TSTP Solution File: SEU169+2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU169+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 : n027.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 12:07:32 EDT 2022
% Result : Theorem 3.68s 3.86s
% Output : CNFRefutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 138
% Syntax : Number of formulae : 1493 ( 803 unt; 46 typ; 0 def)
% Number of atoms : 9503 (3529 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 21083 (3775 ~;3276 |; 256 &;13622 @)
% ( 70 <=>; 84 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 46 usr; 8 con; 0-4 aty)
% Number of variables : 4482 ( 0 ^4460 !; 22 ?;4482 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_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_B,type,
sK10_B: $i > $i ).
thf(tp_sK11_D,type,
sK11_D: $i > $i > $i > $i ).
thf(tp_sK12_D,type,
sK12_D: $i > $i > $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_SY232,type,
sK14_SY232: $i > $i > $i ).
thf(tp_sK15_D,type,
sK15_D: $i > $i > $i > $i ).
thf(tp_sK16_C,type,
sK16_C: $i > $i > $i ).
thf(tp_sK17_E,type,
sK17_E: $i > $i > $i > $i > $i ).
thf(tp_sK18_SY233,type,
sK18_SY233: $i > $i > $i > $i > $i ).
thf(tp_sK19_D,type,
sK19_D: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY236,type,
sK20_SY236: $i > $i > $i > $i ).
thf(tp_sK21_SY238,type,
sK21_SY238: $i > $i > $i > $i ).
thf(tp_sK22_D,type,
sK22_D: $i > $i > $i > $i ).
thf(tp_sK23_D,type,
sK23_D: $i > $i > $i > $i ).
thf(tp_sK24_C,type,
sK24_C: $i > $i > $i ).
thf(tp_sK25_B,type,
sK25_B: $i > $i ).
thf(tp_sK26_C,type,
sK26_C: $i > $i > $i ).
thf(tp_sK27_C,type,
sK27_C: $i > $i > $i ).
thf(tp_sK28_C,type,
sK28_C: $i > $i > $i ).
thf(tp_sK29_B,type,
sK29_B: $i > $i ).
thf(tp_sK2_SY221,type,
sK2_SY221: $i ).
thf(tp_sK3_SY223,type,
sK3_SY223: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $i ).
thf(tp_sK7_SY226,type,
sK7_SY226: $i > $i > $i ).
thf(tp_sK8_C,type,
sK8_C: $i > $i > $i ).
thf(tp_sK9_B,type,
sK9_B: $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] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(4,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(5,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(6,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(8,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(9,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(11,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(12,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(13,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(14,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(21,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(22,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(23,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(47,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(56,axiom,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(61,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(63,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(66,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(72,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ ( unordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ C )
& ( in @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(79,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(82,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(85,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(88,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(89,axiom,
! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(97,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(102,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(103,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(104,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(105,conjecture,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
thf(106,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[105]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[106]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(109,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(110,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(111,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(112,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(113,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(115,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(116,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(117,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(120,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(121,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(122,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(123,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(125,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(126,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(127,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(128,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(131,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(132,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(133,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)],[59]) ).
thf(134,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(135,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(137,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(138,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(139,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(141,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(142,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(143,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(144,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(145,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(146,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(147,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(148,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)],[80]) ).
thf(149,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)],[81]) ).
thf(150,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(151,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(152,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)],[84]) ).
thf(153,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(154,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)],[87]) ).
thf(155,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(156,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(157,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(158,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(159,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)],[93]) ).
thf(160,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(161,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)],[98]) ).
thf(162,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(163,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(164,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ! [E: $i] :
( ( subset @ E @ C )
=> ( in @ E @ D ) ) ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(165,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(166,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(167,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(168,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(169,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(170,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)],[38]) ).
thf(171,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)],[39]) ).
thf(172,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)],[40]) ).
thf(173,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(174,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)],[42]) ).
thf(175,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)],[43]) ).
thf(176,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)],[44]) ).
thf(177,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(178,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(179,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(180,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(181,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(182,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(183,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(184,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
= A )
<=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(185,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)],[67]) ).
thf(186,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(187,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)],[73]) ).
thf(188,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)],[76]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(190,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(191,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( in @ A @ B )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( subset @ D @ C ) )
=> ( in @ D @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ( in @ ( powerset @ C ) @ B ) )
& ! [C: $i] :
~ ( ( subset @ C @ B )
& ~ ( are_equipotent @ C @ B )
& ~ ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(192,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)],[94]) ).
thf(193,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)],[95]) ).
thf(194,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(195,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(196,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(197,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(198,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(199,plain,
( ( ! [SY221: $i] :
( ( element @ SY221 @ ( powerset @ sK1_A ) )
=> ! [SY222: $i] :
( ( in @ SY222 @ SY221 )
=> ( in @ SY222 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[107]) ).
