY462: $i] :
( ~ ( subset @ ( singleton @ SV269 ) @ ( singleton @ SY462 ) )
| ( SV269 = SY462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1370,plain,
! [SV270: $i] :
( ( ! [SY463: $i] : ( subset @ SV270 @ ( set_union2 @ SV270 @ SY463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1371,plain,
! [SV271: $i] :
( ( ! [SY464: $i,SY465: $i] :
( ~ ( subset @ SV271 @ SY464 )
| ~ ( subset @ SY465 @ SY464 )
| ( subset @ ( set_union2 @ SV271 @ SY465 ) @ SY464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1372,plain,
! [SV272: $i] :
( ( ! [SY466: $i] :
( ! [SY467: $i] :
( ( singleton @ SV272 )
!= ( unordered_pair @ SY466 @ SY467 ) )
| ( SV272 = SY466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1373,plain,
! [SV273: $i] :
( ( ! [SY468: $i,SY469: $i] :
( ( ( singleton @ SV273 )
!= ( unordered_pair @ SY468 @ SY469 ) )
| ( SY468 = SY469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1374,plain,
! [SV274: $i] :
( ( ! [SY470: $i] :
( ~ ( in @ SV274 @ SY470 )
| ~ ( in @ SY470 @ SV274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1375,plain,
! [SV275: $i] :
( ( ! [SY471: $i] :
( ~ ( proper_subset @ SV275 @ SY471 )
| ~ ( proper_subset @ SY471 @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1376,plain,
! [SV276: $i] :
( ( ! [SY472: $i] :
( ( unordered_pair @ SV276 @ SY472 )
= ( unordered_pair @ SY472 @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1377,plain,
! [SV277: $i] :
( ( ! [SY473: $i] :
( ( set_union2 @ SV277 @ SY473 )
= ( set_union2 @ SY473 @ SV277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1378,plain,
! [SV278: $i] :
( ( ! [SY474: $i] :
( ( set_intersection2 @ SV278 @ SY474 )
= ( set_intersection2 @ SY474 @ SV278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1379,plain,
! [SV279: $i] :
( ( ! [SY475: $i] :
( ( ordered_pair @ SV279 @ SY475 )
= ( unordered_pair @ ( unordered_pair @ SV279 @ SY475 ) @ ( singleton @ SV279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1380,plain,
! [SV280: $i] :
( ( ! [SY476: $i] :
~ ( empty @ ( ordered_pair @ SV280 @ SY476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1381,plain,
! [SV281: $i] :
( ( ( empty @ SV281 )
| ! [SY477: $i] :
~ ( empty @ ( set_union2 @ SV281 @ SY477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1382,plain,
! [SV282: $i] :
( ( ( empty @ SV282 )
| ! [SY478: $i] :
~ ( empty @ ( set_union2 @ SY478 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1383,plain,
! [SV283: $i] :
( ( ( set_union2 @ SV283 @ SV283 )
= SV283 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1384,plain,
! [SV284: $i] :
( ( ( set_intersection2 @ SV284 @ SV284 )
= SV284 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1385,plain,
! [SV285: $i] :
( ( ~ ( proper_subset @ SV285 @ SV285 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1386,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1387,plain,
! [SV286: $i] :
( ( subset @ SV286 @ SV286 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1388,plain,
! [SV287: $i] :
( ( ! [SY479: $i] :
( ~ ( disjoint @ SV287 @ SY479 )
| ( disjoint @ SY479 @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1389,plain,
! [SV288: $i] :
( ( ( set_union2 @ SV288 @ empty_set )
= SV288 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1390,plain,
! [SV289: $i] :
( ( ( set_intersection2 @ SV289 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1391,plain,
! [SV290: $i] :
( ( ( set_difference @ SV290 @ empty_set )
= SV290 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1392,plain,
! [SV291: $i] :
( ( ( set_difference @ empty_set @ SV291 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1393,plain,
! [SV292: $i] :
( ( ~ ( empty @ SV292 )
| ( SV292 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1394,plain,
! [SV293: $i] :
( ( ! [SY480: $i] :
( ~ ( empty @ SY480 )
| ~ ( in @ SV293 @ SY480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1395,plain,
! [SV294: $i] :
( ( ! [SY481: $i] :
( ( SV294 = SY481 )
| ~ ( empty @ SV294 )
| ~ ( empty @ SY481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1396,plain,
! [SV295: $i] :
( ( ~ ( ~ ! [SY482: $i,SY483: $i] :
( ~ ( in @ SV295 @ SY483 )
| ~ ( in @ SY482 @ SY483 )
| ( subset @ ( unordered_pair @ SV295 @ SY482 ) @ SY483 ) )
| ~ ~ ( ~ ! [SY484: $i,SY485: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY484 ) @ SY485 )
| ( in @ SV295 @ SY485 ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY486 ) @ SY487 )
| ( in @ SY486 @ SY487 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1397,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)],[1320]) ).
thf(1398,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)],[1321]) ).
thf(1399,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)],[1322]) ).
thf(1400,plain,
( ( ~ ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY183 ) ) )
| ~ ~ ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1323]) ).
thf(1401,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)],[1324]) ).
thf(1402,plain,
! [SV296: $i] :
( ( ~ ( ~ ! [SY488: $i,SY489: $i] :
( ~ ( ~ ( ! [SY490: $i,SY491: $i] :
( ~ ( in @ SY490 @ SV296 )
| ~ ( in @ SY491 @ SY488 )
| ( ( sK14_D @ SY489 @ SY488 @ SV296 )
!= ( ordered_pair @ SY490 @ SY491 ) ) )
| ~ ( in @ ( sK14_D @ SY489 @ SY488 @ SV296 ) @ SY489 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SY489 @ SY488 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SY489 @ SY488 @ SV296 ) @ SY488 ) )
| ( ( sK14_D @ SY489 @ SY488 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SY489 @ SY488 @ SV296 ) @ ( sK16_SY191 @ SY489 @ SY488 @ SV296 ) ) ) )
| ( in @ ( sK14_D @ SY489 @ SY488 @ SV296 ) @ SY489 ) ) )
| ( SY489
= ( cartesian_product2 @ SV296 @ SY488 ) ) )
| ~ ! [SY492: $i,SY493: $i] :
( ( SY493
!= ( cartesian_product2 @ SV296 @ SY492 ) )
| ~ ( ~ ! [SY494: $i] :
( ! [SY495: $i,SY496: $i] :
( ~ ( in @ SY495 @ SV296 )
| ~ ( in @ SY496 @ SY492 )
| ( SY494
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ SY494 @ SY493 ) )
| ~ ! [SY497: $i] :
( ~ ( in @ SY497 @ SY493 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY497 @ SY493 @ SY492 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SY497 @ SY493 @ SY492 @ SV296 ) @ SY492 ) )
| ( SY497
!= ( ordered_pair @ ( sK12_E @ SY497 @ SY493 @ SY492 @ SV296 ) @ ( sK13_SY186 @ SY497 @ SY493 @ SY492 @ SV296 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1403,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)],[1326]) ).
thf(1404,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)],[1327]) ).
thf(1405,plain,
! [SV297: $i] :
( ( ~ ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SV297 )
| ~ ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY498 )
| ~ ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY499 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY499 ) )
| ~ ( ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY498 )
| ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY499 ) ) ) )
| ( SY499
= ( set_intersection2 @ SV297 @ SY498 ) ) )
| ~ ! [SY500: $i,SY501: $i] :
( ( SY501
!= ( set_intersection2 @ SV297 @ SY500 ) )
| ~ ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV297 )
| ~ ( in @ SY502 @ SY500 )
| ( in @ SY502 @ SY501 ) )
| ~ ~ ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SY501 )
| ( in @ SY503 @ SV297 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY501 )
| ( in @ SX3 @ SY500 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1406,plain,
! [SV298: $i] :
( ( ! [SY505: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SY505 @ SV298 ) @ SV298 )
| ~ ( in @ ( sK3_C @ SY505 @ SV298 ) @ SY505 ) )
| ~ ( ( in @ ( sK3_C @ SY505 @ SV298 ) @ SV298 )
| ( in @ ( sK3_C @ SY505 @ SV298 ) @ SY505 ) ) )
| ( SV298 = SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1407,plain,
! [SV299: $i] :
( ( ! [SY506: $i] :
~ ( ~ ! [SY507: $i,SY508: $i] :
( ~ ( in @ SV299 @ SY507 )
| ~ ( in @ SY506 @ SY508 )
| ( in @ ( ordered_pair @ SV299 @ SY506 ) @ ( cartesian_product2 @ SY507 @ SY508 ) ) )
| ~ ~ ( ~ ! [SY509: $i] :
( ! [SY510: $i] :
~ ( in @ ( ordered_pair @ SV299 @ SY506 ) @ ( cartesian_product2 @ SY509 @ SY510 ) )
| ( in @ SV299 @ SY509 ) )
| ~ ! [SY511: $i,SY512: $i] :
( ~ ( in @ ( ordered_pair @ SV299 @ SY506 ) @ ( cartesian_product2 @ SY511 @ SY512 ) )
| ( in @ SY506 @ SY512 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1408,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)],[1331]) ).
thf(1409,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)],[1332]) ).
thf(1410,plain,
! [SV300: $i] :
( ( ~ ( ~ ! [SY513: $i,SY514: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY514 @ SY513 @ SV300 ) @ SY514 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
!= SV300 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY514 @ SY513 @ SV300 ) @ SY514 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
!= SY513 ) ) )
| ~ ( ( in @ ( sK18_D @ SY514 @ SY513 @ SV300 ) @ SY514 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
= SV300 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
= SY513 ) ) )
| ( SY514
= ( unordered_pair @ SV300 @ SY513 ) ) )
| ~ ! [SY515: $i,SY516: $i] :
( ( SY516
!= ( unordered_pair @ SV300 @ SY515 ) )
| ~ ( ~ ! [SY517: $i] :
( ~ ( in @ SY517 @ SY516 )
| ( SY517 = SV300 )
| ( SY517 = SY515 ) )
| ~ ~ ( ~ ! [SY518: $i] :
( ( SY518 != SV300 )
| ( in @ SY518 @ SY516 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY515 )
| ( in @ SX3 @ SY516 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1411,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)],[1334]) ).
thf(1412,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)],[1335]) ).
thf(1413,plain,
! [SV301: $i] :
( ( ! [SY520: $i] :
~ ( ~ ! [SY521: $i] :
( ! [SY522: $i] :
( ( ordered_pair @ SV301 @ SY520 )
!= ( ordered_pair @ SY521 @ SY522 ) )
| ( SV301 = SY521 ) )
| ~ ! [SY523: $i,SY524: $i] :
( ( ( ordered_pair @ SV301 @ SY520 )
!= ( ordered_pair @ SY523 @ SY524 ) )
| ( SY520 = SY524 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1414,plain,
! [SV302: $i] :
( ( ~ ( ~ ! [SY525: $i,SY526: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY526 )
| ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SV302 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY526 )
| ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY525 ) ) )
| ~ ( ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY526 )
| ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SV302 )
| ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY525 ) ) )
| ( SY526
= ( set_union2 @ SV302 @ SY525 ) ) )
| ~ ! [SY527: $i,SY528: $i] :
( ( SY528
!= ( set_union2 @ SV302 @ SY527 ) )
| ~ ( ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ SY528 )
| ( in @ SY529 @ SV302 )
| ( in @ SY529 @ SY527 ) )
| ~ ~ ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV302 )
| ( in @ SY530 @ SY528 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY527 )
| ( in @ SX3 @ SY528 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1415,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_SY185 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_SY185 @ 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)],[1338]) ).
thf(1416,plain,
! [SV303: $i] :
( ( ~ ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY532 )
| ~ ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY533 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY533 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY532 )
| ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY533 ) ) ) )
| ( SY533
= ( set_difference @ SV303 @ SY532 ) ) )
| ~ ! [SY534: $i,SY535: $i] :
( ( SY535
!= ( set_difference @ SV303 @ SY534 ) )
| ~ ( ~ ! [SY536: $i] :
( ~ ( in @ SY536 @ SV303 )
| ( in @ SY536 @ SY534 )
| ( in @ SY536 @ SY535 ) )
| ~ ~ ( ~ ! [SY537: $i] :
( ~ ( in @ SY537 @ SY535 )
| ( in @ SY537 @ SV303 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY535 )
| ~ ( in @ SX3 @ SY534 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1417,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)],[1340]) ).
thf(1418,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)],[1341]) ).
thf(1419,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)],[1342]) ).
thf(1420,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)],[1343]) ).
thf(1421,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)],[1344]) ).
thf(1422,plain,
! [SV245: $i] :
( ( ( singleton @ SV245 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1423,plain,
! [SV304: $i,SV246: $i] :
( ( ~ ( in @ SV246 @ SV304 )
| ( ( set_union2 @ ( singleton @ SV246 ) @ SV304 )
= SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1424,plain,
! [SV305: $i,SV247: $i] :
( ( ~ ( disjoint @ ( singleton @ SV247 ) @ SV305 )
| ~ ( in @ SV247 @ SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1425,plain,
! [SV306: $i,SV248: $i] :
( ( ( in @ SV248 @ SV306 )
| ( disjoint @ ( singleton @ SV248 ) @ SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1426,plain,
! [SV307: $i,SV249: $i] :
( ( ~ ( subset @ SV249 @ SV307 )
| ! [SY539: $i] :
( ( in @ SY539 @ SV249 )
| ( subset @ SV249 @ ( set_difference @ SV307 @ ( singleton @ SY539 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1427,plain,
! [SV308: $i,SV250: $i] :
( ( ~ ( in @ SV250 @ SV308 )
| ( subset @ SV250 @ ( union @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1428,plain,
! [SV309: $i,SV251: $i] :
( ( ! [SY540: $i,SY541: $i] :
( ( SV251 = SY541 )
| ( SV251 = SY540 )
| ( ( unordered_pair @ SV251 @ SV309 )
!= ( unordered_pair @ SY540 @ SY541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1429,plain,
! [SV310: $i,SV252: $i] :
( ( ~ ( subset @ SV252 @ SV310 )
| ( ( set_union2 @ SV252 @ SV310 )
= SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1430,plain,
! [SV311: $i,SV253: $i] :
( ( subset @ ( set_intersection2 @ SV253 @ SV311 ) @ SV253 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1431,plain,
! [SV312: $i,SV254: $i] :
( ( ! [SY542: $i] :
( ~ ( subset @ SV254 @ SV312 )
| ~ ( subset @ SV254 @ SY542 )
| ( subset @ SV254 @ ( set_intersection2 @ SV312 @ SY542 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1432,plain,
! [SV313: $i,SV255: $i] :
( ( ! [SY543: $i] :
( ~ ( subset @ SV255 @ SV313 )
| ~ ( subset @ SV313 @ SY543 )
| ( subset @ SV255 @ SY543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1433,plain,
! [SV314: $i,SV256: $i] :
( ( ~ ( subset @ SV256 @ SV314 )
| ! [SY544: $i] : ( subset @ ( set_intersection2 @ SV256 @ SY544 ) @ ( set_intersection2 @ SV314 @ SY544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1434,plain,
! [SV315: $i,SV257: $i] :
( ( ~ ( subset @ SV257 @ SV315 )
| ( ( set_intersection2 @ SV257 @ SV315 )
= SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1435,plain,
! [SV316: $i,SV259: $i] :
( ( ~ ( subset @ SV259 @ SV316 )
| ! [SY545: $i] : ( subset @ ( set_difference @ SV259 @ SY545 ) @ ( set_difference @ SV316 @ SY545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1436,plain,
! [SV317: $i,SV260: $i] :
( ( subset @ ( set_difference @ SV260 @ SV317 ) @ SV260 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1437,plain,
! [SV318: $i,SV261: $i] :
( ( ( set_union2 @ SV261 @ ( set_difference @ SV318 @ SV261 ) )
= ( set_union2 @ SV261 @ SV318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1438,plain,
! [SV262: $i] :
( ( ( ~ ( subset @ SV262 @ empty_set ) )
= $true )
| ( ( SV262 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1362]) ).
thf(1439,plain,
! [SV319: $i,SV263: $i] :
( ( ( set_difference @ ( set_union2 @ SV263 @ SV319 ) @ SV319 )
= ( set_difference @ SV263 @ SV319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1440,plain,
! [SV320: $i,SV264: $i] :
( ( ~ ( subset @ SV264 @ SV320 )
| ( SV320
= ( set_union2 @ SV264 @ ( set_difference @ SV320 @ SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1441,plain,
! [SV321: $i,SV265: $i] :
( ( ( set_difference @ SV265 @ ( set_difference @ SV265 @ SV321 ) )
= ( set_intersection2 @ SV265 @ SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1442,plain,
! [SV266: $i,SV322: $i] :
( ( ~ ( proper_subset @ SV322 @ SV266 )
| ~ ( subset @ SV266 @ SV322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1443,plain,
! [SV267: $i,SV323: $i] :
( ( ! [SY546: $i] :
( ~ ( disjoint @ SV323 @ SY546 )
| ~ ( subset @ SV267 @ SV323 )
| ( disjoint @ SV267 @ SY546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1444,plain,
! [SV324: $i,SV269: $i] :
( ( ~ ( subset @ ( singleton @ SV269 ) @ ( singleton @ SV324 ) )
| ( SV269 = SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1445,plain,
! [SV325: $i,SV270: $i] :
( ( subset @ SV270 @ ( set_union2 @ SV270 @ SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1446,plain,
! [SV326: $i,SV271: $i] :
( ( ! [SY547: $i] :
( ~ ( subset @ SV271 @ SV326 )
| ~ ( subset @ SY547 @ SV326 )
| ( subset @ ( set_union2 @ SV271 @ SY547 ) @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1447,plain,
! [SV327: $i,SV272: $i] :
( ( ! [SY548: $i] :
( ( singleton @ SV272 )
!= ( unordered_pair @ SV327 @ SY548 ) )
| ( SV272 = SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1448,plain,
! [SV328: $i,SV273: $i] :
( ( ! [SY549: $i] :
( ( ( singleton @ SV273 )
!= ( unordered_pair @ SV328 @ SY549 ) )
| ( SV328 = SY549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1449,plain,
! [SV329: $i,SV274: $i] :
( ( ~ ( in @ SV274 @ SV329 )
| ~ ( in @ SV329 @ SV274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1450,plain,
! [SV330: $i,SV275: $i] :
( ( ~ ( proper_subset @ SV275 @ SV330 )
| ~ ( proper_subset @ SV330 @ SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1451,plain,
! [SV331: $i,SV276: $i] :
( ( ( unordered_pair @ SV276 @ SV331 )
= ( unordered_pair @ SV331 @ SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1452,plain,
! [SV332: $i,SV277: $i] :
( ( ( set_union2 @ SV277 @ SV332 )
= ( set_union2 @ SV332 @ SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1453,plain,
! [SV333: $i,SV278: $i] :
( ( ( set_intersection2 @ SV278 @ SV333 )
= ( set_intersection2 @ SV333 @ SV278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1454,plain,
! [SV334: $i,SV279: $i] :
( ( ( ordered_pair @ SV279 @ SV334 )
= ( unordered_pair @ ( unordered_pair @ SV279 @ SV334 ) @ ( singleton @ SV279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1455,plain,
! [SV335: $i,SV280: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV280 @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1456,plain,
! [SV281: $i] :
( ( ( empty @ SV281 )
= $true )
| ( ( ! [SY477: $i] :
~ ( empty @ ( set_union2 @ SV281 @ SY477 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1457,plain,
! [SV282: $i] :
( ( ( empty @ SV282 )
= $true )
| ( ( ! [SY478: $i] :
~ ( empty @ ( set_union2 @ SY478 @ SV282 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1458,plain,
! [SV285: $i] :
( ( proper_subset @ SV285 @ SV285 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1459,plain,
! [SV336: $i,SV287: $i] :
( ( ~ ( disjoint @ SV287 @ SV336 )
| ( disjoint @ SV336 @ SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1460,plain,
! [SV292: $i] :
( ( ( ~ ( empty @ SV292 ) )
= $true )
| ( ( SV292 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1461,plain,
! [SV293: $i,SV337: $i] :
( ( ~ ( empty @ SV337 )
| ~ ( in @ SV293 @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1462,plain,
! [SV338: $i,SV294: $i] :
( ( ( SV294 = SV338 )
| ~ ( empty @ SV294 )
| ~ ( empty @ SV338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1463,plain,
! [SV295: $i] :
( ( ~ ! [SY482: $i,SY483: $i] :
( ~ ( in @ SV295 @ SY483 )
| ~ ( in @ SY482 @ SY483 )
| ( subset @ ( unordered_pair @ SV295 @ SY482 ) @ SY483 ) )
| ~ ~ ( ~ ! [SY484: $i,SY485: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY484 ) @ SY485 )
| ( in @ SV295 @ SY485 ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY486 ) @ SY487 )
| ( in @ SY486 @ SY487 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1464,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1397]) ).
thf(1465,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1397]) ).
thf(1466,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1398]) ).
thf(1467,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1398]) ).
thf(1468,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1469,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1399]) ).
thf(1470,plain,
( ( ~ ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY183 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1400]) ).
thf(1471,plain,
( ( ~ ~ ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1400]) ).
thf(1472,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1473,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1401]) ).
thf(1474,plain,
! [SV296: $i] :
( ( ~ ! [SY488: $i,SY489: $i] :
( ~ ( ~ ( ! [SY490: $i,SY491: $i] :
( ~ ( in @ SY490 @ SV296 )
| ~ ( in @ SY491 @ SY488 )
| ( ( sK14_D @ SY489 @ SY488 @ SV296 )
!= ( ordered_pair @ SY490 @ SY491 ) ) )
| ~ ( in @ ( sK14_D @ SY489 @ SY488 @ SV296 ) @ SY489 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SY489 @ SY488 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SY489 @ SY488 @ SV296 ) @ SY488 ) )
| ( ( sK14_D @ SY489 @ SY488 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SY489 @ SY488 @ SV296 ) @ ( sK16_SY191 @ SY489 @ SY488 @ SV296 ) ) ) )
| ( in @ ( sK14_D @ SY489 @ SY488 @ SV296 ) @ SY489 ) ) )
| ( SY489
= ( cartesian_product2 @ SV296 @ SY488 ) ) )
| ~ ! [SY492: $i,SY493: $i] :
( ( SY493
!= ( cartesian_product2 @ SV296 @ SY492 ) )
| ~ ( ~ ! [SY494: $i] :
( ! [SY495: $i,SY496: $i] :
( ~ ( in @ SY495 @ SV296 )
| ~ ( in @ SY496 @ SY492 )
| ( SY494
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ SY494 @ SY493 ) )
| ~ ! [SY497: $i] :
( ~ ( in @ SY497 @ SY493 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY497 @ SY493 @ SY492 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SY497 @ SY493 @ SY492 @ SV296 ) @ SY492 ) )
| ( SY497
!= ( ordered_pair @ ( sK12_E @ SY497 @ SY493 @ SY492 @ SV296 ) @ ( sK13_SY186 @ SY497 @ SY493 @ SY492 @ SV296 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1475,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1403]) ).
thf(1476,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)],[1403]) ).
thf(1477,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)],[1404]) ).
thf(1478,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)],[1404]) ).
thf(1479,plain,
! [SV297: $i] :
( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SV297 )
| ~ ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY498 )
| ~ ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY499 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY499 ) )
| ~ ( ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY498 )
| ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY499 ) ) ) )
| ( SY499
= ( set_intersection2 @ SV297 @ SY498 ) ) )
| ~ ! [SY500: $i,SY501: $i] :
( ( SY501
!= ( set_intersection2 @ SV297 @ SY500 ) )
| ~ ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV297 )
| ~ ( in @ SY502 @ SY500 )
| ( in @ SY502 @ SY501 ) )
| ~ ~ ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SY501 )
| ( in @ SY503 @ SV297 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY501 )
| ( in @ SX3 @ SY500 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1480,plain,
! [SV298: $i,SV339: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
| ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 ) )
| ~ ( ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
| ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 ) ) )
| ( SV298 = SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1481,plain,
! [SV340: $i,SV299: $i] :
( ( ~ ( ~ ! [SY550: $i,SY551: $i] :
( ~ ( in @ SV299 @ SY550 )
| ~ ( in @ SV340 @ SY551 )
| ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY550 @ SY551 ) ) )
| ~ ~ ( ~ ! [SY552: $i] :
( ! [SY553: $i] :
~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY552 @ SY553 ) )
| ( in @ SV299 @ SY552 ) )
| ~ ! [SY554: $i,SY555: $i] :
( ~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY554 @ SY555 ) )
| ( in @ SV340 @ SY555 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1482,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1408]) ).
thf(1483,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)],[1408]) ).
thf(1484,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1409]) ).
thf(1485,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1409]) ).
thf(1486,plain,
! [SV300: $i] :
( ( ~ ! [SY513: $i,SY514: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY514 @ SY513 @ SV300 ) @ SY514 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
!= SV300 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY514 @ SY513 @ SV300 ) @ SY514 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
!= SY513 ) ) )
| ~ ( ( in @ ( sK18_D @ SY514 @ SY513 @ SV300 ) @ SY514 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
= SV300 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
= SY513 ) ) )
| ( SY514
= ( unordered_pair @ SV300 @ SY513 ) ) )
| ~ ! [SY515: $i,SY516: $i] :
( ( SY516
!= ( unordered_pair @ SV300 @ SY515 ) )
| ~ ( ~ ! [SY517: $i] :
( ~ ( in @ SY517 @ SY516 )
| ( SY517 = SV300 )
| ( SY517 = SY515 ) )
| ~ ~ ( ~ ! [SY518: $i] :
( ( SY518 != SV300 )
| ( in @ SY518 @ SY516 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY515 )
| ( in @ SX3 @ SY516 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1487,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK22_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1411]) ).
thf(1488,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1411]) ).
thf(1489,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)],[1412]) ).
thf(1490,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)],[1412]) ).
thf(1491,plain,
! [SV341: $i,SV301: $i] :
( ( ~ ( ~ ! [SY556: $i] :
( ! [SY557: $i] :
( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SY556 @ SY557 ) )
| ( SV301 = SY556 ) )
| ~ ! [SY558: $i,SY559: $i] :
( ( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SY558 @ SY559 ) )
| ( SV341 = SY559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1492,plain,
! [SV302: $i] :
( ( ~ ! [SY525: $i,SY526: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY526 )
| ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SV302 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY526 )
| ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY525 ) ) )
| ~ ( ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY526 )
| ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SV302 )
| ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY525 ) ) )
| ( SY526
= ( set_union2 @ SV302 @ SY525 ) ) )
| ~ ! [SY527: $i,SY528: $i] :
( ( SY528
!= ( set_union2 @ SV302 @ SY527 ) )
| ~ ( ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ SY528 )
| ( in @ SY529 @ SV302 )
| ( in @ SY529 @ SY527 ) )
| ~ ~ ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV302 )
| ( in @ SY530 @ SY528 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY527 )
| ( in @ SX3 @ SY528 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1493,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_SY185 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_SY185 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1415]) ).
thf(1494,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)],[1415]) ).
thf(1495,plain,
! [SV303: $i] :
( ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY532 )
| ~ ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY533 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY533 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY532 )
| ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY533 ) ) ) )
| ( SY533
= ( set_difference @ SV303 @ SY532 ) ) )
| ~ ! [SY534: $i,SY535: $i] :
( ( SY535
!= ( set_difference @ SV303 @ SY534 ) )
| ~ ( ~ ! [SY536: $i] :
( ~ ( in @ SY536 @ SV303 )
| ( in @ SY536 @ SY534 )
| ( in @ SY536 @ SY535 ) )
| ~ ~ ( ~ ! [SY537: $i] :
( ~ ( in @ SY537 @ SY535 )
| ( in @ SY537 @ SV303 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY535 )
| ~ ( in @ SX3 @ SY534 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1496,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK20_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1417]) ).
thf(1497,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1417]) ).
thf(1498,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1499,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1500,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)],[1419]) ).
thf(1501,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1419]) ).
thf(1502,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1420]) ).
thf(1503,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)],[1420]) ).
thf(1504,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)],[1421]) ).
thf(1505,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1506,plain,
! [SV304: $i,SV246: $i] :
( ( ( ~ ( in @ SV246 @ SV304 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV246 ) @ SV304 )
= SV304 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1423]) ).
thf(1507,plain,
! [SV305: $i,SV247: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV247 ) @ SV305 ) )
= $true )
| ( ( ~ ( in @ SV247 @ SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1508,plain,
! [SV306: $i,SV248: $i] :
( ( ( in @ SV248 @ SV306 )
= $true )
| ( ( disjoint @ ( singleton @ SV248 ) @ SV306 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1425]) ).
thf(1509,plain,
! [SV307: $i,SV249: $i] :
( ( ( ~ ( subset @ SV249 @ SV307 ) )
= $true )
| ( ( ! [SY539: $i] :
( ( in @ SY539 @ SV249 )
| ( subset @ SV249 @ ( set_difference @ SV307 @ ( singleton @ SY539 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1510,plain,
! [SV308: $i,SV250: $i] :
( ( ( ~ ( in @ SV250 @ SV308 ) )
= $true )
| ( ( subset @ SV250 @ ( union @ SV308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1511,plain,
! [SV309: $i,SV342: $i,SV251: $i] :
( ( ! [SY560: $i] :
( ( SV251 = SY560 )
| ( SV251 = SV342 )
| ( ( unordered_pair @ SV251 @ SV309 )
!= ( unordered_pair @ SV342 @ SY560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1512,plain,
! [SV310: $i,SV252: $i] :
( ( ( ~ ( subset @ SV252 @ SV310 ) )
= $true )
| ( ( ( set_union2 @ SV252 @ SV310 )
= SV310 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1429]) ).
thf(1513,plain,
! [SV343: $i,SV312: $i,SV254: $i] :
( ( ~ ( subset @ SV254 @ SV312 )
| ~ ( subset @ SV254 @ SV343 )
| ( subset @ SV254 @ ( set_intersection2 @ SV312 @ SV343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1514,plain,
! [SV344: $i,SV313: $i,SV255: $i] :
( ( ~ ( subset @ SV255 @ SV313 )
| ~ ( subset @ SV313 @ SV344 )
| ( subset @ SV255 @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1515,plain,
! [SV314: $i,SV256: $i] :
( ( ( ~ ( subset @ SV256 @ SV314 ) )
= $true )
| ( ( ! [SY544: $i] : ( subset @ ( set_intersection2 @ SV256 @ SY544 ) @ ( set_intersection2 @ SV314 @ SY544 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1516,plain,
! [SV315: $i,SV257: $i] :
( ( ( ~ ( subset @ SV257 @ SV315 ) )
= $true )
| ( ( ( set_intersection2 @ SV257 @ SV315 )
= SV257 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1517,plain,
! [SV316: $i,SV259: $i] :
( ( ( ~ ( subset @ SV259 @ SV316 ) )
= $true )
| ( ( ! [SY545: $i] : ( subset @ ( set_difference @ SV259 @ SY545 ) @ ( set_difference @ SV316 @ SY545 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1518,plain,
! [SV262: $i] :
( ( ( subset @ SV262 @ empty_set )
= $false )
| ( ( SV262 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1519,plain,
! [SV320: $i,SV264: $i] :
( ( ( ~ ( subset @ SV264 @ SV320 ) )
= $true )
| ( ( SV320
= ( set_union2 @ SV264 @ ( set_difference @ SV320 @ SV264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1520,plain,
! [SV266: $i,SV322: $i] :
( ( ( ~ ( proper_subset @ SV322 @ SV266 ) )
= $true )
| ( ( ~ ( subset @ SV266 @ SV322 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1442]) ).
thf(1521,plain,
! [SV267: $i,SV345: $i,SV323: $i] :
( ( ~ ( disjoint @ SV323 @ SV345 )
| ~ ( subset @ SV267 @ SV323 )
| ( disjoint @ SV267 @ SV345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1522,plain,
! [SV324: $i,SV269: $i] :
( ( ( ~ ( subset @ ( singleton @ SV269 ) @ ( singleton @ SV324 ) ) )
= $true )
| ( ( SV269 = SV324 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1523,plain,
! [SV346: $i,SV326: $i,SV271: $i] :
( ( ~ ( subset @ SV271 @ SV326 )
| ~ ( subset @ SV346 @ SV326 )
| ( subset @ ( set_union2 @ SV271 @ SV346 ) @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1524,plain,
! [SV327: $i,SV272: $i] :
( ( ( ! [SY548: $i] :
( ( singleton @ SV272 )
!= ( unordered_pair @ SV327 @ SY548 ) ) )
= $true )
| ( ( SV272 = SV327 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1447]) ).
thf(1525,plain,
! [SV347: $i,SV328: $i,SV273: $i] :
( ( ( ( singleton @ SV273 )
!= ( unordered_pair @ SV328 @ SV347 ) )
| ( SV328 = SV347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1526,plain,
! [SV329: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ SV329 ) )
= $true )
| ( ( ~ ( in @ SV329 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1527,plain,
! [SV330: $i,SV275: $i] :
( ( ( ~ ( proper_subset @ SV275 @ SV330 ) )
= $true )
| ( ( ~ ( proper_subset @ SV330 @ SV275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1450]) ).
thf(1528,plain,
! [SV335: $i,SV280: $i] :
( ( empty @ ( ordered_pair @ SV280 @ SV335 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1529,plain,
! [SV348: $i,SV281: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV281 @ SV348 ) ) )
= $true )
| ( ( empty @ SV281 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1530,plain,
! [SV282: $i,SV349: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV349 @ SV282 ) ) )
= $true )
| ( ( empty @ SV282 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1531,plain,
! [SV336: $i,SV287: $i] :
( ( ( ~ ( disjoint @ SV287 @ SV336 ) )
= $true )
| ( ( disjoint @ SV336 @ SV287 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1532,plain,
! [SV292: $i] :
( ( ( empty @ SV292 )
= $false )
| ( ( SV292 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1533,plain,
! [SV293: $i,SV337: $i] :
( ( ( ~ ( empty @ SV337 ) )
= $true )
| ( ( ~ ( in @ SV293 @ SV337 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1534,plain,
! [SV338: $i,SV294: $i] :
( ( ( ( SV294 = SV338 )
| ~ ( empty @ SV294 ) )
= $true )
| ( ( ~ ( empty @ SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1535,plain,
! [SV295: $i] :
( ( ~ ! [SY482: $i,SY483: $i] :
( ~ ( in @ SV295 @ SY483 )
| ~ ( in @ SY482 @ SY483 )
| ( subset @ ( unordered_pair @ SV295 @ SY482 ) @ SY483 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1536,plain,
! [SV295: $i] :
( ( ~ ~ ( ~ ! [SY484: $i,SY485: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY484 ) @ SY485 )
| ( in @ SV295 @ SY485 ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY486 ) @ SY487 )
| ( in @ SY486 @ SY487 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1463]) ).
thf(1537,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1464]) ).
thf(1538,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1465]) ).
thf(1539,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1466]) ).
thf(1540,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1467]) ).
thf(1541,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1468]) ).
thf(1542,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1469]) ).
thf(1543,plain,
( ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY183 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1470]) ).
thf(1544,plain,
( ( ~ ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1471]) ).
thf(1545,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1472]) ).
thf(1546,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1473]) ).
thf(1547,plain,
! [SV296: $i] :
( ( ~ ! [SY488: $i,SY489: $i] :
( ~ ( ~ ( ! [SY490: $i,SY491: $i] :
( ~ ( in @ SY490 @ SV296 )
| ~ ( in @ SY491 @ SY488 )
| ( ( sK14_D @ SY489 @ SY488 @ SV296 )
!= ( ordered_pair @ SY490 @ SY491 ) ) )
| ~ ( in @ ( sK14_D @ SY489 @ SY488 @ SV296 ) @ SY489 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SY489 @ SY488 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SY489 @ SY488 @ SV296 ) @ SY488 ) )
| ( ( sK14_D @ SY489 @ SY488 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SY489 @ SY488 @ SV296 ) @ ( sK16_SY191 @ SY489 @ SY488 @ SV296 ) ) ) )
| ( in @ ( sK14_D @ SY489 @ SY488 @ SV296 ) @ SY489 ) ) )
| ( SY489
= ( cartesian_product2 @ SV296 @ SY488 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1474]) ).
thf(1548,plain,
! [SV296: $i] :
( ( ~ ! [SY492: $i,SY493: $i] :
( ( SY493
!= ( cartesian_product2 @ SV296 @ SY492 ) )
| ~ ( ~ ! [SY494: $i] :
( ! [SY495: $i,SY496: $i] :
( ~ ( in @ SY495 @ SV296 )
| ~ ( in @ SY496 @ SY492 )
| ( SY494
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ SY494 @ SY493 ) )
| ~ ! [SY497: $i] :
( ~ ( in @ SY497 @ SY493 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY497 @ SY493 @ SY492 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SY497 @ SY493 @ SY492 @ SV296 ) @ SY492 ) )
| ( SY497
!= ( ordered_pair @ ( sK12_E @ SY497 @ SY493 @ SY492 @ SV296 ) @ ( sK13_SY186 @ SY497 @ SY493 @ SY492 @ SV296 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1474]) ).
thf(1549,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1475]) ).
thf(1550,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)],[1476]) ).
thf(1551,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)],[1477]) ).
thf(1552,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)],[1478]) ).
thf(1553,plain,
! [SV297: $i] :
( ( ~ ! [SY498: $i,SY499: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SV297 )
| ~ ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY498 )
| ~ ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY499 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY499 ) )
| ~ ( ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY498 )
| ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY499 ) ) ) )
| ( SY499
= ( set_intersection2 @ SV297 @ SY498 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1479]) ).
thf(1554,plain,
! [SV297: $i] :
( ( ~ ! [SY500: $i,SY501: $i] :
( ( SY501
!= ( set_intersection2 @ SV297 @ SY500 ) )
| ~ ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV297 )
| ~ ( in @ SY502 @ SY500 )
| ( in @ SY502 @ SY501 ) )
| ~ ~ ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SY501 )
| ( in @ SY503 @ SV297 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY501 )
| ( in @ SX3 @ SY500 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1479]) ).
thf(1555,plain,
! [SV298: $i,SV339: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
| ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 ) )
| ~ ( ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
| ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 ) ) ) )
= $true )
| ( ( SV298 = SV339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1556,plain,
! [SV340: $i,SV299: $i] :
( ( ~ ! [SY550: $i,SY551: $i] :
( ~ ( in @ SV299 @ SY550 )
| ~ ( in @ SV340 @ SY551 )
| ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY550 @ SY551 ) ) )
| ~ ~ ( ~ ! [SY552: $i] :
( ! [SY553: $i] :
~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY552 @ SY553 ) )
| ( in @ SV299 @ SY552 ) )
| ~ ! [SY554: $i,SY555: $i] :
( ~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY554 @ SY555 ) )
| ( in @ SV340 @ SY555 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1557,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1482]) ).
thf(1558,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)],[1483]) ).
thf(1559,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1484]) ).
thf(1560,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1561,plain,
! [SV300: $i] :
( ( ~ ! [SY513: $i,SY514: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY514 @ SY513 @ SV300 ) @ SY514 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
!= SV300 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY514 @ SY513 @ SV300 ) @ SY514 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
!= SY513 ) ) )
| ~ ( ( in @ ( sK18_D @ SY514 @ SY513 @ SV300 ) @ SY514 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
= SV300 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
= SY513 ) ) )
| ( SY514
= ( unordered_pair @ SV300 @ SY513 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1562,plain,
! [SV300: $i] :
( ( ~ ! [SY515: $i,SY516: $i] :
( ( SY516
!= ( unordered_pair @ SV300 @ SY515 ) )
| ~ ( ~ ! [SY517: $i] :
( ~ ( in @ SY517 @ SY516 )
| ( SY517 = SV300 )
| ( SY517 = SY515 ) )
| ~ ~ ( ~ ! [SY518: $i] :
( ( SY518 != SV300 )
| ( in @ SY518 @ SY516 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY515 )
| ( in @ SX3 @ SY516 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1486]) ).
thf(1563,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK22_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1487]) ).
thf(1564,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1488]) ).
thf(1565,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)],[1489]) ).
thf(1566,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)],[1490]) ).
thf(1567,plain,
! [SV341: $i,SV301: $i] :
( ( ~ ! [SY556: $i] :
( ! [SY557: $i] :
( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SY556 @ SY557 ) )
| ( SV301 = SY556 ) )
| ~ ! [SY558: $i,SY559: $i] :
( ( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SY558 @ SY559 ) )
| ( SV341 = SY559 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1568,plain,
! [SV302: $i] :
( ( ~ ! [SY525: $i,SY526: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY526 )
| ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SV302 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY526 )
| ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY525 ) ) )
| ~ ( ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY526 )
| ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SV302 )
| ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY525 ) ) )
| ( SY526
= ( set_union2 @ SV302 @ SY525 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1569,plain,
! [SV302: $i] :
( ( ~ ! [SY527: $i,SY528: $i] :
( ( SY528
!= ( set_union2 @ SV302 @ SY527 ) )
| ~ ( ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ SY528 )
| ( in @ SY529 @ SV302 )
| ( in @ SY529 @ SY527 ) )
| ~ ~ ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV302 )
| ( in @ SY530 @ SY528 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY527 )
| ( in @ SX3 @ SY528 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1492]) ).
thf(1570,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_SY185 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK9_SY185 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1493]) ).
thf(1571,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)],[1494]) ).
thf(1572,plain,
! [SV303: $i] :
( ( ~ ! [SY532: $i,SY533: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY532 )
| ~ ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY533 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY533 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY532 )
| ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY533 ) ) ) )
| ( SY533
= ( set_difference @ SV303 @ SY532 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1573,plain,
! [SV303: $i] :
( ( ~ ! [SY534: $i,SY535: $i] :
( ( SY535
!= ( set_difference @ SV303 @ SY534 ) )
| ~ ( ~ ! [SY536: $i] :
( ~ ( in @ SY536 @ SV303 )
| ( in @ SY536 @ SY534 )
| ( in @ SY536 @ SY535 ) )
| ~ ~ ( ~ ! [SY537: $i] :
( ~ ( in @ SY537 @ SY535 )
| ( in @ SY537 @ SV303 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY535 )
| ~ ( in @ SX3 @ SY534 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1495]) ).
thf(1574,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK20_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1496]) ).
thf(1575,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1497]) ).
thf(1576,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1577,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1499]) ).
thf(1578,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)],[1500]) ).
thf(1579,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1501]) ).
thf(1580,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1502]) ).
thf(1581,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)],[1503]) ).
thf(1582,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)],[1504]) ).
thf(1583,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1505]) ).
thf(1584,plain,
! [SV304: $i,SV246: $i] :
( ( ( in @ SV246 @ SV304 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV246 ) @ SV304 )
= SV304 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1585,plain,
! [SV305: $i,SV247: $i] :
( ( ( disjoint @ ( singleton @ SV247 ) @ SV305 )
= $false )
| ( ( ~ ( in @ SV247 @ SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1586,plain,
! [SV307: $i,SV249: $i] :
( ( ( subset @ SV249 @ SV307 )
= $false )
| ( ( ! [SY539: $i] :
( ( in @ SY539 @ SV249 )
| ( subset @ SV249 @ ( set_difference @ SV307 @ ( singleton @ SY539 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1587,plain,
! [SV308: $i,SV250: $i] :
( ( ( in @ SV250 @ SV308 )
= $false )
| ( ( subset @ SV250 @ ( union @ SV308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1588,plain,
! [SV309: $i,SV342: $i,SV350: $i,SV251: $i] :
( ( ( SV251 = SV350 )
| ( SV251 = SV342 )
| ( ( unordered_pair @ SV251 @ SV309 )
!= ( unordered_pair @ SV342 @ SV350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1589,plain,
! [SV310: $i,SV252: $i] :
( ( ( subset @ SV252 @ SV310 )
= $false )
| ( ( ( set_union2 @ SV252 @ SV310 )
= SV310 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1590,plain,
! [SV343: $i,SV312: $i,SV254: $i] :
( ( ( ~ ( subset @ SV254 @ SV312 )
| ~ ( subset @ SV254 @ SV343 ) )
= $true )
| ( ( subset @ SV254 @ ( set_intersection2 @ SV312 @ SV343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1591,plain,
! [SV344: $i,SV313: $i,SV255: $i] :
( ( ( ~ ( subset @ SV255 @ SV313 )
| ~ ( subset @ SV313 @ SV344 ) )
= $true )
| ( ( subset @ SV255 @ SV344 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1514]) ).
thf(1592,plain,
! [SV314: $i,SV256: $i] :
( ( ( subset @ SV256 @ SV314 )
= $false )
| ( ( ! [SY544: $i] : ( subset @ ( set_intersection2 @ SV256 @ SY544 ) @ ( set_intersection2 @ SV314 @ SY544 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1593,plain,
! [SV315: $i,SV257: $i] :
( ( ( subset @ SV257 @ SV315 )
= $false )
| ( ( ( set_intersection2 @ SV257 @ SV315 )
= SV257 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1594,plain,
! [SV316: $i,SV259: $i] :
( ( ( subset @ SV259 @ SV316 )
= $false )
| ( ( ! [SY545: $i] : ( subset @ ( set_difference @ SV259 @ SY545 ) @ ( set_difference @ SV316 @ SY545 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1595,plain,
! [SV320: $i,SV264: $i] :
( ( ( subset @ SV264 @ SV320 )
= $false )
| ( ( SV320
= ( set_union2 @ SV264 @ ( set_difference @ SV320 @ SV264 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1596,plain,
! [SV266: $i,SV322: $i] :
( ( ( proper_subset @ SV322 @ SV266 )
= $false )
| ( ( ~ ( subset @ SV266 @ SV322 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1597,plain,
! [SV267: $i,SV345: $i,SV323: $i] :
( ( ( ~ ( disjoint @ SV323 @ SV345 )
| ~ ( subset @ SV267 @ SV323 ) )
= $true )
| ( ( disjoint @ SV267 @ SV345 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1521]) ).
thf(1598,plain,
! [SV324: $i,SV269: $i] :
( ( ( subset @ ( singleton @ SV269 ) @ ( singleton @ SV324 ) )
= $false )
| ( ( SV269 = SV324 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1599,plain,
! [SV346: $i,SV326: $i,SV271: $i] :
( ( ( ~ ( subset @ SV271 @ SV326 )
| ~ ( subset @ SV346 @ SV326 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV271 @ SV346 ) @ SV326 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1523]) ).
thf(1600,plain,
! [SV351: $i,SV327: $i,SV272: $i] :
( ( ( ( ( singleton @ SV272 )
!= ( unordered_pair @ SV327 @ SV351 ) ) )
= $true )
| ( ( SV272 = SV327 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1601,plain,
! [SV347: $i,SV328: $i,SV273: $i] :
( ( ( ( ( singleton @ SV273 )
!= ( unordered_pair @ SV328 @ SV347 ) ) )
= $true )
| ( ( SV328 = SV347 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1602,plain,
! [SV329: $i,SV274: $i] :
( ( ( in @ SV274 @ SV329 )
= $false )
| ( ( ~ ( in @ SV329 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1603,plain,
! [SV330: $i,SV275: $i] :
( ( ( proper_subset @ SV275 @ SV330 )
= $false )
| ( ( ~ ( proper_subset @ SV330 @ SV275 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1604,plain,
! [SV348: $i,SV281: $i] :
( ( ( empty @ ( set_union2 @ SV281 @ SV348 ) )
= $false )
| ( ( empty @ SV281 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1529]) ).
thf(1605,plain,
! [SV282: $i,SV349: $i] :
( ( ( empty @ ( set_union2 @ SV349 @ SV282 ) )
= $false )
| ( ( empty @ SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1530]) ).
thf(1606,plain,
! [SV336: $i,SV287: $i] :
( ( ( disjoint @ SV287 @ SV336 )
= $false )
| ( ( disjoint @ SV336 @ SV287 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1607,plain,
! [SV293: $i,SV337: $i] :
( ( ( empty @ SV337 )
= $false )
| ( ( ~ ( in @ SV293 @ SV337 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1608,plain,
! [SV338: $i,SV294: $i] :
( ( ( SV294 = SV338 )
= $true )
| ( ( ~ ( empty @ SV294 ) )
= $true )
| ( ( ~ ( empty @ SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1534]) ).