thf(200,plain,
( ( ( element @ sK2_SY221 @ ( powerset @ sK1_A ) )
=> ! [SY223: $i] :
( ( in @ SY223 @ sK2_SY221 )
=> ( in @ SY223 @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[199]) ).
thf(201,plain,
( ( element @ sK2_SY221 @ ( powerset @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[200]) ).
thf(202,plain,
( ( ! [SY223: $i] :
( ( in @ SY223 @ sK2_SY221 )
=> ( in @ SY223 @ sK1_A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[200]) ).
thf(203,plain,
( ( ~ ! [SY223: $i] :
( ( in @ SY223 @ sK2_SY221 )
=> ( in @ SY223 @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[202]) ).
thf(204,plain,
( ( ( in @ sK3_SY223 @ sK2_SY221 )
& ~ ( in @ sK3_SY223 @ sK1_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[203]) ).
thf(205,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(206,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(207,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(208,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(209,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(210,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[117]) ).
thf(211,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(212,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(213,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[120]) ).
thf(214,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(215,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(216,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[125]) ).
thf(217,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)],[127]) ).
thf(218,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(219,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
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)],[133]) ).
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)],[134]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[136]) ).
thf(223,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[138]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(225,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(226,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(227,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)],[144]) ).
thf(228,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)],[146]) ).
thf(229,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)],[148]) ).
thf(230,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)],[149]) ).
thf(231,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(232,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)],[152]) ).
thf(233,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(234,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)],[154]) ).
thf(235,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[156]) ).
thf(236,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(237,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(238,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)],[159]) ).
thf(239,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)],[160]) ).
thf(240,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)],[161]) ).
thf(241,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)],[162]) ).
thf(242,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(243,plain,
( ( ! [A: $i] :
( ! [SY224: $i] :
( ~ ( subset @ SY224 @ ( sK6_B @ A ) )
| ( are_equipotent @ SY224 @ ( sK6_B @ A ) )
| ( in @ SY224 @ ( sK6_B @ A ) ) )
& ! [SY225: $i] :
( ( ! [SY230: $i] :
( ~ ( subset @ SY230 @ SY225 )
| ( in @ SY230 @ ( sK7_SY226 @ SY225 @ A ) ) )
& ( in @ ( sK7_SY226 @ SY225 @ A ) @ ( sK6_B @ A ) ) )
| ~ ( in @ SY225 @ ( sK6_B @ A ) ) )
& ! [SY228: $i,SY229: $i] :
( ~ ( in @ SY228 @ ( sK6_B @ A ) )
| ~ ( subset @ SY229 @ SY228 )
| ( in @ SY229 @ ( sK6_B @ A ) ) )
& ( in @ A @ ( sK6_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[165]) ).
thf(245,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK8_C @ B @ A ) @ A )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( in @ ( sK8_C @ B @ A ) @ A )
| ( in @ ( sK8_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[166]) ).
thf(246,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK9_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(247,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(248,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK11_D @ C @ B @ A ) @ A )
| ( in @ ( sK11_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK11_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK11_D @ C @ B @ A ) @ A )
| ( in @ ( sK11_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK11_D @ C @ B @ A ) @ B )
| ( in @ ( sK11_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)],[170]) ).
thf(249,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY231: $i] :
( ~ ( in @ ( sK13_C @ B @ A ) @ SY231 )
| ~ ( in @ SY231 @ A ) )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK13_C @ B @ A ) @ ( sK14_SY232 @ B @ A ) )
& ( in @ ( sK14_SY232 @ B @ A ) @ A ) )
| ( in @ ( sK13_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 @ ( sK12_D @ C @ B @ A ) )
& ( in @ ( sK12_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[171]) ).
thf(250,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_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)],[172]) ).
thf(251,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK16_C @ B @ A ) @ A )
& ~ ( in @ ( sK16_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)],[173]) ).
thf(252,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY234: $i,SY235: $i] :
( ~ ( in @ SY234 @ A )
| ~ ( in @ SY235 @ B )
| ( ( sK19_D @ C @ B @ A )
!= ( ordered_pair @ SY234 @ SY235 ) ) )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK20_SY236 @ C @ B @ A ) @ A )
& ( in @ ( sK21_SY238 @ C @ B @ A ) @ B )
& ( ( sK19_D @ C @ B @ A )
= ( ordered_pair @ ( sK20_SY236 @ C @ B @ A ) @ ( sK21_SY238 @ C @ B @ A ) ) ) )
| ( in @ ( sK19_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 @ ( sK17_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK18_SY233 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK17_E @ D @ C @ B @ A ) @ ( sK18_SY233 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(253,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK22_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK22_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK22_D @ C @ B @ A ) @ C )
| ( in @ ( sK22_D @ C @ B @ A ) @ A )
| ( in @ ( sK22_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)],[175]) ).