thf(1609,plain,
! [SV295: $i] :
( ( ! [SY482: $i,SY483: $i] :
( ~ ( in @ SV295 @ SY483 )
| ~ ( in @ SY482 @ SY483 )
| ( subset @ ( unordered_pair @ SV295 @ SY482 ) @ SY483 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1535]) ).
thf(1610,plain,
! [SV295: $i] :
( ( ~ ( ~ ! [SY484: $i,SY485: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY484 ) @ SY485 )
| ( in @ SV295 @ SY485 ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY486 ) @ SY487 )
| ( in @ SY486 @ SY487 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1536]) ).
thf(1611,plain,
! [SV352: $i] :
( ( ! [SY561: $i] :
( ( ( set_difference @ SV352 @ SY561 )
!= empty_set )
| ( subset @ SV352 @ SY561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1612,plain,
! [SV353: $i] :
( ( ! [SY562: $i] :
( ~ ( subset @ SV353 @ SY562 )
| ( ( set_difference @ SV353 @ SY562 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(1613,plain,
! [SV354: $i] :
( ( ! [SY563: $i] :
( ( ( set_difference @ SV354 @ SY563 )
!= SV354 )
| ( disjoint @ SV354 @ SY563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1614,plain,
! [SV355: $i] :
( ( ! [SY564: $i] :
( ~ ( disjoint @ SV355 @ SY564 )
| ( ( set_difference @ SV355 @ SY564 )
= SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1615,plain,
! [SV356: $i] :
( ( ! [SY565: $i] :
( ~ ( in @ SV356 @ SY565 )
| ( subset @ ( singleton @ SV356 ) @ SY565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1616,plain,
! [SV357: $i] :
( ( ! [SY566: $i] :
( ~ ( subset @ ( singleton @ SV357 ) @ SY566 )
| ( in @ SV357 @ SY566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1617,plain,
( ( ( sK1_A = empty_set )
= $true )
| ( ( sK1_A
= ( singleton @ sK2_SY183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1618,plain,
( ( subset @ sK1_A @ ( singleton @ sK2_SY183 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1544]) ).
thf(1619,plain,
! [SV358: $i] :
( ( ! [SY567: $i] :
( ( ( set_difference @ SV358 @ SY567 )
!= empty_set )
| ( subset @ SV358 @ SY567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1620,plain,
! [SV359: $i] :
( ( ! [SY568: $i] :
( ~ ( subset @ SV359 @ SY568 )
| ( ( set_difference @ SV359 @ SY568 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1621,plain,
! [SV296: $i] :
( ( ! [SY488: $i,SY489: $i] :
( ~ ( ~ ( ! [SY490: $i,SY491: $i] :
( ~ ( in @ SY490 @ SV296 )
| ~ ( in @ SY491 @ SY488 )
| ( ( sK14_D @ SY489 @ SY488 @ SV296 )
!= ( ordered_pair @ SY490 @ SY491 ) ) )
| ~ ( in @ ( sK14_D @ SY489 @ SY488 @ SV296 ) @ SY489 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SY489 @ SY488 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SY489 @ SY488 @ SV296 ) @ SY488 ) )
| ( ( sK14_D @ SY489 @ SY488 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SY489 @ SY488 @ SV296 ) @ ( sK16_SY191 @ SY489 @ SY488 @ SV296 ) ) ) )
| ( in @ ( sK14_D @ SY489 @ SY488 @ SV296 ) @ SY489 ) ) )
| ( SY489
= ( cartesian_product2 @ SV296 @ SY488 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1547]) ).
thf(1622,plain,
! [SV296: $i] :
( ( ! [SY492: $i,SY493: $i] :
( ( SY493
!= ( cartesian_product2 @ SV296 @ SY492 ) )
| ~ ( ~ ! [SY494: $i] :
( ! [SY495: $i,SY496: $i] :
( ~ ( in @ SY495 @ SV296 )
| ~ ( in @ SY496 @ SY492 )
| ( SY494
!= ( ordered_pair @ SY495 @ SY496 ) ) )
| ( in @ SY494 @ SY493 ) )
| ~ ! [SY497: $i] :
( ~ ( in @ SY497 @ SY493 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY497 @ SY493 @ SY492 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SY497 @ SY493 @ SY492 @ SV296 ) @ SY492 ) )
| ( SY497
!= ( ordered_pair @ ( sK12_E @ SY497 @ SY493 @ SY492 @ SV296 ) @ ( sK13_SY186 @ SY497 @ SY493 @ SY492 @ SV296 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1548]) ).
thf(1623,plain,
! [SV360: $i] :
( ( ! [SY569: $i] :
( ~ ( subset @ SV360 @ ( singleton @ SY569 ) )
| ( SV360 = empty_set )
| ( SV360
= ( singleton @ SY569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1624,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)],[1550]) ).
thf(1625,plain,
! [SV361: $i] :
( ( ! [SY570: $i] :
( ~ ( ~ ( ( ( sK21_C @ SY570 @ SV361 )
!= SV361 )
| ~ ( in @ ( sK21_C @ SY570 @ SV361 ) @ SY570 ) )
| ~ ( ( ( sK21_C @ SY570 @ SV361 )
= SV361 )
| ( in @ ( sK21_C @ SY570 @ SV361 ) @ SY570 ) ) )
| ( SY570
= ( singleton @ SV361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1626,plain,
! [SV362: $i] :
( ( ! [SY571: $i] :
( ( SY571
!= ( singleton @ SV362 ) )
| ~ ( ~ ! [SY572: $i] :
( ( SY572 != SV362 )
| ( in @ SY572 @ SY571 ) )
| ~ ! [SY573: $i] :
( ~ ( in @ SY573 @ SY571 )
| ( SY573 = SV362 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1627,plain,
! [SV297: $i] :
( ( ! [SY498: $i,SY499: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SV297 )
| ~ ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY498 )
| ~ ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY499 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY499 ) )
| ~ ( ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY498 )
| ( in @ ( sK10_D @ SY499 @ SY498 @ SV297 ) @ SY499 ) ) ) )
| ( SY499
= ( set_intersection2 @ SV297 @ SY498 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1553]) ).
thf(1628,plain,
! [SV297: $i] :
( ( ! [SY500: $i,SY501: $i] :
( ( SY501
!= ( set_intersection2 @ SV297 @ SY500 ) )
| ~ ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV297 )
| ~ ( in @ SY502 @ SY500 )
| ( in @ SY502 @ SY501 ) )
| ~ ~ ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SY501 )
| ( in @ SY503 @ SV297 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY501 )
| ( in @ SX3 @ SY500 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1554]) ).
thf(1629,plain,
! [SV298: $i,SV339: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
| ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 ) )
| ~ ( ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
| ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 ) ) )
= $false )
| ( ( SV298 = SV339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1630,plain,
! [SV340: $i,SV299: $i] :
( ( ~ ! [SY550: $i,SY551: $i] :
( ~ ( in @ SV299 @ SY550 )
| ~ ( in @ SV340 @ SY551 )
| ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY550 @ SY551 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1631,plain,
! [SV340: $i,SV299: $i] :
( ( ~ ~ ( ~ ! [SY552: $i] :
( ! [SY553: $i] :
~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY552 @ SY553 ) )
| ( in @ SV299 @ SY552 ) )
| ~ ! [SY554: $i,SY555: $i] :
( ~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY554 @ SY555 ) )
| ( in @ SV340 @ SY555 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1556]) ).
thf(1632,plain,
! [SV363: $i] :
( ( ! [SY574: $i] :
( ( SV363 = SY574 )
| ~ ( subset @ SV363 @ SY574 )
| ( proper_subset @ SV363 @ SY574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1633,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)],[1558]) ).
thf(1634,plain,
! [SV364: $i] :
( ( ! [SY575: $i] :
( ( ( set_intersection2 @ SV364 @ SY575 )
!= empty_set )
| ( disjoint @ SV364 @ SY575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1635,plain,
! [SV365: $i] :
( ( ! [SY576: $i] :
( ~ ( disjoint @ SV365 @ SY576 )
| ( ( set_intersection2 @ SV365 @ SY576 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1636,plain,
! [SV300: $i] :
( ( ! [SY513: $i,SY514: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY514 @ SY513 @ SV300 ) @ SY514 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
!= SV300 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY514 @ SY513 @ SV300 ) @ SY514 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
!= SY513 ) ) )
| ~ ( ( in @ ( sK18_D @ SY514 @ SY513 @ SV300 ) @ SY514 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
= SV300 )
| ( ( sK18_D @ SY514 @ SY513 @ SV300 )
= SY513 ) ) )
| ( SY514
= ( unordered_pair @ SV300 @ SY513 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1637,plain,
! [SV300: $i] :
( ( ! [SY515: $i,SY516: $i] :
( ( SY516
!= ( unordered_pair @ SV300 @ SY515 ) )
| ~ ( ~ ! [SY517: $i] :
( ~ ( in @ SY517 @ SY516 )
| ( SY517 = SV300 )
| ( SY517 = SY515 ) )
| ~ ~ ( ~ ! [SY518: $i] :
( ( SY518 != SV300 )
| ( in @ SY518 @ SY516 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY515 )
| ( in @ SX3 @ SY516 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1562]) ).
thf(1638,plain,
! [SV366: $i] :
( ( ! [SY577: $i] :
( ( disjoint @ SV366 @ SY577 )
| ( in @ ( sK22_C @ SY577 @ SV366 ) @ ( set_intersection2 @ SV366 @ SY577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1639,plain,
! [SV367: $i] :
( ( ! [SY578: $i] :
( ! [SY579: $i] :
~ ( in @ SY579 @ ( set_intersection2 @ SV367 @ SY578 ) )
| ~ ( disjoint @ SV367 @ SY578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1640,plain,
! [SV368: $i] :
( ( ! [SY580: $i] :
( ~ ( ~ ( ~ ( in @ ( sK19_C @ SY580 @ SV368 ) @ SY580 )
| ~ ( subset @ ( sK19_C @ SY580 @ SV368 ) @ SV368 ) )
| ~ ( ( in @ ( sK19_C @ SY580 @ SV368 ) @ SY580 )
| ( subset @ ( sK19_C @ SY580 @ SV368 ) @ SV368 ) ) )
| ( SY580
= ( powerset @ SV368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1641,plain,
! [SV369: $i] :
( ( ! [SY581: $i] :
( ( SY581
!= ( powerset @ SV369 ) )
| ~ ( ~ ! [SY582: $i] :
( ~ ( in @ SY582 @ SY581 )
| ( subset @ SY582 @ SV369 ) )
| ~ ! [SY583: $i] :
( ~ ( subset @ SY583 @ SV369 )
| ( in @ SY583 @ SY581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1642,plain,
! [SV341: $i,SV301: $i] :
( ( ~ ! [SY556: $i] :
( ! [SY557: $i] :
( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SY556 @ SY557 ) )
| ( SV301 = SY556 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1643,plain,
! [SV341: $i,SV301: $i] :
( ( ~ ! [SY558: $i,SY559: $i] :
( ( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SY558 @ SY559 ) )
| ( SV341 = SY559 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1567]) ).
thf(1644,plain,
! [SV302: $i] :
( ( ! [SY525: $i,SY526: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY526 )
| ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SV302 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY526 )
| ~ ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY525 ) ) )
| ~ ( ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY526 )
| ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SV302 )
| ( in @ ( sK17_D @ SY526 @ SY525 @ SV302 ) @ SY525 ) ) )
| ( SY526
= ( set_union2 @ SV302 @ SY525 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1568]) ).
thf(1645,plain,
! [SV302: $i] :
( ( ! [SY527: $i,SY528: $i] :
( ( SY528
!= ( set_union2 @ SV302 @ SY527 ) )
| ~ ( ~ ! [SY529: $i] :
( ~ ( in @ SY529 @ SY528 )
| ( in @ SY529 @ SV302 )
| ( in @ SY529 @ SY527 ) )
| ~ ~ ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV302 )
| ( in @ SY530 @ SY528 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY527 )
| ( in @ SX3 @ SY528 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1569]) ).
thf(1646,plain,
! [SV370: $i] :
( ( ! [SY584: $i] :
( ~ ( ~ ( ! [SY585: $i] :
( ~ ( in @ ( sK8_C @ SY584 @ SV370 ) @ SY585 )
| ~ ( in @ SY585 @ SV370 ) )
| ~ ( in @ ( sK8_C @ SY584 @ SV370 ) @ SY584 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SY584 @ SV370 ) @ ( sK9_SY185 @ SY584 @ SV370 ) )
| ~ ( in @ ( sK9_SY185 @ SY584 @ SV370 ) @ SV370 ) )
| ( in @ ( sK8_C @ SY584 @ SV370 ) @ SY584 ) ) )
| ( SY584
= ( union @ SV370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(1647,plain,
! [SV371: $i] :
( ( ! [SY586: $i] :
( ( SY586
!= ( union @ SV371 ) )
| ~ ( ~ ! [SY587: $i] :
( ! [SY588: $i] :
( ~ ( in @ SY587 @ SY588 )
| ~ ( in @ SY588 @ SV371 ) )
| ( in @ SY587 @ SY586 ) )
| ~ ! [SY589: $i] :
( ~ ( in @ SY589 @ SY586 )
| ~ ( ~ ( in @ SY589 @ ( sK7_D @ SY589 @ SY586 @ SV371 ) )
| ~ ( in @ ( sK7_D @ SY589 @ SY586 @ SV371 ) @ SV371 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(1648,plain,
! [SV303: $i] :
( ( ! [SY532: $i,SY533: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY532 )
| ~ ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY533 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY533 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY532 )
| ( in @ ( sK6_D @ SY533 @ SY532 @ SV303 ) @ SY533 ) ) ) )
| ( SY533
= ( set_difference @ SV303 @ SY532 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1572]) ).
thf(1649,plain,
! [SV303: $i] :
( ( ! [SY534: $i,SY535: $i] :
( ( SY535
!= ( set_difference @ SV303 @ SY534 ) )
| ~ ( ~ ! [SY536: $i] :
( ~ ( in @ SY536 @ SV303 )
| ( in @ SY536 @ SY534 )
| ( in @ SY536 @ SY535 ) )
| ~ ~ ( ~ ! [SY537: $i] :
( ~ ( in @ SY537 @ SY535 )
| ( in @ SY537 @ SV303 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY535 )
| ~ ( in @ SX3 @ SY534 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1650,plain,
! [SV372: $i] :
( ( ( in @ ( sK20_B @ SV372 ) @ SV372 )
| ( SV372 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(1651,plain,
! [SV373: $i] :
( ( ( SV373 != empty_set )
| ! [SY590: $i] :
~ ( in @ SY590 @ SV373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1652,plain,
! [SV374: $i] :
( ( ! [SY591: $i] :
( ~ ( in @ SV374 @ SY591 )
| ( subset @ ( singleton @ SV374 ) @ SY591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(1653,plain,
! [SV375: $i] :
( ( ! [SY592: $i] :
( ~ ( subset @ ( singleton @ SV375 ) @ SY592 )
| ( in @ SV375 @ SY592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1654,plain,
! [SV376: $i] :
( ( ! [SY593: $i] :
( ( disjoint @ SV376 @ SY593 )
| ~ ( ~ ( in @ ( sK23_C @ SY593 @ SV376 ) @ SV376 )
| ~ ( in @ ( sK23_C @ SY593 @ SV376 ) @ SY593 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1655,plain,
! [SV377: $i] :
( ( ! [SY594: $i] :
( ! [SY595: $i] :
( ~ ( in @ SY595 @ SV377 )
| ~ ( in @ SY595 @ SY594 ) )
| ~ ( disjoint @ SV377 @ SY594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1656,plain,
! [SV378: $i] :
( ( ! [SY596: $i] :
( ~ ( subset @ SV378 @ SY596 )
| ~ ( subset @ SY596 @ SV378 )
| ( SV378 = SY596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1657,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)],[1581]) ).
thf(1658,plain,
! [SV379: $i] :
( ( ! [SY597: $i] :
( ~ ( ~ ( in @ ( sK11_C @ SY597 @ SV379 ) @ SV379 )
| ~ ~ ( in @ ( sK11_C @ SY597 @ SV379 ) @ SY597 ) )
| ( subset @ SV379 @ SY597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(1659,plain,
! [SV380: $i] :
( ( ! [SY598: $i] :
( ~ ( subset @ SV380 @ SY598 )
| ! [SY599: $i] :
( ~ ( in @ SY599 @ SV380 )
| ( in @ SY599 @ SY598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1660,plain,
! [SV305: $i,SV247: $i] :
( ( ( in @ SV247 @ SV305 )
= $false )
| ( ( disjoint @ ( singleton @ SV247 ) @ SV305 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1585]) ).
thf(1661,plain,
! [SV307: $i,SV249: $i,SV381: $i] :
( ( ( ( in @ SV381 @ SV249 )
| ( subset @ SV249 @ ( set_difference @ SV307 @ ( singleton @ SV381 ) ) ) )
= $true )
| ( ( subset @ SV249 @ SV307 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(1662,plain,
! [SV309: $i,SV342: $i,SV350: $i,SV251: $i] :
( ( ( SV251 = SV350 )
= $true )
| ( ( ( SV251 = SV342 )
| ( ( unordered_pair @ SV251 @ SV309 )
!= ( unordered_pair @ SV342 @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1588]) ).
thf(1663,plain,
! [SV343: $i,SV312: $i,SV254: $i] :
( ( ( ~ ( subset @ SV254 @ SV312 ) )
= $true )
| ( ( ~ ( subset @ SV254 @ SV343 ) )
= $true )
| ( ( subset @ SV254 @ ( set_intersection2 @ SV312 @ SV343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1664,plain,
! [SV344: $i,SV313: $i,SV255: $i] :
( ( ( ~ ( subset @ SV255 @ SV313 ) )
= $true )
| ( ( ~ ( subset @ SV313 @ SV344 ) )
= $true )
| ( ( subset @ SV255 @ SV344 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1591]) ).
thf(1665,plain,
! [SV314: $i,SV382: $i,SV256: $i] :
( ( ( subset @ ( set_intersection2 @ SV256 @ SV382 ) @ ( set_intersection2 @ SV314 @ SV382 ) )
= $true )
| ( ( subset @ SV256 @ SV314 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(1666,plain,
! [SV316: $i,SV383: $i,SV259: $i] :
( ( ( subset @ ( set_difference @ SV259 @ SV383 ) @ ( set_difference @ SV316 @ SV383 ) )
= $true )
| ( ( subset @ SV259 @ SV316 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1667,plain,
! [SV322: $i,SV266: $i] :
( ( ( subset @ SV266 @ SV322 )
= $false )
| ( ( proper_subset @ SV322 @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1668,plain,
! [SV267: $i,SV345: $i,SV323: $i] :
( ( ( ~ ( disjoint @ SV323 @ SV345 ) )
= $true )
| ( ( ~ ( subset @ SV267 @ SV323 ) )
= $true )
| ( ( disjoint @ SV267 @ SV345 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1669,plain,
! [SV346: $i,SV326: $i,SV271: $i] :
( ( ( ~ ( subset @ SV271 @ SV326 ) )
= $true )
| ( ( ~ ( subset @ SV346 @ SV326 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV271 @ SV346 ) @ SV326 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1670,plain,
! [SV351: $i,SV327: $i,SV272: $i] :
( ( ( ( singleton @ SV272 )
= ( unordered_pair @ SV327 @ SV351 ) )
= $false )
| ( ( SV272 = SV327 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1671,plain,
! [SV347: $i,SV328: $i,SV273: $i] :
( ( ( ( singleton @ SV273 )
= ( unordered_pair @ SV328 @ SV347 ) )
= $false )
| ( ( SV328 = SV347 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1672,plain,
! [SV274: $i,SV329: $i] :
( ( ( in @ SV329 @ SV274 )
= $false )
| ( ( in @ SV274 @ SV329 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1673,plain,
! [SV275: $i,SV330: $i] :
( ( ( proper_subset @ SV330 @ SV275 )
= $false )
| ( ( proper_subset @ SV275 @ SV330 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1674,plain,
! [SV337: $i,SV293: $i] :
( ( ( in @ SV293 @ SV337 )
= $false )
| ( ( empty @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1675,plain,
! [SV338: $i,SV294: $i] :
( ( ( empty @ SV294 )
= $false )
| ( ( SV294 = SV338 )
= $true )
| ( ( ~ ( empty @ SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1676,plain,
! [SV384: $i,SV295: $i] :
( ( ! [SY600: $i] :
( ~ ( in @ SV295 @ SY600 )
| ~ ( in @ SV384 @ SY600 )
| ( subset @ ( unordered_pair @ SV295 @ SV384 ) @ SY600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(1677,plain,
! [SV295: $i] :
( ( ~ ! [SY484: $i,SY485: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY484 ) @ SY485 )
| ( in @ SV295 @ SY485 ) )
| ~ ! [SY486: $i,SY487: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY486 ) @ SY487 )
| ( in @ SY486 @ SY487 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1678,plain,
! [SV385: $i,SV352: $i] :
( ( ( ( set_difference @ SV352 @ SV385 )
!= empty_set )
| ( subset @ SV352 @ SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1679,plain,
! [SV386: $i,SV353: $i] :
( ( ~ ( subset @ SV353 @ SV386 )
| ( ( set_difference @ SV353 @ SV386 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1680,plain,
! [SV387: $i,SV354: $i] :
( ( ( ( set_difference @ SV354 @ SV387 )
!= SV354 )
| ( disjoint @ SV354 @ SV387 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(1681,plain,
! [SV388: $i,SV355: $i] :
( ( ~ ( disjoint @ SV355 @ SV388 )
| ( ( set_difference @ SV355 @ SV388 )
= SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(1682,plain,
! [SV389: $i,SV356: $i] :
( ( ~ ( in @ SV356 @ SV389 )
| ( subset @ ( singleton @ SV356 ) @ SV389 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(1683,plain,
! [SV390: $i,SV357: $i] :
( ( ~ ( subset @ ( singleton @ SV357 ) @ SV390 )
| ( in @ SV357 @ SV390 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1684,plain,
! [SV391: $i,SV358: $i] :
( ( ( ( set_difference @ SV358 @ SV391 )
!= empty_set )
| ( subset @ SV358 @ SV391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(1685,plain,
! [SV392: $i,SV359: $i] :
( ( ~ ( subset @ SV359 @ SV392 )
| ( ( set_difference @ SV359 @ SV392 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(1686,plain,
! [SV393: $i,SV296: $i] :
( ( ! [SY601: $i] :
( ~ ( ~ ( ! [SY602: $i,SY603: $i] :
( ~ ( in @ SY602 @ SV296 )
| ~ ( in @ SY603 @ SV393 )
| ( ( sK14_D @ SY601 @ SV393 @ SV296 )
!= ( ordered_pair @ SY602 @ SY603 ) ) )
| ~ ( in @ ( sK14_D @ SY601 @ SV393 @ SV296 ) @ SY601 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SY601 @ SV393 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SY601 @ SV393 @ SV296 ) @ SV393 ) )
| ( ( sK14_D @ SY601 @ SV393 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SY601 @ SV393 @ SV296 ) @ ( sK16_SY191 @ SY601 @ SV393 @ SV296 ) ) ) )
| ( in @ ( sK14_D @ SY601 @ SV393 @ SV296 ) @ SY601 ) ) )
| ( SY601
= ( cartesian_product2 @ SV296 @ SV393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1687,plain,
! [SV394: $i,SV296: $i] :
( ( ! [SY604: $i] :
( ( SY604
!= ( cartesian_product2 @ SV296 @ SV394 ) )
| ~ ( ~ ! [SY605: $i] :
( ! [SY606: $i,SY607: $i] :
( ~ ( in @ SY606 @ SV296 )
| ~ ( in @ SY607 @ SV394 )
| ( SY605
!= ( ordered_pair @ SY606 @ SY607 ) ) )
| ( in @ SY605 @ SY604 ) )
| ~ ! [SY608: $i] :
( ~ ( in @ SY608 @ SY604 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY608 @ SY604 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SY608 @ SY604 @ SV394 @ SV296 ) @ SV394 ) )
| ( SY608
!= ( ordered_pair @ ( sK12_E @ SY608 @ SY604 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SY608 @ SY604 @ SV394 @ SV296 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1688,plain,
! [SV395: $i,SV360: $i] :
( ( ~ ( subset @ SV360 @ ( singleton @ SV395 ) )
| ( SV360 = empty_set )
| ( SV360
= ( singleton @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1689,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1624]) ).
thf(1690,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1624]) ).
thf(1691,plain,
! [SV361: $i,SV396: $i] :
( ( ~ ( ~ ( ( ( sK21_C @ SV396 @ SV361 )
!= SV361 )
| ~ ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 ) )
| ~ ( ( ( sK21_C @ SV396 @ SV361 )
= SV361 )
| ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 ) ) )
| ( SV396
= ( singleton @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1692,plain,
! [SV362: $i,SV397: $i] :
( ( ( SV397
!= ( singleton @ SV362 ) )
| ~ ( ~ ! [SY609: $i] :
( ( SY609 != SV362 )
| ( in @ SY609 @ SV397 ) )
| ~ ! [SY610: $i] :
( ~ ( in @ SY610 @ SV397 )
| ( SY610 = SV362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1693,plain,
! [SV297: $i,SV398: $i] :
( ( ! [SY611: $i] :
( ~ ( ~ ( ~ ( in @ ( sK10_D @ SY611 @ SV398 @ SV297 ) @ SV297 )
| ~ ( in @ ( sK10_D @ SY611 @ SV398 @ SV297 ) @ SV398 )
| ~ ( in @ ( sK10_D @ SY611 @ SV398 @ SV297 ) @ SY611 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SY611 @ SV398 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SY611 @ SV398 @ SV297 ) @ SY611 ) )
| ~ ( ( in @ ( sK10_D @ SY611 @ SV398 @ SV297 ) @ SV398 )
| ( in @ ( sK10_D @ SY611 @ SV398 @ SV297 ) @ SY611 ) ) ) )
| ( SY611
= ( set_intersection2 @ SV297 @ SV398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(1694,plain,
! [SV399: $i,SV297: $i] :
( ( ! [SY612: $i] :
( ( SY612
!= ( set_intersection2 @ SV297 @ SV399 ) )
| ~ ( ~ ! [SY613: $i] :
( ~ ( in @ SY613 @ SV297 )
| ~ ( in @ SY613 @ SV399 )
| ( in @ SY613 @ SY612 ) )
| ~ ~ ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SY612 )
| ( in @ SY503 @ SV297 ) )
| ~ ! [SY615: $i] :
( ~ ( in @ SY615 @ SY612 )
| ( in @ SY615 @ SV399 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(1695,plain,
! [SV298: $i,SV339: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
| ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 ) ) )
= $false )
| ( ( SV298 = SV339 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1696,plain,
! [SV298: $i,SV339: $i] :
( ( ( ~ ( ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
| ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 ) ) )
= $false )
| ( ( SV298 = SV339 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1697,plain,
! [SV340: $i,SV299: $i] :
( ( ! [SY550: $i,SY551: $i] :
( ~ ( in @ SV299 @ SY550 )
| ~ ( in @ SV340 @ SY551 )
| ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY550 @ SY551 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1630]) ).
thf(1698,plain,
! [SV340: $i,SV299: $i] :
( ( ~ ( ~ ! [SY552: $i] :
( ! [SY553: $i] :
~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY552 @ SY553 ) )
| ( in @ SV299 @ SY552 ) )
| ~ ! [SY554: $i,SY555: $i] :
( ~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY554 @ SY555 ) )
| ( in @ SV340 @ SY555 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1699,plain,
! [SV400: $i,SV363: $i] :
( ( ( SV363 = SV400 )
| ~ ( subset @ SV363 @ SV400 )
| ( proper_subset @ SV363 @ SV400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1700,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1701,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1633]) ).
thf(1702,plain,
! [SV401: $i,SV364: $i] :
( ( ( ( set_intersection2 @ SV364 @ SV401 )
!= empty_set )
| ( disjoint @ SV364 @ SV401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1703,plain,
! [SV402: $i,SV365: $i] :
( ( ~ ( disjoint @ SV365 @ SV402 )
| ( ( set_intersection2 @ SV365 @ SV402 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(1704,plain,
! [SV300: $i,SV403: $i] :
( ( ! [SY616: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SY616 @ SV403 @ SV300 ) @ SY616 )
| ( ( sK18_D @ SY616 @ SV403 @ SV300 )
!= SV300 ) )
| ~ ( ~ ( in @ ( sK18_D @ SY616 @ SV403 @ SV300 ) @ SY616 )
| ( ( sK18_D @ SY616 @ SV403 @ SV300 )
!= SV403 ) ) )
| ~ ( ( in @ ( sK18_D @ SY616 @ SV403 @ SV300 ) @ SY616 )
| ( ( sK18_D @ SY616 @ SV403 @ SV300 )
= SV300 )
| ( ( sK18_D @ SY616 @ SV403 @ SV300 )
= SV403 ) ) )
| ( SY616
= ( unordered_pair @ SV300 @ SV403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1705,plain,
! [SV404: $i,SV300: $i] :
( ( ! [SY617: $i] :
( ( SY617
!= ( unordered_pair @ SV300 @ SV404 ) )
| ~ ( ~ ! [SY618: $i] :
( ~ ( in @ SY618 @ SY617 )
| ( SY618 = SV300 )
| ( SY618 = SV404 ) )
| ~ ~ ( ~ ! [SY518: $i] :
( ( SY518 != SV300 )
| ( in @ SY518 @ SY617 ) )
| ~ ! [SY620: $i] :
( ( SY620 != SV404 )
| ( in @ SY620 @ SY617 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1706,plain,
! [SV405: $i,SV366: $i] :
( ( ( disjoint @ SV366 @ SV405 )
| ( in @ ( sK22_C @ SV405 @ SV366 ) @ ( set_intersection2 @ SV366 @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1707,plain,
! [SV406: $i,SV367: $i] :
( ( ! [SY621: $i] :
~ ( in @ SY621 @ ( set_intersection2 @ SV367 @ SV406 ) )
| ~ ( disjoint @ SV367 @ SV406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1708,plain,
! [SV368: $i,SV407: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
| ~ ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 ) )
| ~ ( ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
| ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 ) ) )
| ( SV407
= ( powerset @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(1709,plain,
! [SV369: $i,SV408: $i] :
( ( ( SV408
!= ( powerset @ SV369 ) )
| ~ ( ~ ! [SY622: $i] :
( ~ ( in @ SY622 @ SV408 )
| ( subset @ SY622 @ SV369 ) )
| ~ ! [SY623: $i] :
( ~ ( subset @ SY623 @ SV369 )
| ( in @ SY623 @ SV408 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(1710,plain,
! [SV341: $i,SV301: $i] :
( ( ! [SY556: $i] :
( ! [SY557: $i] :
( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SY556 @ SY557 ) )
| ( SV301 = SY556 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1642]) ).
thf(1711,plain,
! [SV341: $i,SV301: $i] :
( ( ! [SY558: $i,SY559: $i] :
( ( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SY558 @ SY559 ) )
| ( SV341 = SY559 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1643]) ).
thf(1712,plain,
! [SV302: $i,SV409: $i] :
( ( ! [SY624: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SY624 @ SV409 @ SV302 ) @ SY624 )
| ~ ( in @ ( sK17_D @ SY624 @ SV409 @ SV302 ) @ SV302 ) )
| ~ ( ~ ( in @ ( sK17_D @ SY624 @ SV409 @ SV302 ) @ SY624 )
| ~ ( in @ ( sK17_D @ SY624 @ SV409 @ SV302 ) @ SV409 ) ) )
| ~ ( ( in @ ( sK17_D @ SY624 @ SV409 @ SV302 ) @ SY624 )
| ( in @ ( sK17_D @ SY624 @ SV409 @ SV302 ) @ SV302 )
| ( in @ ( sK17_D @ SY624 @ SV409 @ SV302 ) @ SV409 ) ) )
| ( SY624
= ( set_union2 @ SV302 @ SV409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1713,plain,
! [SV410: $i,SV302: $i] :
( ( ! [SY625: $i] :
( ( SY625
!= ( set_union2 @ SV302 @ SV410 ) )
| ~ ( ~ ! [SY626: $i] :
( ~ ( in @ SY626 @ SY625 )
| ( in @ SY626 @ SV302 )
| ( in @ SY626 @ SV410 ) )
| ~ ~ ( ~ ! [SY530: $i] :
( ~ ( in @ SY530 @ SV302 )
| ( in @ SY530 @ SY625 ) )
| ~ ! [SY628: $i] :
( ~ ( in @ SY628 @ SV410 )
| ( in @ SY628 @ SY625 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(1714,plain,
! [SV370: $i,SV411: $i] :
( ( ~ ( ~ ( ! [SY629: $i] :
( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SY629 )
| ~ ( in @ SY629 @ SV370 ) )
| ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ ( sK9_SY185 @ SV411 @ SV370 ) )
| ~ ( in @ ( sK9_SY185 @ SV411 @ SV370 ) @ SV370 ) )
| ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) ) )
| ( SV411
= ( union @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(1715,plain,
! [SV371: $i,SV412: $i] :
( ( ( SV412
!= ( union @ SV371 ) )
| ~ ( ~ ! [SY630: $i] :
( ! [SY588: $i] :
( ~ ( in @ SY630 @ SY588 )
| ~ ( in @ SY588 @ SV371 ) )
| ( in @ SY630 @ SV412 ) )
| ~ ! [SY632: $i] :
( ~ ( in @ SY632 @ SV412 )
| ~ ( ~ ( in @ SY632 @ ( sK7_D @ SY632 @ SV412 @ SV371 ) )
| ~ ( in @ ( sK7_D @ SY632 @ SV412 @ SV371 ) @ SV371 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(1716,plain,
! [SV303: $i,SV413: $i] :
( ( ! [SY633: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY633 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SY633 @ SV413 @ SV303 ) @ SV413 )
| ~ ( in @ ( sK6_D @ SY633 @ SV413 @ SV303 ) @ SY633 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY633 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SY633 @ SV413 @ SV303 ) @ SY633 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY633 @ SV413 @ SV303 ) @ SV413 )
| ( in @ ( sK6_D @ SY633 @ SV413 @ SV303 ) @ SY633 ) ) ) )
| ( SY633
= ( set_difference @ SV303 @ SV413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(1717,plain,
! [SV414: $i,SV303: $i] :
( ( ! [SY634: $i] :
( ( SY634
!= ( set_difference @ SV303 @ SV414 ) )
| ~ ( ~ ! [SY635: $i] :
( ~ ( in @ SY635 @ SV303 )
| ( in @ SY635 @ SV414 )
| ( in @ SY635 @ SY634 ) )
| ~ ~ ( ~ ! [SY537: $i] :
( ~ ( in @ SY537 @ SY634 )
| ( in @ SY537 @ SV303 ) )
| ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ SY634 )
| ~ ( in @ SY637 @ SV414 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1718,plain,
! [SV372: $i] :
( ( ( in @ ( sK20_B @ SV372 ) @ SV372 )
= $true )
| ( ( SV372 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1719,plain,
! [SV373: $i] :
( ( ( ( SV373 != empty_set ) )
= $true )
| ( ( ! [SY590: $i] :
~ ( in @ SY590 @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1720,plain,
! [SV415: $i,SV374: $i] :
( ( ~ ( in @ SV374 @ SV415 )
| ( subset @ ( singleton @ SV374 ) @ SV415 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(1721,plain,
! [SV416: $i,SV375: $i] :
( ( ~ ( subset @ ( singleton @ SV375 ) @ SV416 )
| ( in @ SV375 @ SV416 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1722,plain,
! [SV417: $i,SV376: $i] :
( ( ( disjoint @ SV376 @ SV417 )
| ~ ( ~ ( in @ ( sK23_C @ SV417 @ SV376 ) @ SV376 )
| ~ ( in @ ( sK23_C @ SV417 @ SV376 ) @ SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1723,plain,
! [SV418: $i,SV377: $i] :
( ( ! [SY638: $i] :
( ~ ( in @ SY638 @ SV377 )
| ~ ( in @ SY638 @ SV418 ) )
| ~ ( disjoint @ SV377 @ SV418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(1724,plain,
! [SV419: $i,SV378: $i] :
( ( ~ ( subset @ SV378 @ SV419 )
| ~ ( subset @ SV419 @ SV378 )
| ( SV378 = SV419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1725,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1726,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1657]) ).
thf(1727,plain,
! [SV379: $i,SV420: $i] :
( ( ~ ( ~ ( in @ ( sK11_C @ SV420 @ SV379 ) @ SV379 )
| ~ ~ ( in @ ( sK11_C @ SV420 @ SV379 ) @ SV420 ) )
| ( subset @ SV379 @ SV420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(1728,plain,
! [SV421: $i,SV380: $i] :
( ( ~ ( subset @ SV380 @ SV421 )
| ! [SY639: $i] :
( ~ ( in @ SY639 @ SV380 )
| ( in @ SY639 @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(1729,plain,
! [SV307: $i,SV249: $i,SV381: $i] :
( ( ( in @ SV381 @ SV249 )
= $true )
| ( ( subset @ SV249 @ ( set_difference @ SV307 @ ( singleton @ SV381 ) ) )
= $true )
| ( ( subset @ SV249 @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1730,plain,
! [SV350: $i,SV309: $i,SV342: $i,SV251: $i] :
( ( ( SV251 = SV342 )
= $true )
| ( ( ( ( unordered_pair @ SV251 @ SV309 )
!= ( unordered_pair @ SV342 @ SV350 ) ) )
= $true )
| ( ( SV251 = SV350 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1731,plain,
! [SV343: $i,SV312: $i,SV254: $i] :
( ( ( subset @ SV254 @ SV312 )
= $false )
| ( ( ~ ( subset @ SV254 @ SV343 ) )
= $true )
| ( ( subset @ SV254 @ ( set_intersection2 @ SV312 @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1732,plain,
! [SV344: $i,SV313: $i,SV255: $i] :
( ( ( subset @ SV255 @ SV313 )
= $false )
| ( ( ~ ( subset @ SV313 @ SV344 ) )
= $true )
| ( ( subset @ SV255 @ SV344 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1733,plain,
! [SV267: $i,SV345: $i,SV323: $i] :
( ( ( disjoint @ SV323 @ SV345 )
= $false )
| ( ( ~ ( subset @ SV267 @ SV323 ) )
= $true )
| ( ( disjoint @ SV267 @ SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1734,plain,
! [SV346: $i,SV326: $i,SV271: $i] :
( ( ( subset @ SV271 @ SV326 )
= $false )
| ( ( ~ ( subset @ SV346 @ SV326 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV271 @ SV346 ) @ SV326 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1735,plain,
! [SV294: $i,SV338: $i] :
( ( ( empty @ SV338 )
= $false )
| ( ( SV294 = SV338 )
= $true )
| ( ( empty @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1736,plain,
! [SV384: $i,SV422: $i,SV295: $i] :
( ( ~ ( in @ SV295 @ SV422 )
| ~ ( in @ SV384 @ SV422 )
| ( subset @ ( unordered_pair @ SV295 @ SV384 ) @ SV422 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(1737,plain,
! [SV295: $i] :
( ( ~ ! [SY484: $i,SY485: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY484 ) @ SY485 )
| ( in @ SV295 @ SY485 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1677]) ).
thf(1738,plain,
! [SV295: $i] :
( ( ~ ! [SY486: $i,SY487: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY486 ) @ SY487 )
| ( in @ SY486 @ SY487 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1677]) ).
thf(1739,plain,
! [SV385: $i,SV352: $i] :
( ( ( ( ( set_difference @ SV352 @ SV385 )
!= empty_set ) )
= $true )
| ( ( subset @ SV352 @ SV385 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1678]) ).
thf(1740,plain,
! [SV386: $i,SV353: $i] :
( ( ( ~ ( subset @ SV353 @ SV386 ) )
= $true )
| ( ( ( set_difference @ SV353 @ SV386 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(1741,plain,
! [SV387: $i,SV354: $i] :
( ( ( ( ( set_difference @ SV354 @ SV387 )
!= SV354 ) )
= $true )
| ( ( disjoint @ SV354 @ SV387 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1742,plain,
! [SV388: $i,SV355: $i] :
( ( ( ~ ( disjoint @ SV355 @ SV388 ) )
= $true )
| ( ( ( set_difference @ SV355 @ SV388 )
= SV355 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1743,plain,
! [SV389: $i,SV356: $i] :
( ( ( ~ ( in @ SV356 @ SV389 ) )
= $true )
| ( ( subset @ ( singleton @ SV356 ) @ SV389 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(1744,plain,
! [SV390: $i,SV357: $i] :
( ( ( ~ ( subset @ ( singleton @ SV357 ) @ SV390 ) )
= $true )
| ( ( in @ SV357 @ SV390 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1745,plain,
! [SV391: $i,SV358: $i] :
( ( ( ( ( set_difference @ SV358 @ SV391 )
!= empty_set ) )
= $true )
| ( ( subset @ SV358 @ SV391 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1746,plain,
! [SV392: $i,SV359: $i] :
( ( ( ~ ( subset @ SV359 @ SV392 ) )
= $true )
| ( ( ( set_difference @ SV359 @ SV392 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1685]) ).
thf(1747,plain,
! [SV423: $i,SV393: $i,SV296: $i] :
( ( ~ ( ~ ( ! [SY640: $i,SY641: $i] :
( ~ ( in @ SY640 @ SV296 )
| ~ ( in @ SY641 @ SV393 )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ SY640 @ SY641 ) ) )
| ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) @ SV393 ) )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) ) ) )
| ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) ) )
| ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(1748,plain,
! [SV394: $i,SV296: $i,SV424: $i] :
( ( ( SV424
!= ( cartesian_product2 @ SV296 @ SV394 ) )
| ~ ( ~ ! [SY642: $i] :
( ! [SY606: $i,SY607: $i] :
( ~ ( in @ SY606 @ SV296 )
| ~ ( in @ SY607 @ SV394 )
| ( SY642
!= ( ordered_pair @ SY606 @ SY607 ) ) )
| ( in @ SY642 @ SV424 ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV424 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY645 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SY645 @ SV424 @ SV394 @ SV296 ) @ SV394 ) )
| ( SY645
!= ( ordered_pair @ ( sK12_E @ SY645 @ SV424 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SY645 @ SV424 @ SV394 @ SV296 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(1749,plain,
! [SV395: $i,SV360: $i] :
( ( ( ~ ( subset @ SV360 @ ( singleton @ SV395 ) ) )
= $true )
| ( ( ( SV360 = empty_set )
| ( SV360
= ( singleton @ SV395 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(1750,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1689]) ).
thf(1751,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1690]) ).
thf(1752,plain,
! [SV361: $i,SV396: $i] :
( ( ( ~ ( ~ ( ( ( sK21_C @ SV396 @ SV361 )
!= SV361 )
| ~ ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 ) )
| ~ ( ( ( sK21_C @ SV396 @ SV361 )
= SV361 )
| ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 ) ) ) )
= $true )
| ( ( SV396
= ( singleton @ SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(1753,plain,
! [SV362: $i,SV397: $i] :
( ( ( ( SV397
!= ( singleton @ SV362 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY609: $i] :
( ( SY609 != SV362 )
| ( in @ SY609 @ SV397 ) )
| ~ ! [SY610: $i] :
( ~ ( in @ SY610 @ SV397 )
| ( SY610 = SV362 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1692]) ).
thf(1754,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
| ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) ) ) )
| ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(1755,plain,
! [SV399: $i,SV297: $i,SV426: $i] :
( ( ( SV426
!= ( set_intersection2 @ SV297 @ SV399 ) )
| ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV297 )
| ~ ( in @ SY646 @ SV399 )
| ( in @ SY646 @ SV426 ) )
| ~ ~ ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV426 )
| ( in @ SY647 @ SV297 ) )
| ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV426 )
| ( in @ SY648 @ SV399 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(1756,plain,
! [SV298: $i,SV339: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
| ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 ) )
= $true )
| ( ( SV298 = SV339 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1757,plain,
! [SV298: $i,SV339: $i] :
( ( ( ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
| ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 ) )
= $true )
| ( ( SV298 = SV339 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1696]) ).
thf(1758,plain,
! [SV340: $i,SV427: $i,SV299: $i] :
( ( ! [SY649: $i] :
( ~ ( in @ SV299 @ SV427 )
| ~ ( in @ SV340 @ SY649 )
| ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV427 @ SY649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(1759,plain,
! [SV340: $i,SV299: $i] :
( ( ~ ! [SY552: $i] :
( ! [SY553: $i] :
~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY552 @ SY553 ) )
| ( in @ SV299 @ SY552 ) )
| ~ ! [SY554: $i,SY555: $i] :
( ~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY554 @ SY555 ) )
| ( in @ SV340 @ SY555 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(1760,plain,
! [SV400: $i,SV363: $i] :
( ( ( ( SV363 = SV400 )
| ~ ( subset @ SV363 @ SV400 ) )
= $true )
| ( ( proper_subset @ SV363 @ SV400 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1699]) ).
thf(1761,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1700]) ).
thf(1762,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1701]) ).
thf(1763,plain,
! [SV401: $i,SV364: $i] :
( ( ( ( ( set_intersection2 @ SV364 @ SV401 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV364 @ SV401 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1764,plain,
! [SV402: $i,SV365: $i] :
( ( ( ~ ( disjoint @ SV365 @ SV402 ) )
= $true )
| ( ( ( set_intersection2 @ SV365 @ SV402 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1765,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV300 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV403 ) ) )
| ~ ( ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV300 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV403 ) ) )
| ( SV428
= ( unordered_pair @ SV300 @ SV403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(1766,plain,
! [SV404: $i,SV300: $i,SV429: $i] :
( ( ( SV429
!= ( unordered_pair @ SV300 @ SV404 ) )
| ~ ( ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV429 )
| ( SY650 = SV300 )
| ( SY650 = SV404 ) )
| ~ ~ ( ~ ! [SY651: $i] :
( ( SY651 != SV300 )
| ( in @ SY651 @ SV429 ) )
| ~ ! [SY652: $i] :
( ( SY652 != SV404 )
| ( in @ SY652 @ SV429 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(1767,plain,
! [SV405: $i,SV366: $i] :
( ( ( disjoint @ SV366 @ SV405 )
= $true )
| ( ( in @ ( sK22_C @ SV405 @ SV366 ) @ ( set_intersection2 @ SV366 @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1768,plain,
! [SV406: $i,SV367: $i] :
( ( ( ! [SY621: $i] :
~ ( in @ SY621 @ ( set_intersection2 @ SV367 @ SV406 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV367 @ SV406 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(1769,plain,
! [SV368: $i,SV407: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
| ~ ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 ) )
| ~ ( ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
| ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 ) ) ) )
= $true )
| ( ( SV407
= ( powerset @ SV368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1708]) ).
thf(1770,plain,
! [SV369: $i,SV408: $i] :
( ( ( ( SV408
!= ( powerset @ SV369 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY622: $i] :
( ~ ( in @ SY622 @ SV408 )
| ( subset @ SY622 @ SV369 ) )
| ~ ! [SY623: $i] :
( ~ ( subset @ SY623 @ SV369 )
| ( in @ SY623 @ SV408 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1709]) ).
thf(1771,plain,
! [SV430: $i,SV341: $i,SV301: $i] :
( ( ! [SY653: $i] :
( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SV430 @ SY653 ) )
| ( SV301 = SV430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(1772,plain,
! [SV431: $i,SV341: $i,SV301: $i] :
( ( ! [SY654: $i] :
( ( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SV431 @ SY654 ) )
| ( SV341 = SY654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(1773,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) ) )
| ~ ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 )
| ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) ) )
| ( SV432
= ( set_union2 @ SV302 @ SV409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(1774,plain,
! [SV410: $i,SV302: $i,SV433: $i] :
( ( ( SV433
!= ( set_union2 @ SV302 @ SV410 ) )
| ~ ( ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ SV433 )
| ( in @ SY655 @ SV302 )
| ( in @ SY655 @ SV410 ) )
| ~ ~ ( ~ ! [SY656: $i] :
( ~ ( in @ SY656 @ SV302 )
| ( in @ SY656 @ SV433 ) )
| ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV410 )
| ( in @ SY657 @ SV433 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(1775,plain,
! [SV370: $i,SV411: $i] :
( ( ( ~ ( ~ ( ! [SY629: $i] :
( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SY629 )
| ~ ( in @ SY629 @ SV370 ) )
| ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ ( sK9_SY185 @ SV411 @ SV370 ) )
| ~ ( in @ ( sK9_SY185 @ SV411 @ SV370 ) @ SV370 ) )
| ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) ) ) )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1714]) ).