thf(254,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK23_D @ C @ B @ A ) @ C )
| ( ( sK23_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK23_D @ C @ B @ A ) @ C )
| ( ( sK23_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK23_D @ C @ B @ A ) @ C )
| ( ( sK23_D @ C @ B @ A )
= A )
| ( ( sK23_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)],[176]) ).
thf(255,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(256,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK24_C @ B @ A ) @ B )
| ~ ( subset @ ( sK24_C @ B @ A ) @ A ) )
& ( ( in @ ( sK24_C @ B @ A ) @ B )
| ( subset @ ( sK24_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)],[178]) ).
thf(257,plain,
( ( ! [A: $i] :
( ( in @ ( sK25_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(258,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK26_C @ B @ A )
!= A )
| ~ ( in @ ( sK26_C @ B @ A ) @ B ) )
& ( ( ( sK26_C @ B @ A )
= A )
| ( in @ ( sK26_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)],[180]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(260,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[183]) ).
thf(261,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[184]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK27_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)],[185]) ).
thf(263,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[186]) ).
thf(264,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK28_C @ B @ A ) @ A )
& ( in @ ( sK28_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)],[187]) ).
thf(265,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)],[188]) ).
thf(266,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)],[189]) ).
thf(267,plain,
( ( ! [A: $i] :
( ! [SY239: $i] :
( ~ ( subset @ SY239 @ ( sK29_B @ A ) )
| ( are_equipotent @ SY239 @ ( sK29_B @ A ) )
| ( in @ SY239 @ ( sK29_B @ A ) ) )
& ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK29_B @ A ) )
| ( in @ ( powerset @ SY240 ) @ ( sK29_B @ A ) ) )
& ! [SY241: $i,SY242: $i] :
( ~ ( in @ SY241 @ ( sK29_B @ A ) )
| ~ ( subset @ SY242 @ SY241 )
| ( in @ SY242 @ ( sK29_B @ A ) ) )
& ( in @ A @ ( sK29_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[191]) ).
thf(268,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)],[192]) ).
thf(269,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)],[193]) ).
thf(270,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[194]) ).
thf(271,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)],[195]) ).
thf(272,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[196]) ).
thf(273,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[197]) ).
thf(274,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[198]) ).
thf(275,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(276,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(277,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(278,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)],[271]) ).
thf(279,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(280,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)],[269]) ).
thf(281,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)],[268]) ).
thf(282,plain,
( ( ! [A: $i] :
( ! [SY239: $i] :
( ~ ( subset @ SY239 @ ( sK29_B @ A ) )
| ( are_equipotent @ SY239 @ ( sK29_B @ A ) )
| ( in @ SY239 @ ( sK29_B @ A ) ) )
& ! [SY240: $i] :
( ~ ( in @ SY240 @ ( sK29_B @ A ) )
| ( in @ ( powerset @ SY240 ) @ ( sK29_B @ A ) ) )
& ! [SY241: $i,SY242: $i] :
( ~ ( in @ SY241 @ ( sK29_B @ A ) )
| ~ ( subset @ SY242 @ SY241 )
| ( in @ SY242 @ ( sK29_B @ A ) ) )
& ( in @ A @ ( sK29_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(283,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(284,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)],[266]) ).
thf(285,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)],[265]) ).
thf(286,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK28_C @ B @ A ) @ A )
& ( in @ ( sK28_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(287,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(288,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK27_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)],[262]) ).
thf(289,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ ( singleton @ B ) )
!= A )
| ~ ( in @ B @ A ) )
& ! [A: $i,B: $i] :
( ( in @ B @ A )
| ( ( set_difference @ A @ ( singleton @ B ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(290,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(291,plain,
( ( ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(292,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(293,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK26_C @ B @ A )
!= A )
| ~ ( in @ ( sK26_C @ B @ A ) @ B ) )
& ( ( ( sK26_C @ B @ A )
= A )
| ( in @ ( sK26_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)],[258]) ).
thf(294,plain,
( ( ! [A: $i] :
( ( in @ ( sK25_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(295,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK24_C @ B @ A ) @ B )
| ~ ( subset @ ( sK24_C @ B @ A ) @ A ) )
& ( ( in @ ( sK24_C @ B @ A ) @ B )
| ( subset @ ( sK24_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)],[256]) ).
thf(296,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( in @ B @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
( ~ ( in @ B @ A )
| ( element @ B @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( element @ B @ A )
| ( empty @ B ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ! [B: $i] :
( ~ ( empty @ B )
| ( element @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(297,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK23_D @ C @ B @ A ) @ C )
| ( ( sK23_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK23_D @ C @ B @ A ) @ C )
| ( ( sK23_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK23_D @ C @ B @ A ) @ C )
| ( ( sK23_D @ C @ B @ A )
= A )
| ( ( sK23_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)],[254]) ).
thf(298,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK22_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK22_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK22_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK22_D @ C @ B @ A ) @ C )
| ( in @ ( sK22_D @ C @ B @ A ) @ A )
| ( in @ ( sK22_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)],[253]) ).
thf(299,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY234: $i,SY235: $i] :
( ~ ( in @ SY234 @ A )
| ~ ( in @ SY235 @ B )
| ( ( sK19_D @ C @ B @ A )
!= ( ordered_pair @ SY234 @ SY235 ) ) )
| ~ ( in @ ( sK19_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK20_SY236 @ C @ B @ A ) @ A )
& ( in @ ( sK21_SY238 @ C @ B @ A ) @ B )
& ( ( sK19_D @ C @ B @ A )
= ( ordered_pair @ ( sK20_SY236 @ C @ B @ A ) @ ( sK21_SY238 @ C @ B @ A ) ) ) )
| ( in @ ( sK19_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 @ ( sK17_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK18_SY233 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK17_E @ D @ C @ B @ A ) @ ( sK18_SY233 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK16_C @ B @ A ) @ A )
& ~ ( in @ ( sK16_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)],[251]) ).
thf(301,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ A )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK15_D @ C @ B @ A ) @ B )
| ( in @ ( sK15_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_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)],[250]) ).
thf(302,plain,
( ( ! [A: $i,B: $i] :
( ( ( ! [SY231: $i] :
( ~ ( in @ ( sK13_C @ B @ A ) @ SY231 )
| ~ ( in @ SY231 @ A ) )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( ( in @ ( sK13_C @ B @ A ) @ ( sK14_SY232 @ B @ A ) )
& ( in @ ( sK14_SY232 @ B @ A ) @ A ) )
| ( in @ ( sK13_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 @ ( sK12_D @ C @ B @ A ) )
& ( in @ ( sK12_D @ C @ B @ A ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(303,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK11_D @ C @ B @ A ) @ A )
| ( in @ ( sK11_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK11_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK11_D @ C @ B @ A ) @ A )
| ( in @ ( sK11_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK11_D @ C @ B @ A ) @ B )
| ( in @ ( sK11_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)],[248]) ).
thf(304,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(305,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(306,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK9_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(307,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK8_C @ B @ A ) @ A )
| ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
& ( ( in @ ( sK8_C @ B @ A ) @ A )
| ( in @ ( sK8_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(308,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(309,plain,
( ( ! [A: $i] :
( ! [SY224: $i] :
( ~ ( subset @ SY224 @ ( sK6_B @ A ) )
| ( are_equipotent @ SY224 @ ( sK6_B @ A ) )
| ( in @ SY224 @ ( sK6_B @ A ) ) )
& ! [SY225: $i] :
( ( ! [SY230: $i] :
( ~ ( subset @ SY230 @ SY225 )
| ( in @ SY230 @ ( sK7_SY226 @ SY225 @ A ) ) )
& ( in @ ( sK7_SY226 @ SY225 @ A ) @ ( sK6_B @ A ) ) )
| ~ ( in @ SY225 @ ( sK6_B @ A ) ) )
& ! [SY228: $i,SY229: $i] :
( ~ ( in @ SY228 @ ( sK6_B @ A ) )
| ~ ( subset @ SY229 @ SY228 )
| ( in @ SY229 @ ( sK6_B @ A ) ) )
& ( in @ A @ ( sK6_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(310,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(311,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)],[241]) ).
thf(312,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)],[240]) ).
thf(313,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)],[239]) ).
thf(314,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)],[238]) ).
thf(315,plain,
( ( ! [A: $i] :
( ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) ) )
& ! [B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(316,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ D )
| ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(317,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(318,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(319,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(320,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(321,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(322,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(323,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(324,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(325,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)],[229]) ).
thf(326,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(327,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)],[228]) ).
thf(328,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(329,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)],[227]) ).
thf(330,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(331,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(332,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(333,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(334,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(335,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(336,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(337,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(338,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(339,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(340,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(341,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(342,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(343,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(344,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(345,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(346,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)],[217]) ).