thf(1776,plain,
! [SV371: $i,SV412: $i] :
( ( ( ( SV412
!= ( union @ SV371 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY630: $i] :
( ! [SY588: $i] :
( ~ ( in @ SY630 @ SY588 )
| ~ ( in @ SY588 @ SV371 ) )
| ( in @ SY630 @ SV412 ) )
| ~ ! [SY632: $i] :
( ~ ( in @ SY632 @ SV412 )
| ~ ( ~ ( in @ SY632 @ ( sK7_D @ SY632 @ SV412 @ SV371 ) )
| ~ ( in @ ( sK7_D @ SY632 @ SV412 @ SV371 ) @ SV371 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1715]) ).
thf(1777,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) ) ) )
| ( SV434
= ( set_difference @ SV303 @ SV413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(1778,plain,
! [SV414: $i,SV303: $i,SV435: $i] :
( ( ( SV435
!= ( set_difference @ SV303 @ SV414 ) )
| ~ ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV303 )
| ( in @ SY658 @ SV414 )
| ( in @ SY658 @ SV435 ) )
| ~ ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV435 )
| ( in @ SY659 @ SV303 ) )
| ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV435 )
| ~ ( in @ SY660 @ SV414 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(1779,plain,
! [SV373: $i] :
( ( ( SV373 = empty_set )
= $false )
| ( ( ! [SY590: $i] :
~ ( in @ SY590 @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(1780,plain,
! [SV415: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ SV415 ) )
= $true )
| ( ( subset @ ( singleton @ SV374 ) @ SV415 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1720]) ).
thf(1781,plain,
! [SV416: $i,SV375: $i] :
( ( ( ~ ( subset @ ( singleton @ SV375 ) @ SV416 ) )
= $true )
| ( ( in @ SV375 @ SV416 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1721]) ).
thf(1782,plain,
! [SV417: $i,SV376: $i] :
( ( ( disjoint @ SV376 @ SV417 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK23_C @ SV417 @ SV376 ) @ SV376 )
| ~ ( in @ ( sK23_C @ SV417 @ SV376 ) @ SV417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1722]) ).
thf(1783,plain,
! [SV418: $i,SV377: $i] :
( ( ( ! [SY638: $i] :
( ~ ( in @ SY638 @ SV377 )
| ~ ( in @ SY638 @ SV418 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV377 @ SV418 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(1784,plain,
! [SV419: $i,SV378: $i] :
( ( ( ~ ( subset @ SV378 @ SV419 )
| ~ ( subset @ SV419 @ SV378 ) )
= $true )
| ( ( SV378 = SV419 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1785,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1725]) ).
thf(1786,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1787,plain,
! [SV379: $i,SV420: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_C @ SV420 @ SV379 ) @ SV379 )
| ~ ~ ( in @ ( sK11_C @ SV420 @ SV379 ) @ SV420 ) ) )
= $true )
| ( ( subset @ SV379 @ SV420 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(1788,plain,
! [SV421: $i,SV380: $i] :
( ( ( ~ ( subset @ SV380 @ SV421 ) )
= $true )
| ( ( ! [SY639: $i] :
( ~ ( in @ SY639 @ SV380 )
| ( in @ SY639 @ SV421 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1728]) ).
thf(1789,plain,
! [SV350: $i,SV342: $i,SV309: $i,SV251: $i] :
( ( ( ( unordered_pair @ SV251 @ SV309 )
= ( unordered_pair @ SV342 @ SV350 ) )
= $false )
| ( ( SV251 = SV342 )
= $true )
| ( ( SV251 = SV350 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1790,plain,
! [SV312: $i,SV343: $i,SV254: $i] :
( ( ( subset @ SV254 @ SV343 )
= $false )
| ( ( subset @ SV254 @ SV312 )
= $false )
| ( ( subset @ SV254 @ ( set_intersection2 @ SV312 @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1791,plain,
! [SV255: $i,SV344: $i,SV313: $i] :
( ( ( subset @ SV313 @ SV344 )
= $false )
| ( ( subset @ SV255 @ SV313 )
= $false )
| ( ( subset @ SV255 @ SV344 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(1792,plain,
! [SV345: $i,SV323: $i,SV267: $i] :
( ( ( subset @ SV267 @ SV323 )
= $false )
| ( ( disjoint @ SV323 @ SV345 )
= $false )
| ( ( disjoint @ SV267 @ SV345 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1793,plain,
! [SV271: $i,SV326: $i,SV346: $i] :
( ( ( subset @ SV346 @ SV326 )
= $false )
| ( ( subset @ SV271 @ SV326 )
= $false )
| ( ( subset @ ( set_union2 @ SV271 @ SV346 ) @ SV326 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(1794,plain,
! [SV384: $i,SV422: $i,SV295: $i] :
( ( ( ~ ( in @ SV295 @ SV422 )
| ~ ( in @ SV384 @ SV422 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV295 @ SV384 ) @ SV422 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(1795,plain,
! [SV295: $i] :
( ( ! [SY484: $i,SY485: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY484 ) @ SY485 )
| ( in @ SV295 @ SY485 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1737]) ).
thf(1796,plain,
! [SV295: $i] :
( ( ! [SY486: $i,SY487: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SY486 ) @ SY487 )
| ( in @ SY486 @ SY487 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1738]) ).
thf(1797,plain,
! [SV385: $i,SV352: $i] :
( ( ( ( set_difference @ SV352 @ SV385 )
= empty_set )
= $false )
| ( ( subset @ SV352 @ SV385 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1798,plain,
! [SV386: $i,SV353: $i] :
( ( ( subset @ SV353 @ SV386 )
= $false )
| ( ( ( set_difference @ SV353 @ SV386 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1799,plain,
! [SV387: $i,SV354: $i] :
( ( ( ( set_difference @ SV354 @ SV387 )
= SV354 )
= $false )
| ( ( disjoint @ SV354 @ SV387 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1800,plain,
! [SV388: $i,SV355: $i] :
( ( ( disjoint @ SV355 @ SV388 )
= $false )
| ( ( ( set_difference @ SV355 @ SV388 )
= SV355 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1801,plain,
! [SV389: $i,SV356: $i] :
( ( ( in @ SV356 @ SV389 )
= $false )
| ( ( subset @ ( singleton @ SV356 ) @ SV389 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1802,plain,
! [SV390: $i,SV357: $i] :
( ( ( subset @ ( singleton @ SV357 ) @ SV390 )
= $false )
| ( ( in @ SV357 @ SV390 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1803,plain,
! [SV391: $i,SV358: $i] :
( ( ( ( set_difference @ SV358 @ SV391 )
= empty_set )
= $false )
| ( ( subset @ SV358 @ SV391 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1804,plain,
! [SV392: $i,SV359: $i] :
( ( ( subset @ SV359 @ SV392 )
= $false )
| ( ( ( set_difference @ SV359 @ SV392 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1805,plain,
! [SV423: $i,SV393: $i,SV296: $i] :
( ( ( ~ ( ~ ( ! [SY640: $i,SY641: $i] :
( ~ ( in @ SY640 @ SV296 )
| ~ ( in @ SY641 @ SV393 )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ SY640 @ SY641 ) ) )
| ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) @ SV393 ) )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) ) ) )
| ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) ) ) )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1747]) ).
thf(1806,plain,
! [SV394: $i,SV296: $i,SV424: $i] :
( ( ( ( SV424
!= ( cartesian_product2 @ SV296 @ SV394 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY606: $i,SY607: $i] :
( ~ ( in @ SY606 @ SV296 )
| ~ ( in @ SY607 @ SV394 )
| ( SY642
!= ( ordered_pair @ SY606 @ SY607 ) ) )
| ( in @ SY642 @ SV424 ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV424 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY645 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SY645 @ SV424 @ SV394 @ SV296 ) @ SV394 ) )
| ( SY645
!= ( ordered_pair @ ( sK12_E @ SY645 @ SV424 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SY645 @ SV424 @ SV394 @ SV296 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(1807,plain,
! [SV395: $i,SV360: $i] :
( ( ( subset @ SV360 @ ( singleton @ SV395 ) )
= $false )
| ( ( ( SV360 = empty_set )
| ( SV360
= ( singleton @ SV395 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(1808,plain,
! [SV436: $i] :
( ( ( SV436 != empty_set )
| ! [SY661: $i] : ( subset @ SV436 @ ( singleton @ SY661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(1809,plain,
! [SV437: $i] :
( ( ! [SY662: $i] :
( ( SV437
!= ( singleton @ SY662 ) )
| ( subset @ SV437 @ ( singleton @ SY662 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(1810,plain,
! [SV361: $i,SV396: $i] :
( ( ( ~ ( ( ( sK21_C @ SV396 @ SV361 )
!= SV361 )
| ~ ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 ) )
| ~ ( ( ( sK21_C @ SV396 @ SV361 )
= SV361 )
| ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 ) ) )
= $false )
| ( ( SV396
= ( singleton @ SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(1811,plain,
! [SV362: $i,SV397: $i] :
( ( ( SV397
= ( singleton @ SV362 ) )
= $false )
| ( ( ~ ( ~ ! [SY609: $i] :
( ( SY609 != SV362 )
| ( in @ SY609 @ SV397 ) )
| ~ ! [SY610: $i] :
( ~ ( in @ SY610 @ SV397 )
| ( SY610 = SV362 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1812,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
| ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) ) ) ) )
= $true )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(1813,plain,
! [SV399: $i,SV297: $i,SV426: $i] :
( ( ( ( SV426
!= ( set_intersection2 @ SV297 @ SV399 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV297 )
| ~ ( in @ SY646 @ SV399 )
| ( in @ SY646 @ SV426 ) )
| ~ ~ ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV426 )
| ( in @ SY647 @ SV297 ) )
| ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV426 )
| ( in @ SY648 @ SV399 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(1814,plain,
! [SV298: $i,SV339: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 ) )
= $true )
| ( ( ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 ) )
= $true )
| ( ( SV298 = SV339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(1815,plain,
! [SV298: $i,SV339: $i] :
( ( ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
= $true )
| ( ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 )
= $true )
| ( ( SV298 = SV339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1757]) ).
thf(1816,plain,
! [SV438: $i,SV340: $i,SV427: $i,SV299: $i] :
( ( ~ ( in @ SV299 @ SV427 )
| ~ ( in @ SV340 @ SV438 )
| ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV427 @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(1817,plain,
! [SV340: $i,SV299: $i] :
( ( ~ ! [SY552: $i] :
( ! [SY553: $i] :
~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY552 @ SY553 ) )
| ( in @ SV299 @ SY552 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1759]) ).
thf(1818,plain,
! [SV340: $i,SV299: $i] :
( ( ~ ! [SY554: $i,SY555: $i] :
( ~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY554 @ SY555 ) )
| ( in @ SV340 @ SY555 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1759]) ).
thf(1819,plain,
! [SV400: $i,SV363: $i] :
( ( ( SV363 = SV400 )
= $true )
| ( ( ~ ( subset @ SV363 @ SV400 ) )
= $true )
| ( ( proper_subset @ SV363 @ SV400 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(1820,plain,
! [SV439: $i] :
( ( ! [SY663: $i] :
( ~ ( proper_subset @ SV439 @ SY663 )
| ( SV439 != SY663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(1821,plain,
! [SV440: $i] :
( ( ! [SY664: $i] :
( ~ ( proper_subset @ SV440 @ SY664 )
| ( subset @ SV440 @ SY664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(1822,plain,
! [SV401: $i,SV364: $i] :
( ( ( ( set_intersection2 @ SV364 @ SV401 )
= empty_set )
= $false )
| ( ( disjoint @ SV364 @ SV401 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1823,plain,
! [SV402: $i,SV365: $i] :
( ( ( disjoint @ SV365 @ SV402 )
= $false )
| ( ( ( set_intersection2 @ SV365 @ SV402 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1824,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV300 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV403 ) ) )
| ~ ( ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV300 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV403 ) ) ) )
= $true )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(1825,plain,
! [SV404: $i,SV300: $i,SV429: $i] :
( ( ( ( SV429
!= ( unordered_pair @ SV300 @ SV404 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV429 )
| ( SY650 = SV300 )
| ( SY650 = SV404 ) )
| ~ ~ ( ~ ! [SY651: $i] :
( ( SY651 != SV300 )
| ( in @ SY651 @ SV429 ) )
| ~ ! [SY652: $i] :
( ( SY652 != SV404 )
| ( in @ SY652 @ SV429 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1826,plain,
! [SV406: $i,SV367: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ ( set_intersection2 @ SV367 @ SV406 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV367 @ SV406 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(1827,plain,
! [SV368: $i,SV407: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
| ~ ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 ) )
| ~ ( ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
| ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 ) ) )
= $false )
| ( ( SV407
= ( powerset @ SV368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1828,plain,
! [SV369: $i,SV408: $i] :
( ( ( SV408
= ( powerset @ SV369 ) )
= $false )
| ( ( ~ ( ~ ! [SY622: $i] :
( ~ ( in @ SY622 @ SV408 )
| ( subset @ SY622 @ SV369 ) )
| ~ ! [SY623: $i] :
( ~ ( subset @ SY623 @ SV369 )
| ( in @ SY623 @ SV408 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1829,plain,
! [SV430: $i,SV341: $i,SV301: $i] :
( ( ( ! [SY653: $i] :
( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SV430 @ SY653 ) ) )
= $true )
| ( ( SV301 = SV430 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(1830,plain,
! [SV442: $i,SV431: $i,SV341: $i,SV301: $i] :
( ( ( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SV431 @ SV442 ) )
| ( SV341 = SV442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(1831,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) ) )
| ~ ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 )
| ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) ) ) )
= $true )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(1832,plain,
! [SV410: $i,SV302: $i,SV433: $i] :
( ( ( ( SV433
!= ( set_union2 @ SV302 @ SV410 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ SV433 )
| ( in @ SY655 @ SV302 )
| ( in @ SY655 @ SV410 ) )
| ~ ~ ( ~ ! [SY656: $i] :
( ~ ( in @ SY656 @ SV302 )
| ( in @ SY656 @ SV433 ) )
| ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV410 )
| ( in @ SY657 @ SV433 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(1833,plain,
! [SV370: $i,SV411: $i] :
( ( ( ~ ( ! [SY629: $i] :
( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SY629 )
| ~ ( in @ SY629 @ SV370 ) )
| ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) )
| ~ ( ~ ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ ( sK9_SY185 @ SV411 @ SV370 ) )
| ~ ( in @ ( sK9_SY185 @ SV411 @ SV370 ) @ SV370 ) )
| ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) ) )
= $false )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(1834,plain,
! [SV371: $i,SV412: $i] :
( ( ( SV412
= ( union @ SV371 ) )
= $false )
| ( ( ~ ( ~ ! [SY630: $i] :
( ! [SY588: $i] :
( ~ ( in @ SY630 @ SY588 )
| ~ ( in @ SY588 @ SV371 ) )
| ( in @ SY630 @ SV412 ) )
| ~ ! [SY632: $i] :
( ~ ( in @ SY632 @ SV412 )
| ~ ( ~ ( in @ SY632 @ ( sK7_D @ SY632 @ SV412 @ SV371 ) )
| ~ ( in @ ( sK7_D @ SY632 @ SV412 @ SV371 ) @ SV371 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1835,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) ) ) ) )
= $true )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(1836,plain,
! [SV414: $i,SV303: $i,SV435: $i] :
( ( ( ( SV435
!= ( set_difference @ SV303 @ SV414 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV303 )
| ( in @ SY658 @ SV414 )
| ( in @ SY658 @ SV435 ) )
| ~ ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV435 )
| ( in @ SY659 @ SV303 ) )
| ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV435 )
| ~ ( in @ SY660 @ SV414 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(1837,plain,
! [SV373: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ SV373 ) )
= $true )
| ( ( SV373 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(1838,plain,
! [SV415: $i,SV374: $i] :
( ( ( in @ SV374 @ SV415 )
= $false )
| ( ( subset @ ( singleton @ SV374 ) @ SV415 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1839,plain,
! [SV416: $i,SV375: $i] :
( ( ( subset @ ( singleton @ SV375 ) @ SV416 )
= $false )
| ( ( in @ SV375 @ SV416 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1840,plain,
! [SV376: $i,SV417: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV417 @ SV376 ) @ SV376 )
| ~ ( in @ ( sK23_C @ SV417 @ SV376 ) @ SV417 ) )
= $false )
| ( ( disjoint @ SV376 @ SV417 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1841,plain,
! [SV418: $i,SV377: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ SV377 )
| ~ ( in @ SV444 @ SV418 ) )
= $true )
| ( ( ~ ( disjoint @ SV377 @ SV418 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(1842,plain,
! [SV419: $i,SV378: $i] :
( ( ( ~ ( subset @ SV378 @ SV419 ) )
= $true )
| ( ( ~ ( subset @ SV419 @ SV378 ) )
= $true )
| ( ( SV378 = SV419 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1784]) ).
thf(1843,plain,
! [SV445: $i] :
( ( ! [SY665: $i] :
( ( SV445 != SY665 )
| ( subset @ SV445 @ SY665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(1844,plain,
! [SV446: $i] :
( ( ! [SY666: $i] :
( ( SV446 != SY666 )
| ( subset @ SY666 @ SV446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(1845,plain,
! [SV379: $i,SV420: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV420 @ SV379 ) @ SV379 )
| ~ ~ ( in @ ( sK11_C @ SV420 @ SV379 ) @ SV420 ) )
= $false )
| ( ( subset @ SV379 @ SV420 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1846,plain,
! [SV421: $i,SV380: $i] :
( ( ( subset @ SV380 @ SV421 )
= $false )
| ( ( ! [SY639: $i] :
( ~ ( in @ SY639 @ SV380 )
| ( in @ SY639 @ SV421 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(1847,plain,
! [SV384: $i,SV422: $i,SV295: $i] :
( ( ( ~ ( in @ SV295 @ SV422 ) )
= $true )
| ( ( ~ ( in @ SV384 @ SV422 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV295 @ SV384 ) @ SV422 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(1848,plain,
! [SV447: $i,SV295: $i] :
( ( ! [SY667: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SV447 ) @ SY667 )
| ( in @ SV295 @ SY667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(1849,plain,
! [SV448: $i,SV295: $i] :
( ( ! [SY668: $i] :
( ~ ( subset @ ( unordered_pair @ SV295 @ SV448 ) @ SY668 )
| ( in @ SV448 @ SY668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(1850,plain,
! [SV423: $i,SV393: $i,SV296: $i] :
( ( ( ~ ( ! [SY640: $i,SY641: $i] :
( ~ ( in @ SY640 @ SV296 )
| ~ ( in @ SY641 @ SV393 )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ SY640 @ SY641 ) ) )
| ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) @ SV393 ) )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) ) ) )
| ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) ) )
= $false )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1805]) ).
thf(1851,plain,
! [SV394: $i,SV296: $i,SV424: $i] :
( ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false )
| ( ( ~ ( ~ ! [SY642: $i] :
( ! [SY606: $i,SY607: $i] :
( ~ ( in @ SY606 @ SV296 )
| ~ ( in @ SY607 @ SV394 )
| ( SY642
!= ( ordered_pair @ SY606 @ SY607 ) ) )
| ( in @ SY642 @ SV424 ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV424 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY645 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SY645 @ SV424 @ SV394 @ SV296 ) @ SV394 ) )
| ( SY645
!= ( ordered_pair @ ( sK12_E @ SY645 @ SV424 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SY645 @ SV424 @ SV394 @ SV296 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(1852,plain,
! [SV395: $i,SV360: $i] :
( ( ( SV360 = empty_set )
= $true )
| ( ( SV360
= ( singleton @ SV395 ) )
= $true )
| ( ( subset @ SV360 @ ( singleton @ SV395 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1807]) ).
thf(1853,plain,
! [SV436: $i] :
( ( ( ( SV436 != empty_set ) )
= $true )
| ( ( ! [SY661: $i] : ( subset @ SV436 @ ( singleton @ SY661 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(1854,plain,
! [SV449: $i,SV437: $i] :
( ( ( SV437
!= ( singleton @ SV449 ) )
| ( subset @ SV437 @ ( singleton @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(1855,plain,
! [SV361: $i,SV396: $i] :
( ( ( ~ ( ( ( sK21_C @ SV396 @ SV361 )
!= SV361 )
| ~ ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 ) ) )
= $false )
| ( ( SV396
= ( singleton @ SV361 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1810]) ).
thf(1856,plain,
! [SV361: $i,SV396: $i] :
( ( ( ~ ( ( ( sK21_C @ SV396 @ SV361 )
= SV361 )
| ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 ) ) )
= $false )
| ( ( SV396
= ( singleton @ SV361 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1810]) ).
thf(1857,plain,
! [SV397: $i,SV362: $i] :
( ( ( ~ ! [SY609: $i] :
( ( SY609 != SV362 )
| ( in @ SY609 @ SV397 ) )
| ~ ! [SY610: $i] :
( ~ ( in @ SY610 @ SV397 )
| ( SY610 = SV362 ) ) )
= $false )
| ( ( SV397
= ( singleton @ SV362 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1858,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
| ~ ~ ( ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
| ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) ) ) )
= $false )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1859,plain,
! [SV399: $i,SV297: $i,SV426: $i] :
( ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false )
| ( ( ~ ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV297 )
| ~ ( in @ SY646 @ SV399 )
| ( in @ SY646 @ SV426 ) )
| ~ ~ ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV426 )
| ( in @ SY647 @ SV297 ) )
| ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV426 )
| ( in @ SY648 @ SV399 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(1860,plain,
! [SV298: $i,SV339: $i] :
( ( ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
= $false )
| ( ( ~ ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 ) )
= $true )
| ( ( SV298 = SV339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1861,plain,
! [SV438: $i,SV340: $i,SV427: $i,SV299: $i] :
( ( ( ~ ( in @ SV299 @ SV427 )
| ~ ( in @ SV340 @ SV438 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV427 @ SV438 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1816]) ).
thf(1862,plain,
! [SV340: $i,SV299: $i] :
( ( ! [SY552: $i] :
( ! [SY553: $i] :
~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY552 @ SY553 ) )
| ( in @ SV299 @ SY552 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1817]) ).
thf(1863,plain,
! [SV340: $i,SV299: $i] :
( ( ! [SY554: $i,SY555: $i] :
( ~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SY554 @ SY555 ) )
| ( in @ SV340 @ SY555 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(1864,plain,
! [SV400: $i,SV363: $i] :
( ( ( subset @ SV363 @ SV400 )
= $false )
| ( ( SV363 = SV400 )
= $true )
| ( ( proper_subset @ SV363 @ SV400 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1865,plain,
! [SV450: $i,SV439: $i] :
( ( ~ ( proper_subset @ SV439 @ SV450 )
| ( SV439 != SV450 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(1866,plain,
! [SV451: $i,SV440: $i] :
( ( ~ ( proper_subset @ SV440 @ SV451 )
| ( subset @ SV440 @ SV451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(1867,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV300 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV403 ) ) )
| ~ ( ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV300 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV403 ) ) )
= $false )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1868,plain,
! [SV404: $i,SV300: $i,SV429: $i] :
( ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false )
| ( ( ~ ( ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV429 )
| ( SY650 = SV300 )
| ( SY650 = SV404 ) )
| ~ ~ ( ~ ! [SY651: $i] :
( ( SY651 != SV300 )
| ( in @ SY651 @ SV429 ) )
| ~ ! [SY652: $i] :
( ( SY652 != SV404 )
| ( in @ SY652 @ SV429 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(1869,plain,
! [SV406: $i,SV367: $i,SV441: $i] :
( ( ( in @ SV441 @ ( set_intersection2 @ SV367 @ SV406 ) )
= $false )
| ( ( ~ ( disjoint @ SV367 @ SV406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(1870,plain,
! [SV368: $i,SV407: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
| ~ ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 ) ) )
= $false )
| ( ( SV407
= ( powerset @ SV368 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1827]) ).
thf(1871,plain,
! [SV368: $i,SV407: $i] :
( ( ( ~ ( ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
| ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 ) ) )
= $false )
| ( ( SV407
= ( powerset @ SV368 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1827]) ).
thf(1872,plain,
! [SV369: $i,SV408: $i] :
( ( ( ~ ! [SY622: $i] :
( ~ ( in @ SY622 @ SV408 )
| ( subset @ SY622 @ SV369 ) )
| ~ ! [SY623: $i] :
( ~ ( subset @ SY623 @ SV369 )
| ( in @ SY623 @ SV408 ) ) )
= $false )
| ( ( SV408
= ( powerset @ SV369 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1828]) ).