thf(347,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(348,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(349,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(350,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(351,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(352,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(353,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(354,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(355,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(356,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(357,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(358,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(359,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(360,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(361,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(362,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(363,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(364,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(365,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(366,plain,
( ( element @ sK2_SY221 @ ( powerset @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(367,plain,
( ( ( in @ sK3_SY223 @ sK2_SY221 )
& ~ ( in @ sK3_SY223 @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(368,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)],[327]) ).
thf(369,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK29_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK29_B @ SX0 ) )
| ( in @ SX1 @ ( sK29_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK29_B @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( sK29_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK29_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK29_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK29_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(370,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)],[311]) ).
thf(371,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)],[278]) ).
thf(372,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK16_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)],[300]) ).
thf(373,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK19_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK19_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK21_SY238 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK19_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK20_SY236 @ SX2 @ SX1 @ SX0 ) @ ( sK21_SY238 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK19_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 @ ( sK17_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK18_SY233 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK17_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK18_SY233 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(374,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK27_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)],[288]) ).
thf(375,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)],[346]) ).
thf(376,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)],[284]) ).
thf(377,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)],[329]) ).
thf(378,plain,
( ( ~ ( ~ ( in @ sK3_SY223 @ sK2_SY221 )
| ~ ~ ( in @ sK3_SY223 @ sK1_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(379,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX1 @ ( sK6_B @ SX0 ) )
| ( are_equipotent @ SX1 @ ( sK6_B @ SX0 ) )
| ( in @ SX1 @ ( sK6_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK7_SY226 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK7_SY226 @ SX1 @ SX0 ) @ ( sK6_B @ SX0 ) ) )
| ~ ( in @ SX1 @ ( sK6_B @ SX0 ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK6_B @ SX0 ) )
| ~ ( subset @ SX2 @ SX1 )
| ( in @ SX2 @ ( sK6_B @ SX0 ) ) )
| ~ ( in @ SX0 @ ( sK6_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(380,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)],[325]) ).
thf(381,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK22_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK22_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)],[298]) ).
thf(382,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)],[281]) ).
thf(383,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(384,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(385,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK9_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK9_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(386,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK15_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_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)],[301]) ).
thf(387,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK26_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK26_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK26_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)],[293]) ).
thf(388,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)],[348]) ).
thf(389,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)],[339]) ).
thf(390,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)],[285]) ).
thf(391,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK11_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)],[303]) ).
thf(392,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK25_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(393,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) ) )