thf(1873,plain,
! [SV452: $i,SV430: $i,SV341: $i,SV301: $i] :
( ( ( ( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SV430 @ SV452 ) ) )
= $true )
| ( ( SV301 = SV430 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(1874,plain,
! [SV442: $i,SV431: $i,SV341: $i,SV301: $i] :
( ( ( ( ( ordered_pair @ SV301 @ SV341 )
!= ( ordered_pair @ SV431 @ SV442 ) ) )
= $true )
| ( ( SV341 = SV442 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(1875,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) ) )
| ~ ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 )
| ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) ) )
= $false )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(1876,plain,
! [SV410: $i,SV302: $i,SV433: $i] :
( ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false )
| ( ( ~ ( ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ SV433 )
| ( in @ SY655 @ SV302 )
| ( in @ SY655 @ SV410 ) )
| ~ ~ ( ~ ! [SY656: $i] :
( ~ ( in @ SY656 @ SV302 )
| ( in @ SY656 @ SV433 ) )
| ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV410 )
| ( in @ SY657 @ SV433 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(1877,plain,
! [SV370: $i,SV411: $i] :
( ( ( ~ ( ! [SY629: $i] :
( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SY629 )
| ~ ( in @ SY629 @ SV370 ) )
| ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) ) )
= $false )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1833]) ).
thf(1878,plain,
! [SV370: $i,SV411: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ ( sK9_SY185 @ SV411 @ SV370 ) )
| ~ ( in @ ( sK9_SY185 @ SV411 @ SV370 ) @ SV370 ) )
| ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) ) )
= $false )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1833]) ).
thf(1879,plain,
! [SV412: $i,SV371: $i] :
( ( ( ~ ! [SY630: $i] :
( ! [SY588: $i] :
( ~ ( in @ SY630 @ SY588 )
| ~ ( in @ SY588 @ SV371 ) )
| ( in @ SY630 @ SV412 ) )
| ~ ! [SY632: $i] :
( ~ ( in @ SY632 @ SV412 )
| ~ ( ~ ( in @ SY632 @ ( sK7_D @ SY632 @ SV412 @ SV371 ) )
| ~ ( in @ ( sK7_D @ SY632 @ SV412 @ SV371 ) @ SV371 ) ) ) )
= $false )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(1880,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) ) ) )
= $false )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(1881,plain,
! [SV414: $i,SV303: $i,SV435: $i] :
( ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false )
| ( ( ~ ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV303 )
| ( in @ SY658 @ SV414 )
| ( in @ SY658 @ SV435 ) )
| ~ ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV435 )
| ( in @ SY659 @ SV303 ) )
| ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV435 )
| ~ ( in @ SY660 @ SV414 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1836]) ).
thf(1882,plain,
! [SV373: $i,SV443: $i] :
( ( ( in @ SV443 @ SV373 )
= $false )
| ( ( SV373 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1883,plain,
! [SV376: $i,SV417: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV417 @ SV376 ) @ SV376 ) )
= $false )
| ( ( disjoint @ SV376 @ SV417 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1884,plain,
! [SV376: $i,SV417: $i] :
( ( ( ~ ( in @ ( sK23_C @ SV417 @ SV376 ) @ SV417 ) )
= $false )
| ( ( disjoint @ SV376 @ SV417 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1885,plain,
! [SV418: $i,SV377: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ SV377 ) )
= $true )
| ( ( ~ ( in @ SV444 @ SV418 ) )
= $true )
| ( ( ~ ( disjoint @ SV377 @ SV418 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(1886,plain,
! [SV419: $i,SV378: $i] :
( ( ( subset @ SV378 @ SV419 )
= $false )
| ( ( ~ ( subset @ SV419 @ SV378 ) )
= $true )
| ( ( SV378 = SV419 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1842]) ).
thf(1887,plain,
! [SV453: $i,SV445: $i] :
( ( ( SV445 != SV453 )
| ( subset @ SV445 @ SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(1888,plain,
! [SV454: $i,SV446: $i] :
( ( ( SV446 != SV454 )
| ( subset @ SV454 @ SV446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(1889,plain,
! [SV379: $i,SV420: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV420 @ SV379 ) @ SV379 ) )
= $false )
| ( ( subset @ SV379 @ SV420 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1845]) ).
thf(1890,plain,
! [SV379: $i,SV420: $i] :
( ( ( ~ ~ ( in @ ( sK11_C @ SV420 @ SV379 ) @ SV420 ) )
= $false )
| ( ( subset @ SV379 @ SV420 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1845]) ).
thf(1891,plain,
! [SV421: $i,SV380: $i,SV455: $i] :
( ( ( ~ ( in @ SV455 @ SV380 )
| ( in @ SV455 @ SV421 ) )
= $true )
| ( ( subset @ SV380 @ SV421 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(1892,plain,
! [SV384: $i,SV422: $i,SV295: $i] :
( ( ( in @ SV295 @ SV422 )
= $false )
| ( ( ~ ( in @ SV384 @ SV422 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV295 @ SV384 ) @ SV422 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1893,plain,
! [SV456: $i,SV447: $i,SV295: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV295 @ SV447 ) @ SV456 )
| ( in @ SV295 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(1894,plain,
! [SV457: $i,SV448: $i,SV295: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV295 @ SV448 ) @ SV457 )
| ( in @ SV448 @ SV457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(1895,plain,
! [SV423: $i,SV393: $i,SV296: $i] :
( ( ( ~ ( ! [SY640: $i,SY641: $i] :
( ~ ( in @ SY640 @ SV296 )
| ~ ( in @ SY641 @ SV393 )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ SY640 @ SY641 ) ) )
| ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) ) )
= $false )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1850]) ).
thf(1896,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) @ SV393 ) )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) ) ) )
| ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) ) )
= $false )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1850]) ).
thf(1897,plain,
! [SV424: $i,SV394: $i,SV296: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY606: $i,SY607: $i] :
( ~ ( in @ SY606 @ SV296 )
| ~ ( in @ SY607 @ SV394 )
| ( SY642
!= ( ordered_pair @ SY606 @ SY607 ) ) )
| ( in @ SY642 @ SV424 ) )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV424 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY645 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SY645 @ SV424 @ SV394 @ SV296 ) @ SV394 ) )
| ( SY645
!= ( ordered_pair @ ( sK12_E @ SY645 @ SV424 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SY645 @ SV424 @ SV394 @ SV296 ) ) ) ) ) )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1898,plain,
! [SV436: $i] :
( ( ( SV436 = empty_set )
= $false )
| ( ( ! [SY661: $i] : ( subset @ SV436 @ ( singleton @ SY661 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1899,plain,
! [SV449: $i,SV437: $i] :
( ( ( ( SV437
!= ( singleton @ SV449 ) ) )
= $true )
| ( ( subset @ SV437 @ ( singleton @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(1900,plain,
! [SV361: $i,SV396: $i] :
( ( ( ( ( sK21_C @ SV396 @ SV361 )
!= SV361 )
| ~ ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 ) )
= $true )
| ( ( SV396
= ( singleton @ SV361 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1855]) ).
thf(1901,plain,
! [SV361: $i,SV396: $i] :
( ( ( ( ( sK21_C @ SV396 @ SV361 )
= SV361 )
| ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 ) )
= $true )
| ( ( SV396
= ( singleton @ SV361 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(1902,plain,
! [SV397: $i,SV362: $i] :
( ( ( ~ ! [SY609: $i] :
( ( SY609 != SV362 )
| ( in @ SY609 @ SV397 ) ) )
= $false )
| ( ( SV397
= ( singleton @ SV362 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(1903,plain,
! [SV362: $i,SV397: $i] :
( ( ( ~ ! [SY610: $i] :
( ~ ( in @ SY610 @ SV397 )
| ( SY610 = SV362 ) ) )
= $false )
| ( ( SV397
= ( singleton @ SV362 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(1904,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) ) )
= $false )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1905,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
| ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) ) ) )
= $false )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1906,plain,
! [SV426: $i,SV399: $i,SV297: $i] :
( ( ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV297 )
| ~ ( in @ SY646 @ SV399 )
| ( in @ SY646 @ SV426 ) )
| ~ ~ ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV426 )
| ( in @ SY647 @ SV297 ) )
| ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV426 )
| ( in @ SY648 @ SV399 ) ) ) )
= $false )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1907,plain,
! [SV298: $i,SV339: $i] :
( ( ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV339 )
= $false )
| ( ( in @ ( sK3_C @ SV339 @ SV298 ) @ SV298 )
= $false )
| ( ( SV298 = SV339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(1908,plain,
! [SV438: $i,SV340: $i,SV427: $i,SV299: $i] :
( ( ( ~ ( in @ SV299 @ SV427 ) )
= $true )
| ( ( ~ ( in @ SV340 @ SV438 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV427 @ SV438 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(1909,plain,
! [SV458: $i,SV340: $i,SV299: $i] :
( ( ! [SY669: $i] :
~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV458 @ SY669 ) )
| ( in @ SV299 @ SV458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(1910,plain,
! [SV459: $i,SV340: $i,SV299: $i] :
( ( ! [SY670: $i] :
( ~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV459 @ SY670 ) )
| ( in @ SV340 @ SY670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(1911,plain,
! [SV450: $i,SV439: $i] :
( ( ( ~ ( proper_subset @ SV439 @ SV450 ) )
= $true )
| ( ( ( SV439 != SV450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(1912,plain,
! [SV451: $i,SV440: $i] :
( ( ( ~ ( proper_subset @ SV440 @ SV451 ) )
= $true )
| ( ( subset @ SV440 @ SV451 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1866]) ).
thf(1913,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV300 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV403 ) ) ) )
= $false )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1914,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ~ ( ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV300 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV403 ) ) )
= $false )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1915,plain,
! [SV404: $i,SV300: $i,SV429: $i] :
( ( ( ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV429 )
| ( SY650 = SV300 )
| ( SY650 = SV404 ) )
| ~ ~ ( ~ ! [SY651: $i] :
( ( SY651 != SV300 )
| ( in @ SY651 @ SV429 ) )
| ~ ! [SY652: $i] :
( ( SY652 != SV404 )
| ( in @ SY652 @ SV429 ) ) ) )
= $false )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1916,plain,
! [SV441: $i,SV406: $i,SV367: $i] :
( ( ( disjoint @ SV367 @ SV406 )
= $false )
| ( ( in @ SV441 @ ( set_intersection2 @ SV367 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1917,plain,
! [SV368: $i,SV407: $i] :
( ( ( ~ ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
| ~ ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 ) )
= $true )
| ( ( SV407
= ( powerset @ SV368 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1870]) ).
thf(1918,plain,
! [SV368: $i,SV407: $i] :
( ( ( ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
| ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 ) )
= $true )
| ( ( SV407
= ( powerset @ SV368 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1871]) ).
thf(1919,plain,
! [SV369: $i,SV408: $i] :
( ( ( ~ ! [SY622: $i] :
( ~ ( in @ SY622 @ SV408 )
| ( subset @ SY622 @ SV369 ) ) )
= $false )
| ( ( SV408
= ( powerset @ SV369 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(1920,plain,
! [SV408: $i,SV369: $i] :
( ( ( ~ ! [SY623: $i] :
( ~ ( subset @ SY623 @ SV369 )
| ( in @ SY623 @ SV408 ) ) )
= $false )
| ( ( SV408
= ( powerset @ SV369 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(1921,plain,
! [SV452: $i,SV430: $i,SV341: $i,SV301: $i] :
( ( ( ( ordered_pair @ SV301 @ SV341 )
= ( ordered_pair @ SV430 @ SV452 ) )
= $false )
| ( ( SV301 = SV430 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1873]) ).
thf(1922,plain,
! [SV442: $i,SV431: $i,SV341: $i,SV301: $i] :
( ( ( ( ordered_pair @ SV301 @ SV341 )
= ( ordered_pair @ SV431 @ SV442 ) )
= $false )
| ( ( SV341 = SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(1923,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) ) ) )
= $false )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1875]) ).
thf(1924,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ~ ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 )
| ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) ) )
= $false )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1875]) ).
thf(1925,plain,
! [SV410: $i,SV302: $i,SV433: $i] :
( ( ( ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ SV433 )
| ( in @ SY655 @ SV302 )
| ( in @ SY655 @ SV410 ) )
| ~ ~ ( ~ ! [SY656: $i] :
( ~ ( in @ SY656 @ SV302 )
| ( in @ SY656 @ SV433 ) )
| ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV410 )
| ( in @ SY657 @ SV433 ) ) ) )
= $false )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(1926,plain,
! [SV370: $i,SV411: $i] :
( ( ( ! [SY629: $i] :
( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SY629 )
| ~ ( in @ SY629 @ SV370 ) )
| ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1877]) ).
thf(1927,plain,
! [SV370: $i,SV411: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ ( sK9_SY185 @ SV411 @ SV370 ) )
| ~ ( in @ ( sK9_SY185 @ SV411 @ SV370 ) @ SV370 ) )
| ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1878]) ).
thf(1928,plain,
! [SV412: $i,SV371: $i] :
( ( ( ~ ! [SY630: $i] :
( ! [SY588: $i] :
( ~ ( in @ SY630 @ SY588 )
| ~ ( in @ SY588 @ SV371 ) )
| ( in @ SY630 @ SV412 ) ) )
= $false )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1879]) ).
thf(1929,plain,
! [SV371: $i,SV412: $i] :
( ( ( ~ ! [SY632: $i] :
( ~ ( in @ SY632 @ SV412 )
| ~ ( ~ ( in @ SY632 @ ( sK7_D @ SY632 @ SV412 @ SV371 ) )
| ~ ( in @ ( sK7_D @ SY632 @ SV412 @ SV371 ) @ SV371 ) ) ) )
= $false )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1879]) ).
thf(1930,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) ) )
= $false )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1880]) ).
thf(1931,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) ) ) )
= $false )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1880]) ).
thf(1932,plain,
! [SV435: $i,SV414: $i,SV303: $i] :
( ( ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV303 )
| ( in @ SY658 @ SV414 )
| ( in @ SY658 @ SV435 ) )
| ~ ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV435 )
| ( in @ SY659 @ SV303 ) )
| ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV435 )
| ~ ( in @ SY660 @ SV414 ) ) ) )
= $false )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(1933,plain,
! [SV376: $i,SV417: $i] :
( ( ( in @ ( sK23_C @ SV417 @ SV376 ) @ SV376 )
= $true )
| ( ( disjoint @ SV376 @ SV417 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1883]) ).
thf(1934,plain,
! [SV376: $i,SV417: $i] :
( ( ( in @ ( sK23_C @ SV417 @ SV376 ) @ SV417 )
= $true )
| ( ( disjoint @ SV376 @ SV417 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1884]) ).
thf(1935,plain,
! [SV418: $i,SV377: $i,SV444: $i] :
( ( ( in @ SV444 @ SV377 )
= $false )
| ( ( ~ ( in @ SV444 @ SV418 ) )
= $true )
| ( ( ~ ( disjoint @ SV377 @ SV418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1936,plain,
! [SV378: $i,SV419: $i] :
( ( ( subset @ SV419 @ SV378 )
= $false )
| ( ( subset @ SV378 @ SV419 )
= $false )
| ( ( SV378 = SV419 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(1937,plain,
! [SV453: $i,SV445: $i] :
( ( ( ( SV445 != SV453 ) )
= $true )
| ( ( subset @ SV445 @ SV453 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(1938,plain,
! [SV454: $i,SV446: $i] :
( ( ( ( SV446 != SV454 ) )
= $true )
| ( ( subset @ SV454 @ SV446 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1888]) ).
thf(1939,plain,
! [SV379: $i,SV420: $i] :
( ( ( in @ ( sK11_C @ SV420 @ SV379 ) @ SV379 )
= $true )
| ( ( subset @ SV379 @ SV420 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1889]) ).
thf(1940,plain,
! [SV379: $i,SV420: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV420 @ SV379 ) @ SV420 ) )
= $true )
| ( ( subset @ SV379 @ SV420 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1890]) ).
thf(1941,plain,
! [SV421: $i,SV380: $i,SV455: $i] :
( ( ( ~ ( in @ SV455 @ SV380 ) )
= $true )
| ( ( in @ SV455 @ SV421 )
= $true )
| ( ( subset @ SV380 @ SV421 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(1942,plain,
! [SV295: $i,SV422: $i,SV384: $i] :
( ( ( in @ SV384 @ SV422 )
= $false )
| ( ( in @ SV295 @ SV422 )
= $false )
| ( ( subset @ ( unordered_pair @ SV295 @ SV384 ) @ SV422 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1892]) ).
thf(1943,plain,
! [SV456: $i,SV447: $i,SV295: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV295 @ SV447 ) @ SV456 ) )
= $true )
| ( ( in @ SV295 @ SV456 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(1944,plain,
! [SV457: $i,SV448: $i,SV295: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV295 @ SV448 ) @ SV457 ) )
= $true )
| ( ( in @ SV448 @ SV457 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(1945,plain,
! [SV423: $i,SV393: $i,SV296: $i] :
( ( ( ! [SY640: $i,SY641: $i] :
( ~ ( in @ SY640 @ SV296 )
| ~ ( in @ SY641 @ SV393 )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ SY640 @ SY641 ) ) )
| ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1895]) ).
thf(1946,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) @ SV393 ) )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) ) ) )
| ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1896]) ).
thf(1947,plain,
! [SV424: $i,SV394: $i,SV296: $i] :
( ( ( ~ ! [SY642: $i] :
( ! [SY606: $i,SY607: $i] :
( ~ ( in @ SY606 @ SV296 )
| ~ ( in @ SY607 @ SV394 )
| ( SY642
!= ( ordered_pair @ SY606 @ SY607 ) ) )
| ( in @ SY642 @ SV424 ) ) )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1897]) ).
thf(1948,plain,
! [SV296: $i,SV394: $i,SV424: $i] :
( ( ( ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV424 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY645 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SY645 @ SV424 @ SV394 @ SV296 ) @ SV394 ) )
| ( SY645
!= ( ordered_pair @ ( sK12_E @ SY645 @ SV424 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SY645 @ SV424 @ SV394 @ SV296 ) ) ) ) ) )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1897]) ).
thf(1949,plain,
! [SV460: $i,SV436: $i] :
( ( ( subset @ SV436 @ ( singleton @ SV460 ) )
= $true )
| ( ( SV436 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(1950,plain,
! [SV449: $i,SV437: $i] :
( ( ( SV437
= ( singleton @ SV449 ) )
= $false )
| ( ( subset @ SV437 @ ( singleton @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(1951,plain,
! [SV361: $i,SV396: $i] :
( ( ( ( ( sK21_C @ SV396 @ SV361 )
!= SV361 ) )
= $true )
| ( ( ~ ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 ) )
= $true )
| ( ( SV396
= ( singleton @ SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(1952,plain,
! [SV361: $i,SV396: $i] :
( ( ( ( sK21_C @ SV396 @ SV361 )
= SV361 )
= $true )
| ( ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 )
= $true )
| ( ( SV396
= ( singleton @ SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(1953,plain,
! [SV397: $i,SV362: $i] :
( ( ( ! [SY609: $i] :
( ( SY609 != SV362 )
| ( in @ SY609 @ SV397 ) ) )
= $true )
| ( ( SV397
= ( singleton @ SV362 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1902]) ).
thf(1954,plain,
! [SV362: $i,SV397: $i] :
( ( ( ! [SY610: $i] :
( ~ ( in @ SY610 @ SV397 )
| ( SY610 = SV362 ) ) )
= $true )
| ( ( SV397
= ( singleton @ SV362 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1903]) ).
thf(1955,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
= $true )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(1956,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
| ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) ) ) )
= $true )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1905]) ).
thf(1957,plain,
! [SV426: $i,SV399: $i,SV297: $i] :
( ( ( ~ ! [SY646: $i] :
( ~ ( in @ SY646 @ SV297 )
| ~ ( in @ SY646 @ SV399 )
| ( in @ SY646 @ SV426 ) ) )
= $false )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(1958,plain,
! [SV399: $i,SV297: $i,SV426: $i] :
( ( ( ~ ~ ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV426 )
| ( in @ SY647 @ SV297 ) )
| ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV426 )
| ( in @ SY648 @ SV399 ) ) ) )
= $false )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(1959,plain,
! [SV438: $i,SV340: $i,SV427: $i,SV299: $i] :
( ( ( in @ SV299 @ SV427 )
= $false )
| ( ( ~ ( in @ SV340 @ SV438 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV427 @ SV438 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(1960,plain,
! [SV458: $i,SV340: $i,SV299: $i] :
( ( ( ! [SY669: $i] :
~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV458 @ SY669 ) ) )
= $true )
| ( ( in @ SV299 @ SV458 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(1961,plain,
! [SV461: $i,SV459: $i,SV340: $i,SV299: $i] :
( ( ~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV459 @ SV461 ) )
| ( in @ SV340 @ SV461 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(1962,plain,
! [SV450: $i,SV439: $i] :
( ( ( proper_subset @ SV439 @ SV450 )
= $false )
| ( ( ( SV439 != SV450 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(1963,plain,
! [SV451: $i,SV440: $i] :
( ( ( proper_subset @ SV440 @ SV451 )
= $false )
| ( ( subset @ SV440 @ SV451 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(1964,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV300 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV403 ) ) ) )
= $true )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(1965,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV300 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV403 ) )
= $true )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1914]) ).
thf(1966,plain,
! [SV404: $i,SV300: $i,SV429: $i] :
( ( ( ~ ! [SY650: $i] :
( ~ ( in @ SY650 @ SV429 )
| ( SY650 = SV300 )
| ( SY650 = SV404 ) ) )
= $false )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(1967,plain,
! [SV404: $i,SV429: $i,SV300: $i] :
( ( ( ~ ~ ( ~ ! [SY651: $i] :
( ( SY651 != SV300 )
| ( in @ SY651 @ SV429 ) )
| ~ ! [SY652: $i] :
( ( SY652 != SV404 )
| ( in @ SY652 @ SV429 ) ) ) )
= $false )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1915]) ).
thf(1968,plain,
! [SV368: $i,SV407: $i] :
( ( ( ~ ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 ) )
= $true )
| ( ( ~ ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 ) )
= $true )
| ( ( SV407
= ( powerset @ SV368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(1969,plain,
! [SV368: $i,SV407: $i] :
( ( ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
= $true )
| ( ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 )
= $true )
| ( ( SV407
= ( powerset @ SV368 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(1970,plain,
! [SV369: $i,SV408: $i] :
( ( ( ! [SY622: $i] :
( ~ ( in @ SY622 @ SV408 )
| ( subset @ SY622 @ SV369 ) ) )
= $true )
| ( ( SV408
= ( powerset @ SV369 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1919]) ).
thf(1971,plain,
! [SV408: $i,SV369: $i] :
( ( ( ! [SY623: $i] :
( ~ ( subset @ SY623 @ SV369 )
| ( in @ SY623 @ SV408 ) ) )
= $true )
| ( ( SV408
= ( powerset @ SV369 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1920]) ).
thf(1972,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) ) ) )
= $true )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1923]) ).
thf(1973,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 )
| ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) )
= $true )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1924]) ).
thf(1974,plain,
! [SV410: $i,SV302: $i,SV433: $i] :
( ( ( ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ SV433 )
| ( in @ SY655 @ SV302 )
| ( in @ SY655 @ SV410 ) ) )
= $false )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1925]) ).
thf(1975,plain,
! [SV410: $i,SV433: $i,SV302: $i] :
( ( ( ~ ~ ( ~ ! [SY656: $i] :
( ~ ( in @ SY656 @ SV302 )
| ( in @ SY656 @ SV433 ) )
| ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV410 )
| ( in @ SY657 @ SV433 ) ) ) )
= $false )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1925]) ).
thf(1976,plain,
! [SV370: $i,SV411: $i] :
( ( ( ! [SY629: $i] :
( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SY629 )
| ~ ( in @ SY629 @ SV370 ) ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(1977,plain,
! [SV370: $i,SV411: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ ( sK9_SY185 @ SV411 @ SV370 ) )
| ~ ( in @ ( sK9_SY185 @ SV411 @ SV370 ) @ SV370 ) ) )
= $true )
| ( ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(1978,plain,
! [SV412: $i,SV371: $i] :
( ( ( ! [SY630: $i] :
( ! [SY588: $i] :
( ~ ( in @ SY630 @ SY588 )
| ~ ( in @ SY588 @ SV371 ) )
| ( in @ SY630 @ SV412 ) ) )
= $true )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1928]) ).