| ~ ! [SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] : ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(394,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)],[280]) ).
thf(395,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK28_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)],[286]) ).
thf(396,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(397,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK24_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK24_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)],[295]) ).
thf(398,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)],[313]) ).
thf(399,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)],[349]) ).
thf(400,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK23_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK23_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK23_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)],[297]) ).
thf(401,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY232 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_SY232 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK13_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 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(402,plain,
! [SV1: $i] :
( ( ! [SY243: $i] :
( ~ ( in @ SV1 @ SY243 )
| ( ( set_union2 @ ( singleton @ SV1 ) @ SY243 )
= SY243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(403,plain,
! [SV2: $i] :
( ( ! [SY244: $i] :
( ~ ( disjoint @ ( singleton @ SV2 ) @ SY244 )
| ~ ( in @ SV2 @ SY244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(404,plain,
! [SV3: $i] :
( ( ! [SY245: $i] :
( ( in @ SV3 @ SY245 )
| ( disjoint @ ( singleton @ SV3 ) @ SY245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(405,plain,
! [SV4: $i] :
( ( ! [SY246: $i] :
( ~ ( in @ SV4 @ SY246 )
| ( subset @ SV4 @ ( union @ SY246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(406,plain,
! [SV5: $i] :
( ( ! [SY247: $i] :
( ~ ( in @ SV5 @ SY247 )
| ( ( set_union2 @ ( singleton @ SV5 ) @ SY247 )
= SY247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(407,plain,
! [SV6: $i] :
( ( ! [SY248: $i] :
( ~ ( in @ SV6 @ SY248 )
| ( subset @ SV6 @ ( union @ SY248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(408,plain,
! [SV7: $i] :
( ( ( union @ ( powerset @ SV7 ) )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(409,plain,
! [SV8: $i] :
( ( ! [SY249: $i] :
( ~ ( in @ SV8 @ SY249 )
| ~ ( in @ SY249 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(410,plain,
! [SV9: $i] :
( ( element @ ( sK10_B @ SV9 ) @ SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(411,plain,
! [SV10: $i] :
( ( ~ ( empty @ ( powerset @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(412,plain,
! [SV11: $i] :
( ( ! [SY250: $i] :
( ~ ( empty @ SY250 )
| ~ ( in @ SV11 @ SY250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(413,plain,
! [SV12: $i] :
( ( ( ( singleton @ SV12 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(414,plain,
! [SV13: $i] :
( ( ! [SY251: $i] :
( ~ ( subset @ SV13 @ SY251 )
| ! [SY252: $i] :
( ( in @ SY252 @ SV13 )
| ( subset @ SV13 @ ( set_difference @ SY251 @ ( singleton @ SY252 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(415,plain,
! [SV14: $i] :
( ( ! [SY253: $i,SY254: $i,SY255: $i] :
( ( SV14 = SY255 )
| ( SV14 = SY254 )
| ( ( unordered_pair @ SV14 @ SY253 )
!= ( unordered_pair @ SY254 @ SY255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(416,plain,
! [SV15: $i] :
( ( ! [SY256: $i,SY257: $i,SY258: $i] :
( ~ ( subset @ SV15 @ SY256 )
| ~ ( subset @ SY257 @ SY258 )
| ( subset @ ( cartesian_product2 @ SV15 @ SY257 ) @ ( cartesian_product2 @ SY256 @ SY258 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(417,plain,
! [SV16: $i] :
( ( ! [SY259: $i] :
( ~ ( subset @ SV16 @ SY259 )
| ( ( set_union2 @ SV16 @ SY259 )
= SY259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(418,plain,
! [SV17: $i] :
( ( ! [SY260: $i] : ( subset @ ( set_intersection2 @ SV17 @ SY260 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(419,plain,
! [SV18: $i] :
( ( ! [SY261: $i,SY262: $i] :
( ~ ( subset @ SV18 @ SY261 )
| ~ ( subset @ SV18 @ SY262 )
| ( subset @ SV18 @ ( set_intersection2 @ SY261 @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(420,plain,
! [SV19: $i] :
( ( ! [SY263: $i,SY264: $i] :
( ~ ( subset @ SV19 @ SY263 )
| ~ ( subset @ SY263 @ SY264 )
| ( subset @ SV19 @ SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(421,plain,
! [SV20: $i] :
( ( ! [SY265: $i] :
( ~ ( subset @ SV20 @ SY265 )
| ! [SY266: $i] : ( subset @ ( set_intersection2 @ SV20 @ SY266 ) @ ( set_intersection2 @ SY265 @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(422,plain,
! [SV21: $i] :
( ( ! [SY267: $i] :
( ~ ( subset @ SV21 @ SY267 )
| ( ( set_intersection2 @ SV21 @ SY267 )
= SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(423,plain,
! [SV22: $i] :
( ( subset @ empty_set @ SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(424,plain,
! [SV23: $i] :
( ( ! [SY268: $i] :
( ~ ( subset @ SV23 @ SY268 )
| ! [SY269: $i] : ( subset @ ( set_difference @ SV23 @ SY269 ) @ ( set_difference @ SY268 @ SY269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(425,plain,
! [SV24: $i] :
( ( ! [SY270: $i] : ( subset @ ( set_difference @ SV24 @ SY270 ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(426,plain,
! [SV25: $i] :
( ( ! [SY271: $i] :
( ( set_union2 @ SV25 @ ( set_difference @ SY271 @ SV25 ) )
= ( set_union2 @ SV25 @ SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(427,plain,