thf(1979,plain,
! [SV371: $i,SV412: $i] :
( ( ( ! [SY632: $i] :
( ~ ( in @ SY632 @ SV412 )
| ~ ( ~ ( in @ SY632 @ ( sK7_D @ SY632 @ SV412 @ SV371 ) )
| ~ ( in @ ( sK7_D @ SY632 @ SV412 @ SV371 ) @ SV371 ) ) ) )
= $true )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1929]) ).
thf(1980,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
= $true )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1930]) ).
thf(1981,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) ) ) )
= $true )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1931]) ).
thf(1982,plain,
! [SV435: $i,SV414: $i,SV303: $i] :
( ( ( ~ ! [SY658: $i] :
( ~ ( in @ SY658 @ SV303 )
| ( in @ SY658 @ SV414 )
| ( in @ SY658 @ SV435 ) ) )
= $false )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1932]) ).
thf(1983,plain,
! [SV414: $i,SV303: $i,SV435: $i] :
( ( ( ~ ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV435 )
| ( in @ SY659 @ SV303 ) )
| ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV435 )
| ~ ( in @ SY660 @ SV414 ) ) ) )
= $false )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1932]) ).
thf(1984,plain,
! [SV377: $i,SV418: $i,SV444: $i] :
( ( ( in @ SV444 @ SV418 )
= $false )
| ( ( in @ SV444 @ SV377 )
= $false )
| ( ( ~ ( disjoint @ SV377 @ SV418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(1985,plain,
! [SV453: $i,SV445: $i] :
( ( ( SV445 = SV453 )
= $false )
| ( ( subset @ SV445 @ SV453 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(1986,plain,
! [SV454: $i,SV446: $i] :
( ( ( SV446 = SV454 )
= $false )
| ( ( subset @ SV454 @ SV446 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(1987,plain,
! [SV379: $i,SV420: $i] :
( ( ( in @ ( sK11_C @ SV420 @ SV379 ) @ SV420 )
= $false )
| ( ( subset @ SV379 @ SV420 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(1988,plain,
! [SV421: $i,SV380: $i,SV455: $i] :
( ( ( in @ SV455 @ SV380 )
= $false )
| ( ( in @ SV455 @ SV421 )
= $true )
| ( ( subset @ SV380 @ SV421 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1941]) ).
thf(1989,plain,
! [SV456: $i,SV447: $i,SV295: $i] :
( ( ( subset @ ( unordered_pair @ SV295 @ SV447 ) @ SV456 )
= $false )
| ( ( in @ SV295 @ SV456 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(1990,plain,
! [SV457: $i,SV448: $i,SV295: $i] :
( ( ( subset @ ( unordered_pair @ SV295 @ SV448 ) @ SV457 )
= $false )
| ( ( in @ SV448 @ SV457 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(1991,plain,
! [SV423: $i,SV393: $i,SV296: $i] :
( ( ( ! [SY640: $i,SY641: $i] :
( ~ ( in @ SY640 @ SV296 )
| ~ ( in @ SY641 @ SV393 )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ SY640 @ SY641 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(1992,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) @ SV393 ) )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) ) ) ) )
= $true )
| ( ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(1993,plain,
! [SV424: $i,SV394: $i,SV296: $i] :
( ( ( ! [SY642: $i] :
( ! [SY606: $i,SY607: $i] :
( ~ ( in @ SY606 @ SV296 )
| ~ ( in @ SY607 @ SV394 )
| ( SY642
!= ( ordered_pair @ SY606 @ SY607 ) ) )
| ( in @ SY642 @ SV424 ) ) )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1947]) ).
thf(1994,plain,
! [SV296: $i,SV394: $i,SV424: $i] :
( ( ( ! [SY645: $i] :
( ~ ( in @ SY645 @ SV424 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SY645 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SY645 @ SV424 @ SV394 @ SV296 ) @ SV394 ) )
| ( SY645
!= ( ordered_pair @ ( sK12_E @ SY645 @ SV424 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SY645 @ SV424 @ SV394 @ SV296 ) ) ) ) ) )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1948]) ).
thf(1995,plain,
! [SV361: $i,SV396: $i] :
( ( ( ( sK21_C @ SV396 @ SV361 )
= SV361 )
= $false )
| ( ( ~ ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 ) )
= $true )
| ( ( SV396
= ( singleton @ SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(1996,plain,
! [SV397: $i,SV362: $i,SV462: $i] :
( ( ( ( SV462 != SV362 )
| ( in @ SV462 @ SV397 ) )
= $true )
| ( ( SV397
= ( singleton @ SV362 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(1997,plain,
! [SV362: $i,SV397: $i,SV463: $i] :
( ( ( ~ ( in @ SV463 @ SV397 )
| ( SV463 = SV362 ) )
= $true )
| ( ( SV397
= ( singleton @ SV362 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(1998,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
= $true )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(1999,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
| ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) ) )
= $false )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2000,plain,
! [SV426: $i,SV399: $i,SV297: $i] :
( ( ( ! [SY646: $i] :
( ~ ( in @ SY646 @ SV297 )
| ~ ( in @ SY646 @ SV399 )
| ( in @ SY646 @ SV426 ) ) )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1957]) ).
thf(2001,plain,
! [SV399: $i,SV297: $i,SV426: $i] :
( ( ( ~ ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV426 )
| ( in @ SY647 @ SV297 ) )
| ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV426 )
| ( in @ SY648 @ SV399 ) ) ) )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1958]) ).
thf(2002,plain,
! [SV427: $i,SV299: $i,SV438: $i,SV340: $i] :
( ( ( in @ SV340 @ SV438 )
= $false )
| ( ( in @ SV299 @ SV427 )
= $false )
| ( ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV427 @ SV438 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1959]) ).
thf(2003,plain,
! [SV464: $i,SV458: $i,SV340: $i,SV299: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV458 @ SV464 ) ) )
= $true )
| ( ( in @ SV299 @ SV458 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2004,plain,
! [SV461: $i,SV459: $i,SV340: $i,SV299: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV459 @ SV461 ) ) )
= $true )
| ( ( in @ SV340 @ SV461 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2005,plain,
! [SV450: $i,SV439: $i] :
( ( ( SV439 = SV450 )
= $false )
| ( ( proper_subset @ SV439 @ SV450 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2006,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV300 ) )
| ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV403 ) ) )
= $false )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2007,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
= $true )
| ( ( ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV300 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV403 ) )
= $true )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2008,plain,
! [SV404: $i,SV300: $i,SV429: $i] :
( ( ( ! [SY650: $i] :
( ~ ( in @ SY650 @ SV429 )
| ( SY650 = SV300 )
| ( SY650 = SV404 ) ) )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1966]) ).
thf(2009,plain,
! [SV404: $i,SV429: $i,SV300: $i] :
( ( ( ~ ( ~ ! [SY651: $i] :
( ( SY651 != SV300 )
| ( in @ SY651 @ SV429 ) )
| ~ ! [SY652: $i] :
( ( SY652 != SV404 )
| ( in @ SY652 @ SV429 ) ) ) )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1967]) ).
thf(2010,plain,
! [SV368: $i,SV407: $i] :
( ( ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
= $false )
| ( ( ~ ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 ) )
= $true )
| ( ( SV407
= ( powerset @ SV368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2011,plain,
! [SV369: $i,SV408: $i,SV465: $i] :
( ( ( ~ ( in @ SV465 @ SV408 )
| ( subset @ SV465 @ SV369 ) )
= $true )
| ( ( SV408
= ( powerset @ SV369 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2012,plain,
! [SV408: $i,SV369: $i,SV466: $i] :
( ( ( ~ ( subset @ SV466 @ SV369 )
| ( in @ SV466 @ SV408 ) )
= $true )
| ( ( SV408
= ( powerset @ SV369 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2013,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 ) )
| ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) ) )
= $false )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2014,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
= $true )
| ( ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 )
| ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) )
= $true )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2015,plain,
! [SV410: $i,SV302: $i,SV433: $i] :
( ( ( ! [SY655: $i] :
( ~ ( in @ SY655 @ SV433 )
| ( in @ SY655 @ SV302 )
| ( in @ SY655 @ SV410 ) ) )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2016,plain,
! [SV410: $i,SV433: $i,SV302: $i] :
( ( ( ~ ( ~ ! [SY656: $i] :
( ~ ( in @ SY656 @ SV302 )
| ( in @ SY656 @ SV433 ) )
| ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV410 )
| ( in @ SY657 @ SV433 ) ) ) )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1975]) ).
thf(2017,plain,
! [SV467: $i,SV370: $i,SV411: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV467 )
| ~ ( in @ SV467 @ SV370 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2018,plain,
! [SV370: $i,SV411: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ ( sK9_SY185 @ SV411 @ SV370 ) )
| ~ ( in @ ( sK9_SY185 @ SV411 @ SV370 ) @ SV370 ) )
= $false )
| ( ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2019,plain,
! [SV412: $i,SV371: $i,SV468: $i] :
( ( ( ! [SY671: $i] :
( ~ ( in @ SV468 @ SY671 )
| ~ ( in @ SY671 @ SV371 ) )
| ( in @ SV468 @ SV412 ) )
= $true )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2020,plain,
! [SV371: $i,SV412: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ SV412 )
| ~ ( ~ ( in @ SV469 @ ( sK7_D @ SV469 @ SV412 @ SV371 ) )
| ~ ( in @ ( sK7_D @ SV469 @ SV412 @ SV371 ) @ SV371 ) ) )
= $true )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2021,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
= $true )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2022,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) ) )
= $false )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2023,plain,
! [SV435: $i,SV414: $i,SV303: $i] :
( ( ( ! [SY658: $i] :
( ~ ( in @ SY658 @ SV303 )
| ( in @ SY658 @ SV414 )
| ( in @ SY658 @ SV435 ) ) )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1982]) ).
thf(2024,plain,
! [SV414: $i,SV303: $i,SV435: $i] :
( ( ( ~ ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV435 )
| ( in @ SY659 @ SV303 ) )
| ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV435 )
| ~ ( in @ SY660 @ SV414 ) ) ) )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1983]) ).
thf(2025,plain,
! [SV444: $i,SV418: $i,SV377: $i] :
( ( ( disjoint @ SV377 @ SV418 )
= $false )
| ( ( in @ SV444 @ SV377 )
= $false )
| ( ( in @ SV444 @ SV418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2026,plain,
! [SV423: $i,SV393: $i,SV296: $i,SV470: $i] :
( ( ( ! [SY672: $i] :
( ~ ( in @ SV470 @ SV296 )
| ~ ( in @ SY672 @ SV393 )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ SV470 @ SY672 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2027,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) @ SV393 ) )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) ) ) )
= $false )
| ( ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2028,plain,
! [SV424: $i,SV471: $i,SV394: $i,SV296: $i] :
( ( ( ! [SY673: $i,SY674: $i] :
( ~ ( in @ SY673 @ SV296 )
| ~ ( in @ SY674 @ SV394 )
| ( SV471
!= ( ordered_pair @ SY673 @ SY674 ) ) )
| ( in @ SV471 @ SV424 ) )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2029,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( ~ ( in @ SV472 @ SV424 )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV394 ) )
| ( SV472
!= ( ordered_pair @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) ) ) ) )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2030,plain,
! [SV361: $i,SV396: $i] :
( ( ( in @ ( sK21_C @ SV396 @ SV361 ) @ SV396 )
= $false )
| ( ( ( sK21_C @ SV396 @ SV361 )
= SV361 )
= $false )
| ( ( SV396
= ( singleton @ SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2031,plain,
! [SV397: $i,SV362: $i,SV462: $i] :
( ( ( ( SV462 != SV362 ) )
= $true )
| ( ( in @ SV462 @ SV397 )
= $true )
| ( ( SV397
= ( singleton @ SV362 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2032,plain,
! [SV362: $i,SV397: $i,SV463: $i] :
( ( ( ~ ( in @ SV463 @ SV397 ) )
= $true )
| ( ( SV463 = SV362 )
= $true )
| ( ( SV397
= ( singleton @ SV362 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2033,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
= $true )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1998]) ).
thf(2034,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) ) )
= $false )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2035,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) ) )
= $false )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2036,plain,
! [SV426: $i,SV399: $i,SV297: $i,SV473: $i] :
( ( ( ~ ( in @ SV473 @ SV297 )
| ~ ( in @ SV473 @ SV399 )
| ( in @ SV473 @ SV426 ) )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2037,plain,
! [SV399: $i,SV297: $i,SV426: $i] :
( ( ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV426 )
| ( in @ SY647 @ SV297 ) )
| ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV426 )
| ( in @ SY648 @ SV399 ) ) )
= $false )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2038,plain,
! [SV464: $i,SV458: $i,SV340: $i,SV299: $i] :
( ( ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV458 @ SV464 ) )
= $false )
| ( ( in @ SV299 @ SV458 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2039,plain,
! [SV461: $i,SV459: $i,SV340: $i,SV299: $i] :
( ( ( in @ ( ordered_pair @ SV299 @ SV340 ) @ ( cartesian_product2 @ SV459 @ SV461 ) )
= $false )
| ( ( in @ SV340 @ SV461 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2040,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV300 ) ) )
= $false )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2006]) ).
thf(2041,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV403 ) ) )
= $false )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2006]) ).
thf(2042,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV300 )
= $true )
| ( ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV403 )
= $true )
| ( ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
= $true )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2007]) ).
thf(2043,plain,
! [SV404: $i,SV300: $i,SV429: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ SV429 )
| ( SV474 = SV300 )
| ( SV474 = SV404 ) )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2044,plain,
! [SV404: $i,SV429: $i,SV300: $i] :
( ( ( ~ ! [SY651: $i] :
( ( SY651 != SV300 )
| ( in @ SY651 @ SV429 ) )
| ~ ! [SY652: $i] :
( ( SY652 != SV404 )
| ( in @ SY652 @ SV429 ) ) )
= $false )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2045,plain,
! [SV368: $i,SV407: $i] :
( ( ( subset @ ( sK19_C @ SV407 @ SV368 ) @ SV368 )
= $false )
| ( ( in @ ( sK19_C @ SV407 @ SV368 ) @ SV407 )
= $false )
| ( ( SV407
= ( powerset @ SV368 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2046,plain,
! [SV369: $i,SV408: $i,SV465: $i] :
( ( ( ~ ( in @ SV465 @ SV408 ) )
= $true )
| ( ( subset @ SV465 @ SV369 )
= $true )
| ( ( SV408
= ( powerset @ SV369 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2047,plain,
! [SV408: $i,SV369: $i,SV466: $i] :
( ( ( ~ ( subset @ SV466 @ SV369 ) )
= $true )
| ( ( in @ SV466 @ SV408 )
= $true )
| ( ( SV408
= ( powerset @ SV369 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2048,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 ) ) )
= $false )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2013]) ).
thf(2049,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) ) )
= $false )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2013]) ).
thf(2050,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 )
= $true )
| ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 )
= $true )
| ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
= $true )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2014]) ).
thf(2051,plain,
! [SV410: $i,SV302: $i,SV433: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV433 )
| ( in @ SV475 @ SV302 )
| ( in @ SV475 @ SV410 ) )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2052,plain,
! [SV410: $i,SV433: $i,SV302: $i] :
( ( ( ~ ! [SY656: $i] :
( ~ ( in @ SY656 @ SV302 )
| ( in @ SY656 @ SV433 ) )
| ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV410 )
| ( in @ SY657 @ SV433 ) ) )
= $false )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2053,plain,
! [SV467: $i,SV370: $i,SV411: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV467 ) )
= $true )
| ( ( ~ ( in @ SV467 @ SV370 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2054,plain,
! [SV370: $i,SV411: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ ( sK9_SY185 @ SV411 @ SV370 ) ) )
= $false )
| ( ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2018]) ).
thf(2055,plain,
! [SV370: $i,SV411: $i] :
( ( ( ~ ( in @ ( sK9_SY185 @ SV411 @ SV370 ) @ SV370 ) )
= $false )
| ( ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2018]) ).
thf(2056,plain,
! [SV412: $i,SV371: $i,SV468: $i] :
( ( ( ! [SY671: $i] :
( ~ ( in @ SV468 @ SY671 )
| ~ ( in @ SY671 @ SV371 ) ) )
= $true )
| ( ( in @ SV468 @ SV412 )
= $true )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2057,plain,
! [SV371: $i,SV412: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ SV412 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV469 @ ( sK7_D @ SV469 @ SV412 @ SV371 ) )
| ~ ( in @ ( sK7_D @ SV469 @ SV412 @ SV371 ) @ SV371 ) ) )
= $true )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2058,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 ) )
= $true )
| ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
= $true )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2021]) ).
thf(2059,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) ) )
= $false )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2022]) ).
thf(2060,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) ) )
= $false )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2022]) ).
thf(2061,plain,
! [SV435: $i,SV414: $i,SV303: $i,SV476: $i] :
( ( ( ~ ( in @ SV476 @ SV303 )
| ( in @ SV476 @ SV414 )
| ( in @ SV476 @ SV435 ) )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2062,plain,
! [SV414: $i,SV303: $i,SV435: $i] :
( ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV435 )
| ( in @ SY659 @ SV303 ) )
| ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV435 )
| ~ ( in @ SY660 @ SV414 ) ) )
= $false )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2024]) ).
thf(2063,plain,
! [SV423: $i,SV393: $i,SV477: $i,SV296: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ SV296 )
| ~ ( in @ SV477 @ SV393 )
| ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ SV470 @ SV477 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2064,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) @ SV393 ) ) )
= $false )
| ( ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2027]) ).
thf(2065,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) ) ) )
= $false )
| ( ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2027]) ).
thf(2066,plain,
! [SV424: $i,SV471: $i,SV394: $i,SV296: $i] :
( ( ( ! [SY673: $i,SY674: $i] :
( ~ ( in @ SY673 @ SV296 )
| ~ ( in @ SY674 @ SV394 )
| ( SV471
!= ( ordered_pair @ SY673 @ SY674 ) ) ) )
= $true )
| ( ( in @ SV471 @ SV424 )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2028]) ).
thf(2067,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( ~ ( in @ SV472 @ SV424 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV394 ) )
| ( SV472
!= ( ordered_pair @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) ) ) ) )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2029]) ).
thf(2068,plain,
! [SV397: $i,SV362: $i,SV462: $i] :
( ( ( SV462 = SV362 )
= $false )
| ( ( in @ SV462 @ SV397 )
= $true )
| ( ( SV397
= ( singleton @ SV362 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2069,plain,
! [SV362: $i,SV397: $i,SV463: $i] :
( ( ( in @ SV463 @ SV397 )
= $false )
| ( ( SV463 = SV362 )
= $true )
| ( ( SV397
= ( singleton @ SV362 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2032]) ).
thf(2070,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
= $false )
| ( ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 ) )
= $true )
| ( ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
= $true )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2071,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
= $true )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2034]) ).
thf(2072,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
| ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
= $true )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2035]) ).
thf(2073,plain,
! [SV426: $i,SV399: $i,SV297: $i,SV473: $i] :
( ( ( ~ ( in @ SV473 @ SV297 )
| ~ ( in @ SV473 @ SV399 ) )
= $true )
| ( ( in @ SV473 @ SV426 )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2036]) ).
thf(2074,plain,
! [SV399: $i,SV297: $i,SV426: $i] :
( ( ( ~ ! [SY647: $i] :
( ~ ( in @ SY647 @ SV426 )
| ( in @ SY647 @ SV297 ) ) )
= $false )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2075,plain,
! [SV297: $i,SV399: $i,SV426: $i] :
( ( ( ~ ! [SY648: $i] :
( ~ ( in @ SY648 @ SV426 )
| ( in @ SY648 @ SV399 ) ) )
= $false )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2076,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV300 ) )
= $true )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2040]) ).
thf(2077,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
| ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV403 ) )
= $true )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2041]) ).
thf(2078,plain,
! [SV404: $i,SV300: $i,SV429: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ SV429 ) )
= $true )
| ( ( ( SV474 = SV300 )
| ( SV474 = SV404 ) )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2079,plain,
! [SV404: $i,SV429: $i,SV300: $i] :
( ( ( ~ ! [SY651: $i] :
( ( SY651 != SV300 )
| ( in @ SY651 @ SV429 ) ) )
= $false )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2044]) ).
thf(2080,plain,
! [SV300: $i,SV429: $i,SV404: $i] :
( ( ( ~ ! [SY652: $i] :
( ( SY652 != SV404 )
| ( in @ SY652 @ SV429 ) ) )
= $false )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2044]) ).
thf(2081,plain,
! [SV369: $i,SV408: $i,SV465: $i] :
( ( ( in @ SV465 @ SV408 )
= $false )
| ( ( subset @ SV465 @ SV369 )
= $true )
| ( ( SV408
= ( powerset @ SV369 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2082,plain,
! [SV408: $i,SV369: $i,SV466: $i] :
( ( ( subset @ SV466 @ SV369 )
= $false )
| ( ( in @ SV466 @ SV408 )
= $true )
| ( ( SV408
= ( powerset @ SV369 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2083,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 ) )
= $true )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2048]) ).
thf(2084,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
| ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) )
= $true )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2049]) ).
thf(2085,plain,
! [SV410: $i,SV302: $i,SV433: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV433 ) )
= $true )
| ( ( ( in @ SV475 @ SV302 )
| ( in @ SV475 @ SV410 ) )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2051]) ).
thf(2086,plain,
! [SV410: $i,SV433: $i,SV302: $i] :
( ( ( ~ ! [SY656: $i] :
( ~ ( in @ SY656 @ SV302 )
| ( in @ SY656 @ SV433 ) ) )
= $false )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2052]) ).
thf(2087,plain,
! [SV302: $i,SV433: $i,SV410: $i] :
( ( ( ~ ! [SY657: $i] :
( ~ ( in @ SY657 @ SV410 )
| ( in @ SY657 @ SV433 ) ) )
= $false )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2052]) ).
thf(2088,plain,
! [SV467: $i,SV370: $i,SV411: $i] :
( ( ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV467 )
= $false )
| ( ( ~ ( in @ SV467 @ SV370 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2089,plain,
! [SV370: $i,SV411: $i] :
( ( ( in @ ( sK8_C @ SV411 @ SV370 ) @ ( sK9_SY185 @ SV411 @ SV370 ) )
= $true )
| ( ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2090,plain,
! [SV370: $i,SV411: $i] :
( ( ( in @ ( sK9_SY185 @ SV411 @ SV370 ) @ SV370 )
= $true )
| ( ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2055]) ).
thf(2091,plain,
! [SV412: $i,SV371: $i,SV478: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV478 )
| ~ ( in @ SV478 @ SV371 ) )
= $true )
| ( ( in @ SV468 @ SV412 )
= $true )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2092,plain,
! [SV371: $i,SV412: $i,SV469: $i] :
( ( ( in @ SV469 @ SV412 )
= $false )
| ( ( ~ ( ~ ( in @ SV469 @ ( sK7_D @ SV469 @ SV412 @ SV371 ) )
| ~ ( in @ ( sK7_D @ SV469 @ SV412 @ SV371 ) @ SV371 ) ) )
= $true )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2093,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
= $false )
| ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
= $true )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2058]) ).
thf(2094,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
= $true )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2059]) ).
thf(2095,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
| ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 ) )
= $true )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2060]) ).
thf(2096,plain,
! [SV435: $i,SV414: $i,SV303: $i,SV476: $i] :
( ( ( ~ ( in @ SV476 @ SV303 )
| ( in @ SV476 @ SV414 ) )
= $true )
| ( ( in @ SV476 @ SV435 )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2097,plain,
! [SV414: $i,SV303: $i,SV435: $i] :
( ( ( ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV435 )
| ( in @ SY659 @ SV303 ) ) )
= $false )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2062]) ).
thf(2098,plain,
! [SV303: $i,SV414: $i,SV435: $i] :
( ( ( ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV435 )
| ~ ( in @ SY660 @ SV414 ) ) )
= $false )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2062]) ).
thf(2099,plain,
! [SV423: $i,SV393: $i,SV477: $i,SV296: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ SV296 )
| ~ ( in @ SV477 @ SV393 ) )
= $true )
| ( ( ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ SV470 @ SV477 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2100,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) @ SV393 ) ) )
= $true )
| ( ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2101,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( ( sK14_D @ SV423 @ SV393 @ SV296 )
= ( ordered_pair @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) ) )
= $true )
| ( ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2065]) ).