! [SV26: $i] :
( ( ~ ( subset @ SV26 @ empty_set )
| ( SV26 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(428,plain,
! [SV27: $i] :
( ( ! [SY272: $i] :
( ( set_difference @ ( set_union2 @ SV27 @ SY272 ) @ SY272 )
= ( set_difference @ SV27 @ SY272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(429,plain,
! [SV28: $i] :
( ( ! [SY273: $i] :
( ~ ( subset @ SV28 @ SY273 )
| ( SY273
= ( set_union2 @ SV28 @ ( set_difference @ SY273 @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(430,plain,
! [SV29: $i] :
( ( ! [SY274: $i] :
( ( set_difference @ SV29 @ ( set_difference @ SV29 @ SY274 ) )
= ( set_intersection2 @ SV29 @ SY274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(431,plain,
! [SV30: $i] :
( ( ! [SY275: $i] :
( ~ ( proper_subset @ SY275 @ SV30 )
| ~ ( subset @ SV30 @ SY275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(432,plain,
! [SV31: $i] :
( ( ! [SY276: $i,SY277: $i] :
( ~ ( disjoint @ SY276 @ SY277 )
| ~ ( subset @ SV31 @ SY276 )
| ( disjoint @ SV31 @ SY277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(433,plain,
! [SV32: $i] :
( ( ( unordered_pair @ SV32 @ SV32 )
= ( singleton @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(434,plain,
! [SV33: $i] :
( ( ! [SY278: $i] :
( ~ ( subset @ ( singleton @ SV33 ) @ ( singleton @ SY278 ) )
| ( SV33 = SY278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(435,plain,
! [SV34: $i] :
( ( ! [SY279: $i] : ( subset @ SV34 @ ( set_union2 @ SV34 @ SY279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(436,plain,
! [SV35: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ~ ( subset @ SV35 @ SY280 )
| ~ ( subset @ SY281 @ SY280 )
| ( subset @ ( set_union2 @ SV35 @ SY281 ) @ SY280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(437,plain,
! [SV36: $i] :
( ( ! [SY282: $i] :
( ! [SY283: $i] :
( ( singleton @ SV36 )
!= ( unordered_pair @ SY282 @ SY283 ) )
| ( SV36 = SY282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(438,plain,
! [SV37: $i] :
( ( ! [SY284: $i,SY285: $i] :
( ( ( singleton @ SV37 )
!= ( unordered_pair @ SY284 @ SY285 ) )
| ( SY284 = SY285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(439,plain,
! [SV38: $i] :
( ( ! [SY286: $i] :
( ( unordered_pair @ SV38 @ SY286 )
= ( unordered_pair @ SY286 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(440,plain,
! [SV39: $i] :
( ( ! [SY287: $i] :
( ( set_union2 @ SV39 @ SY287 )
= ( set_union2 @ SY287 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(441,plain,
! [SV40: $i] :
( ( ! [SY288: $i] :
( ( set_intersection2 @ SV40 @ SY288 )
= ( set_intersection2 @ SY288 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(442,plain,
! [SV41: $i] :
( ( ! [SY289: $i] :
( ( ordered_pair @ SV41 @ SY289 )
= ( unordered_pair @ ( unordered_pair @ SV41 @ SY289 ) @ ( singleton @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(443,plain,
! [SV42: $i] :
( ( ! [SY290: $i] :
~ ( empty @ ( ordered_pair @ SV42 @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(444,plain,
! [SV43: $i] :
( ( ( empty @ SV43 )
| ! [SY291: $i] :
~ ( empty @ ( set_union2 @ SV43 @ SY291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(445,plain,
! [SV44: $i] :
( ( ( empty @ SV44 )
| ! [SY292: $i] :
~ ( empty @ ( set_union2 @ SY292 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(446,plain,
! [SV45: $i] :
( ( ( set_union2 @ SV45 @ SV45 )
= SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(447,plain,
! [SV46: $i] :
( ( ( set_intersection2 @ SV46 @ SV46 )
= SV46 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(448,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(449,plain,
! [SV47: $i] :
( ( subset @ SV47 @ SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(450,plain,
! [SV48: $i] :
( ( ! [SY293: $i] :
( ~ ( disjoint @ SV48 @ SY293 )
| ( disjoint @ SY293 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(451,plain,
! [SV49: $i] :
( ( ( set_union2 @ SV49 @ empty_set )
= SV49 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(452,plain,
! [SV50: $i] :
( ( ( set_intersection2 @ SV50 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(453,plain,
! [SV51: $i] :
( ( ( set_difference @ SV51 @ empty_set )
= SV51 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(454,plain,
! [SV52: $i] :
( ( ( set_difference @ empty_set @ SV52 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(455,plain,
! [SV53: $i] :
( ( ~ ( empty @ SV53 )
| ( SV53 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(456,plain,
! [SV54: $i] :
( ( ! [SY294: $i] :
( ( SV54 = SY294 )
| ~ ( empty @ SV54 )
| ~ ( empty @ SY294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(457,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)],[368]) ).
thf(458,plain,
! [SV55: $i] :
( ( ~ ( ~ ! [SY295: $i] :
( ~ ( subset @ SY295 @ ( sK29_B @ SV55 ) )
| ( are_equipotent @ SY295 @ ( sK29_B @ SV55 ) )
| ( in @ SY295 @ ( sK29_B @ SV55 ) ) )
| ~ ~ ( ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ ( sK29_B @ SV55 ) )
| ( in @ ( powerset @ SY296 ) @ ( sK29_B @ SV55 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( in @ SY297 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SY298 @ SY297 )
| ( in @ SY298 @ ( sK29_B @ SV55 ) ) )
| ~ ( in @ SV55 @ ( sK29_B @ SV55 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(459,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)],[370]) ).
thf(460,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)],[371]) ).
thf(461,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK16_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)],[372]) ).