thf(2102,plain,
! [SV424: $i,SV471: $i,SV394: $i,SV296: $i,SV479: $i] :
( ( ( ! [SY675: $i] :
( ~ ( in @ SV479 @ SV296 )
| ~ ( in @ SY675 @ SV394 )
| ( SV471
!= ( ordered_pair @ SV479 @ SY675 ) ) ) )
= $true )
| ( ( in @ SV471 @ SV424 )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2103,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( in @ SV472 @ SV424 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV394 ) )
| ( SV472
!= ( ordered_pair @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) ) ) ) )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2104,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
= $false )
| ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
= $false )
| ( ( ~ ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 ) )
= $true )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2105,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
= $true )
| ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 )
= $true )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2106,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
= $true )
| ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 )
= $true )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2072]) ).
thf(2107,plain,
! [SV426: $i,SV399: $i,SV297: $i,SV473: $i] :
( ( ( ~ ( in @ SV473 @ SV297 ) )
= $true )
| ( ( ~ ( in @ SV473 @ SV399 ) )
= $true )
| ( ( in @ SV473 @ SV426 )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2073]) ).
thf(2108,plain,
! [SV399: $i,SV297: $i,SV426: $i] :
( ( ( ! [SY647: $i] :
( ~ ( in @ SY647 @ SV426 )
| ( in @ SY647 @ SV297 ) ) )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2074]) ).
thf(2109,plain,
! [SV297: $i,SV399: $i,SV426: $i] :
( ( ( ! [SY648: $i] :
( ~ ( in @ SY648 @ SV426 )
| ( in @ SY648 @ SV399 ) ) )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2075]) ).
thf(2110,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 ) )
= $true )
| ( ( ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV300 ) )
= $true )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2111,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ~ ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 ) )
= $true )
| ( ( ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV403 ) )
= $true )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2077]) ).
thf(2112,plain,
! [SV404: $i,SV300: $i,SV429: $i,SV474: $i] :
( ( ( in @ SV474 @ SV429 )
= $false )
| ( ( ( SV474 = SV300 )
| ( SV474 = SV404 ) )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2113,plain,
! [SV404: $i,SV429: $i,SV300: $i] :
( ( ( ! [SY651: $i] :
( ( SY651 != SV300 )
| ( in @ SY651 @ SV429 ) ) )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2079]) ).
thf(2114,plain,
! [SV300: $i,SV429: $i,SV404: $i] :
( ( ( ! [SY652: $i] :
( ( SY652 != SV404 )
| ( in @ SY652 @ SV429 ) ) )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2080]) ).
thf(2115,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 ) )
= $true )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2083]) ).
thf(2116,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 ) )
= $true )
| ( ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) )
= $true )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2084]) ).
thf(2117,plain,
! [SV410: $i,SV302: $i,SV433: $i,SV475: $i] :
( ( ( in @ SV475 @ SV433 )
= $false )
| ( ( ( in @ SV475 @ SV302 )
| ( in @ SV475 @ SV410 ) )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2085]) ).
thf(2118,plain,
! [SV410: $i,SV433: $i,SV302: $i] :
( ( ( ! [SY656: $i] :
( ~ ( in @ SY656 @ SV302 )
| ( in @ SY656 @ SV433 ) ) )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2086]) ).
thf(2119,plain,
! [SV302: $i,SV433: $i,SV410: $i] :
( ( ( ! [SY657: $i] :
( ~ ( in @ SY657 @ SV410 )
| ( in @ SY657 @ SV433 ) ) )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2087]) ).
thf(2120,plain,
! [SV411: $i,SV370: $i,SV467: $i] :
( ( ( in @ SV467 @ SV370 )
= $false )
| ( ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV467 )
= $false )
| ( ( ~ ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 ) )
= $true )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2088]) ).
thf(2121,plain,
! [SV412: $i,SV371: $i,SV478: $i,SV468: $i] :
( ( ( ~ ( in @ SV468 @ SV478 ) )
= $true )
| ( ( ~ ( in @ SV478 @ SV371 ) )
= $true )
| ( ( in @ SV468 @ SV412 )
= $true )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2122,plain,
! [SV371: $i,SV412: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ ( sK7_D @ SV469 @ SV412 @ SV371 ) )
| ~ ( in @ ( sK7_D @ SV469 @ SV412 @ SV371 ) @ SV371 ) )
= $false )
| ( ( in @ SV469 @ SV412 )
= $false )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2123,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 )
= $false )
| ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
= $true )
| ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
= $false )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2124,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV303 )
= $true )
| ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 )
= $true )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2094]) ).
thf(2125,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 ) )
= $true )
| ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 )
= $true )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2126,plain,
! [SV435: $i,SV414: $i,SV303: $i,SV476: $i] :
( ( ( ~ ( in @ SV476 @ SV303 ) )
= $true )
| ( ( in @ SV476 @ SV414 )
= $true )
| ( ( in @ SV476 @ SV435 )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2096]) ).
thf(2127,plain,
! [SV414: $i,SV303: $i,SV435: $i] :
( ( ( ! [SY659: $i] :
( ~ ( in @ SY659 @ SV435 )
| ( in @ SY659 @ SV303 ) ) )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2097]) ).
thf(2128,plain,
! [SV303: $i,SV414: $i,SV435: $i] :
( ( ( ! [SY660: $i] :
( ~ ( in @ SY660 @ SV435 )
| ~ ( in @ SY660 @ SV414 ) ) )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2098]) ).
thf(2129,plain,
! [SV423: $i,SV393: $i,SV477: $i,SV296: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ SV296 ) )
= $true )
| ( ( ~ ( in @ SV477 @ SV393 ) )
= $true )
| ( ( ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ SV470 @ SV477 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2099]) ).
thf(2130,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( ~ ( in @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) @ SV393 ) )
= $false )
| ( ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2131,plain,
! [SV424: $i,SV471: $i,SV394: $i,SV480: $i,SV296: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ SV296 )
| ~ ( in @ SV480 @ SV394 )
| ( SV471
!= ( ordered_pair @ SV479 @ SV480 ) ) )
= $true )
| ( ( in @ SV471 @ SV424 )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2132,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV394 ) )
| ( SV472
!= ( ordered_pair @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) ) ) )
= $false )
| ( ( in @ SV472 @ SV424 )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2133,plain,
! [SV297: $i,SV398: $i,SV425: $i] :
( ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV425 )
= $false )
| ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV297 )
= $false )
| ( ( in @ ( sK10_D @ SV425 @ SV398 @ SV297 ) @ SV398 )
= $false )
| ( ( SV425
= ( set_intersection2 @ SV297 @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2104]) ).
thf(2134,plain,
! [SV426: $i,SV399: $i,SV297: $i,SV473: $i] :
( ( ( in @ SV473 @ SV297 )
= $false )
| ( ( ~ ( in @ SV473 @ SV399 ) )
= $true )
| ( ( in @ SV473 @ SV426 )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2135,plain,
! [SV399: $i,SV297: $i,SV426: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ SV426 )
| ( in @ SV481 @ SV297 ) )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2136,plain,
! [SV297: $i,SV399: $i,SV426: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV426 )
| ( in @ SV482 @ SV399 ) )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2137,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
= $false )
| ( ( ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV300 ) )
= $true )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2138,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
= $false )
| ( ( ( ( sK18_D @ SV428 @ SV403 @ SV300 )
!= SV403 ) )
= $true )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2139,plain,
! [SV429: $i,SV404: $i,SV300: $i,SV474: $i] :
( ( ( SV474 = SV300 )
= $true )
| ( ( SV474 = SV404 )
= $true )
| ( ( in @ SV474 @ SV429 )
= $false )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2112]) ).
thf(2140,plain,
! [SV404: $i,SV429: $i,SV300: $i,SV483: $i] :
( ( ( ( SV483 != SV300 )
| ( in @ SV483 @ SV429 ) )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2141,plain,
! [SV300: $i,SV429: $i,SV404: $i,SV484: $i] :
( ( ( ( SV484 != SV404 )
| ( in @ SV484 @ SV429 ) )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2142,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
= $false )
| ( ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 ) )
= $true )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2115]) ).
thf(2143,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
= $false )
| ( ( ~ ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 ) )
= $true )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2144,plain,
! [SV433: $i,SV410: $i,SV302: $i,SV475: $i] :
( ( ( in @ SV475 @ SV302 )
= $true )
| ( ( in @ SV475 @ SV410 )
= $true )
| ( ( in @ SV475 @ SV433 )
= $false )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2117]) ).
thf(2145,plain,
! [SV410: $i,SV433: $i,SV302: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ SV302 )
| ( in @ SV485 @ SV433 ) )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2146,plain,
! [SV302: $i,SV433: $i,SV410: $i,SV486: $i] :
( ( ( ~ ( in @ SV486 @ SV410 )
| ( in @ SV486 @ SV433 ) )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2147,plain,
! [SV467: $i,SV370: $i,SV411: $i] :
( ( ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV411 )
= $false )
| ( ( in @ ( sK8_C @ SV411 @ SV370 ) @ SV467 )
= $false )
| ( ( in @ SV467 @ SV370 )
= $false )
| ( ( SV411
= ( union @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2148,plain,
! [SV412: $i,SV371: $i,SV478: $i,SV468: $i] :
( ( ( in @ SV468 @ SV478 )
= $false )
| ( ( ~ ( in @ SV478 @ SV371 ) )
= $true )
| ( ( in @ SV468 @ SV412 )
= $true )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2149,plain,
! [SV371: $i,SV412: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ ( sK7_D @ SV469 @ SV412 @ SV371 ) ) )
= $false )
| ( ( in @ SV469 @ SV412 )
= $false )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2122]) ).
thf(2150,plain,
! [SV371: $i,SV412: $i,SV469: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV469 @ SV412 @ SV371 ) @ SV371 ) )
= $false )
| ( ( in @ SV469 @ SV412 )
= $false )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2122]) ).
thf(2151,plain,
! [SV303: $i,SV413: $i,SV434: $i] :
( ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV413 )
= $false )
| ( ( in @ ( sK6_D @ SV434 @ SV413 @ SV303 ) @ SV434 )
= $true )
| ( ( SV434
= ( set_difference @ SV303 @ SV413 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2152,plain,
! [SV435: $i,SV414: $i,SV303: $i,SV476: $i] :
( ( ( in @ SV476 @ SV303 )
= $false )
| ( ( in @ SV476 @ SV414 )
= $true )
| ( ( in @ SV476 @ SV435 )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2153,plain,
! [SV414: $i,SV303: $i,SV435: $i,SV487: $i] :
( ( ( ~ ( in @ SV487 @ SV435 )
| ( in @ SV487 @ SV303 ) )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2154,plain,
! [SV303: $i,SV414: $i,SV435: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV435 )
| ~ ( in @ SV488 @ SV414 ) )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2155,plain,
! [SV423: $i,SV393: $i,SV477: $i,SV296: $i,SV470: $i] :
( ( ( in @ SV470 @ SV296 )
= $false )
| ( ( ~ ( in @ SV477 @ SV393 ) )
= $true )
| ( ( ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ SV470 @ SV477 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2156,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( ~ ( in @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ SV296 ) )
= $false )
| ( ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2130]) ).
thf(2157,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( ~ ( in @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) @ SV393 ) )
= $false )
| ( ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2130]) ).
thf(2158,plain,
! [SV424: $i,SV471: $i,SV394: $i,SV480: $i,SV296: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ SV296 )
| ~ ( in @ SV480 @ SV394 ) )
= $true )
| ( ( ( SV471
!= ( ordered_pair @ SV479 @ SV480 ) ) )
= $true )
| ( ( in @ SV471 @ SV424 )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2131]) ).
thf(2159,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV394 ) ) )
= $false )
| ( ( in @ SV472 @ SV424 )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2160,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( ( SV472
!= ( ordered_pair @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) ) ) )
= $false )
| ( ( in @ SV472 @ SV424 )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2161,plain,
! [SV426: $i,SV297: $i,SV399: $i,SV473: $i] :
( ( ( in @ SV473 @ SV399 )
= $false )
| ( ( in @ SV473 @ SV297 )
= $false )
| ( ( in @ SV473 @ SV426 )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2162,plain,
! [SV399: $i,SV297: $i,SV426: $i,SV481: $i] :
( ( ( ~ ( in @ SV481 @ SV426 ) )
= $true )
| ( ( in @ SV481 @ SV297 )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2135]) ).
thf(2163,plain,
! [SV297: $i,SV399: $i,SV426: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV426 ) )
= $true )
| ( ( in @ SV482 @ SV399 )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2164,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV300 )
= $false )
| ( ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
= $false )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2165,plain,
! [SV300: $i,SV403: $i,SV428: $i] :
( ( ( ( sK18_D @ SV428 @ SV403 @ SV300 )
= SV403 )
= $false )
| ( ( in @ ( sK18_D @ SV428 @ SV403 @ SV300 ) @ SV428 )
= $false )
| ( ( SV428
= ( unordered_pair @ SV300 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2166,plain,
! [SV404: $i,SV429: $i,SV300: $i,SV483: $i] :
( ( ( ( SV483 != SV300 ) )
= $true )
| ( ( in @ SV483 @ SV429 )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2167,plain,
! [SV300: $i,SV429: $i,SV404: $i,SV484: $i] :
( ( ( ( SV484 != SV404 ) )
= $true )
| ( ( in @ SV484 @ SV429 )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2141]) ).
thf(2168,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV302 )
= $false )
| ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
= $false )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2169,plain,
! [SV302: $i,SV409: $i,SV432: $i] :
( ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV409 )
= $false )
| ( ( in @ ( sK17_D @ SV432 @ SV409 @ SV302 ) @ SV432 )
= $false )
| ( ( SV432
= ( set_union2 @ SV302 @ SV409 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2170,plain,
! [SV410: $i,SV433: $i,SV302: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ SV302 ) )
= $true )
| ( ( in @ SV485 @ SV433 )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2171,plain,
! [SV302: $i,SV433: $i,SV410: $i,SV486: $i] :
( ( ( ~ ( in @ SV486 @ SV410 ) )
= $true )
| ( ( in @ SV486 @ SV433 )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2172,plain,
! [SV412: $i,SV468: $i,SV371: $i,SV478: $i] :
( ( ( in @ SV478 @ SV371 )
= $false )
| ( ( in @ SV468 @ SV478 )
= $false )
| ( ( in @ SV468 @ SV412 )
= $true )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2148]) ).
thf(2173,plain,
! [SV371: $i,SV412: $i,SV469: $i] :
( ( ( in @ SV469 @ ( sK7_D @ SV469 @ SV412 @ SV371 ) )
= $true )
| ( ( in @ SV469 @ SV412 )
= $false )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2149]) ).
thf(2174,plain,
! [SV371: $i,SV412: $i,SV469: $i] :
( ( ( in @ ( sK7_D @ SV469 @ SV412 @ SV371 ) @ SV371 )
= $true )
| ( ( in @ SV469 @ SV412 )
= $false )
| ( ( SV412
= ( union @ SV371 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2150]) ).
thf(2175,plain,
! [SV414: $i,SV303: $i,SV435: $i,SV487: $i] :
( ( ( ~ ( in @ SV487 @ SV435 ) )
= $true )
| ( ( in @ SV487 @ SV303 )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2176,plain,
! [SV303: $i,SV414: $i,SV435: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV435 ) )
= $true )
| ( ( ~ ( in @ SV488 @ SV414 ) )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2177,plain,
! [SV423: $i,SV296: $i,SV470: $i,SV393: $i,SV477: $i] :
( ( ( in @ SV477 @ SV393 )
= $false )
| ( ( in @ SV470 @ SV296 )
= $false )
| ( ( ( ( sK14_D @ SV423 @ SV393 @ SV296 )
!= ( ordered_pair @ SV470 @ SV477 ) ) )
= $true )
| ( ( ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2178,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( in @ ( sK15_SY189 @ SV423 @ SV393 @ SV296 ) @ SV296 )
= $true )
| ( ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2156]) ).
thf(2179,plain,
! [SV296: $i,SV393: $i,SV423: $i] :
( ( ( in @ ( sK16_SY191 @ SV423 @ SV393 @ SV296 ) @ SV393 )
= $true )
| ( ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2157]) ).
thf(2180,plain,
! [SV424: $i,SV471: $i,SV394: $i,SV480: $i,SV296: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ SV296 ) )
= $true )
| ( ( ~ ( in @ SV480 @ SV394 ) )
= $true )
| ( ( ( SV471
!= ( ordered_pair @ SV479 @ SV480 ) ) )
= $true )
| ( ( in @ SV471 @ SV424 )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2181,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV394 ) ) )
= $true )
| ( ( in @ SV472 @ SV424 )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2159]) ).
thf(2182,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( SV472
= ( ordered_pair @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) ) )
= $true )
| ( ( in @ SV472 @ SV424 )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2160]) ).
thf(2183,plain,
! [SV399: $i,SV297: $i,SV426: $i,SV481: $i] :
( ( ( in @ SV481 @ SV426 )
= $false )
| ( ( in @ SV481 @ SV297 )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2184,plain,
! [SV297: $i,SV399: $i,SV426: $i,SV482: $i] :
( ( ( in @ SV482 @ SV426 )
= $false )
| ( ( in @ SV482 @ SV399 )
= $true )
| ( ( SV426
= ( set_intersection2 @ SV297 @ SV399 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2185,plain,
! [SV404: $i,SV429: $i,SV300: $i,SV483: $i] :
( ( ( SV483 = SV300 )
= $false )
| ( ( in @ SV483 @ SV429 )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2186,plain,
! [SV300: $i,SV429: $i,SV404: $i,SV484: $i] :
( ( ( SV484 = SV404 )
= $false )
| ( ( in @ SV484 @ SV429 )
= $true )
| ( ( SV429
= ( unordered_pair @ SV300 @ SV404 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2187,plain,
! [SV410: $i,SV433: $i,SV302: $i,SV485: $i] :
( ( ( in @ SV485 @ SV302 )
= $false )
| ( ( in @ SV485 @ SV433 )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2188,plain,
! [SV302: $i,SV433: $i,SV410: $i,SV486: $i] :
( ( ( in @ SV486 @ SV410 )
= $false )
| ( ( in @ SV486 @ SV433 )
= $true )
| ( ( SV433
= ( set_union2 @ SV302 @ SV410 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2189,plain,
! [SV414: $i,SV303: $i,SV435: $i,SV487: $i] :
( ( ( in @ SV487 @ SV435 )
= $false )
| ( ( in @ SV487 @ SV303 )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2190,plain,
! [SV303: $i,SV414: $i,SV435: $i,SV488: $i] :
( ( ( in @ SV488 @ SV435 )
= $false )
| ( ( ~ ( in @ SV488 @ SV414 ) )
= $true )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2176]) ).
thf(2191,plain,
! [SV477: $i,SV470: $i,SV296: $i,SV393: $i,SV423: $i] :
( ( ( ( sK14_D @ SV423 @ SV393 @ SV296 )
= ( ordered_pair @ SV470 @ SV477 ) )
= $false )
| ( ( in @ SV470 @ SV296 )
= $false )
| ( ( in @ SV477 @ SV393 )
= $false )
| ( ( ~ ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 ) )
= $true )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2192,plain,
! [SV424: $i,SV471: $i,SV394: $i,SV480: $i,SV296: $i,SV479: $i] :
( ( ( in @ SV479 @ SV296 )
= $false )
| ( ( ~ ( in @ SV480 @ SV394 ) )
= $true )
| ( ( ( SV471
!= ( ordered_pair @ SV479 @ SV480 ) ) )
= $true )
| ( ( in @ SV471 @ SV424 )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2193,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( ~ ( in @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV394 ) )
= $false )
| ( ( in @ SV472 @ SV424 )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2194,plain,
! [SV303: $i,SV435: $i,SV414: $i,SV488: $i] :
( ( ( in @ SV488 @ SV414 )
= $false )
| ( ( in @ SV488 @ SV435 )
= $false )
| ( ( SV435
= ( set_difference @ SV303 @ SV414 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2195,plain,
! [SV470: $i,SV477: $i,SV296: $i,SV393: $i,SV423: $i] :
( ( ( in @ ( sK14_D @ SV423 @ SV393 @ SV296 ) @ SV423 )
= $false )
| ( ( in @ SV477 @ SV393 )
= $false )
| ( ( in @ SV470 @ SV296 )
= $false )
| ( ( ( sK14_D @ SV423 @ SV393 @ SV296 )
= ( ordered_pair @ SV470 @ SV477 ) )
= $false )
| ( ( SV423
= ( cartesian_product2 @ SV296 @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2196,plain,
! [SV424: $i,SV471: $i,SV296: $i,SV479: $i,SV394: $i,SV480: $i] :
( ( ( in @ SV480 @ SV394 )
= $false )
| ( ( in @ SV479 @ SV296 )
= $false )
| ( ( ( SV471
!= ( ordered_pair @ SV479 @ SV480 ) ) )
= $true )
| ( ( in @ SV471 @ SV424 )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2197,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( ~ ( in @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV296 ) )
= $false )
| ( ( in @ SV472 @ SV424 )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2193]) ).
thf(2198,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( ~ ( in @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV394 ) )
= $false )
| ( ( in @ SV472 @ SV424 )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2193]) ).
thf(2199,plain,
! [SV424: $i,SV394: $i,SV296: $i,SV480: $i,SV479: $i,SV471: $i] :
( ( ( SV471
= ( ordered_pair @ SV479 @ SV480 ) )
= $false )
| ( ( in @ SV479 @ SV296 )
= $false )
| ( ( in @ SV480 @ SV394 )
= $false )
| ( ( in @ SV471 @ SV424 )
= $true )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2196]) ).
thf(2200,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( in @ ( sK12_E @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV296 )
= $true )
| ( ( in @ SV472 @ SV424 )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2197]) ).
thf(2201,plain,
! [SV296: $i,SV394: $i,SV424: $i,SV472: $i] :
( ( ( in @ ( sK13_SY186 @ SV472 @ SV424 @ SV394 @ SV296 ) @ SV394 )
= $true )
| ( ( in @ SV472 @ SV424 )
= $false )
| ( ( SV424
= ( cartesian_product2 @ SV296 @ SV394 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2198]) ).
thf(2202,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1244,2201,2200,2199,2195,2194,2189,2188,2187,2186,2185,2184,2183,2182,2179,2178,2174,2173,2172,2169,2168,2165,2164,2161,2152,2151,2147,2144,2139,2133,2124,2123,2106,2105,2101,2090,2089,2082,2081,2069,2068,2050,2045,2042,2039,2038,2030,2025,2005,2002,1990,1989,1988,1987,1986,1985,1969,1963,1952,1950,1949,1942,1939,1936,1934,1933,1922,1921,1916,1907,1882,1864,1852,1839,1838,1823,1822,1815,1804,1803,1802,1801,1800,1799,1798,1797,1793,1792,1791,1790,1789,1767,1735,1729,1718,1674,1673,1672,1671,1670,1667,1666,1665,1660,1618,1617,1606,1605,1604,1598,1595,1593,1589,1587,1584,1532,1528,1518,1508,1458,1454,1453,1452,1451,1445,1441,1439,1437,1436,1430,1422,1392,1391,1390,1389,1387,1386,1384,1383,1368,1358,1306,1299,1298,1297,1296,1295,1294,1293,1292,1291,1290,1289]) ).
thf(2203,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2202,1228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU160+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sun Jun 19 02:18:55 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.38 ..
% 0.21/0.40
% 0.21/0.40 No.of.Axioms: 89
% 0.21/0.40
% 0.21/0.40 Length.of.Defs: 0
% 0.21/0.40
% 0.21/0.40 Contains.Choice.Funs: false
% 0.21/0.44 ..
% 0.21/0.45 (rf:0,axioms:89,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:91,loop_count:0,foatp_calls:0,translation:fof_full).............................................................................................................................................
% 1.03/1.27
% 1.03/1.27 ********************************
% 1.03/1.27 * All subproblems solved! *
% 1.03/1.27 ********************************
% 1.03/1.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:89,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:2202,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.24/2.40
% 2.24/2.40 %**** Beginning of derivation protocol ****
% 2.24/2.40 % SZS output start CNFRefutation
% See solution above
% 2.24/2.41
% 2.24/2.41 %**** End of derivation protocol ****
% 2.24/2.41 %**** no. of clauses in derivation: 2203 ****
% 2.24/2.41 %**** clause counter: 2202 ****
% 2.24/2.41
% 2.24/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:89,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:2202,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------