thf(462,plain,
! [SV56: $i] :
( ( ~ ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( ~ ( ! [SY301: $i,SY302: $i] :
( ~ ( in @ SY301 @ SV56 )
| ~ ( in @ SY302 @ SY299 )
| ( ( sK19_D @ SY300 @ SY299 @ SV56 )
!= ( ordered_pair @ SY301 @ SY302 ) ) )
| ~ ( in @ ( sK19_D @ SY300 @ SY299 @ SV56 ) @ SY300 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SY300 @ SY299 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SY300 @ SY299 @ SV56 ) @ SY299 ) )
| ( ( sK19_D @ SY300 @ SY299 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SY300 @ SY299 @ SV56 ) @ ( sK21_SY238 @ SY300 @ SY299 @ SV56 ) ) ) )
| ( in @ ( sK19_D @ SY300 @ SY299 @ SV56 ) @ SY300 ) ) )
| ( SY300
= ( cartesian_product2 @ SV56 @ SY299 ) ) )
| ~ ! [SY303: $i,SY304: $i] :
( ( SY304
!= ( cartesian_product2 @ SV56 @ SY303 ) )
| ~ ( ~ ! [SY305: $i] :
( ! [SY306: $i,SY307: $i] :
( ~ ( in @ SY306 @ SV56 )
| ~ ( in @ SY307 @ SY303 )
| ( SY305
!= ( ordered_pair @ SY306 @ SY307 ) ) )
| ( in @ SY305 @ SY304 ) )
| ~ ! [SY308: $i] :
( ~ ( in @ SY308 @ SY304 )
| ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SY308 @ SY304 @ SY303 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SY308 @ SY304 @ SY303 @ SV56 ) @ SY303 ) )
| ( SY308
!= ( ordered_pair @ ( sK17_E @ SY308 @ SY304 @ SY303 @ SV56 ) @ ( sK18_SY233 @ SY308 @ SY304 @ SY303 @ SV56 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(463,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK27_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)],[374]) ).
thf(464,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)],[375]) ).
thf(465,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)],[376]) ).
thf(466,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)],[377]) ).
thf(467,plain,
( ( ~ ( in @ sK3_SY223 @ sK2_SY221 )
| ~ ~ ( in @ sK3_SY223 @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(468,plain,
! [SV57: $i] :
( ( ~ ( ~ ! [SY309: $i] :
( ~ ( subset @ SY309 @ ( sK6_B @ SV57 ) )
| ( are_equipotent @ SY309 @ ( sK6_B @ SV57 ) )
| ( in @ SY309 @ ( sK6_B @ SV57 ) ) )
| ~ ~ ( ~ ! [SY310: $i] :
( ~ ( ~ ! [SY311: $i] :
( ~ ( subset @ SY311 @ SY310 )
| ( in @ SY311 @ ( sK7_SY226 @ SY310 @ SV57 ) ) )
| ~ ( in @ ( sK7_SY226 @ SY310 @ SV57 ) @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SY310 @ ( sK6_B @ SV57 ) ) )
| ~ ~ ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ SY312 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SV57 @ ( sK6_B @ SV57 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(469,plain,
! [SV58: $i] :
( ( ! [SY314: $i] :
~ ( ~ ! [SY315: $i] :
( ! [SY316: $i] :
( ( ordered_pair @ SV58 @ SY314 )
!= ( ordered_pair @ SY315 @ SY316 ) )
| ( SV58 = SY315 ) )
| ~ ! [SY317: $i,SY318: $i] :
( ( ( ordered_pair @ SV58 @ SY314 )
!= ( ordered_pair @ SY317 @ SY318 ) )
| ( SY314 = SY318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(470,plain,
! [SV59: $i] :
( ( ~ ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY320 )
| ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SV59 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY320 )
| ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY319 ) ) )
| ~ ( ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY320 )
| ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SV59 )
| ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY319 ) ) )
| ( SY320
= ( set_union2 @ SV59 @ SY319 ) ) )
| ~ ! [SY321: $i,SY322: $i] :
( ( SY322
!= ( set_union2 @ SV59 @ SY321 ) )
| ~ ( ~ ! [SY323: $i] :
( ~ ( in @ SY323 @ SY322 )
| ( in @ SY323 @ SV59 )
| ( in @ SY323 @ SY321 ) )
| ~ ~ ( ~ ! [SY324: $i] :
( ~ ( in @ SY324 @ SV59 )
| ( in @ SY324 @ SY322 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY321 )
| ( in @ SX3 @ SY322 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(471,plain,
! [SV60: $i] :
( ( ! [SY326: $i] :
~ ( ~ ! [SY327: $i,SY328: $i] :
( ~ ( in @ SV60 @ SY327 )
| ~ ( in @ SY326 @ SY328 )
| ( in @ ( ordered_pair @ SV60 @ SY326 ) @ ( cartesian_product2 @ SY327 @ SY328 ) ) )
| ~ ~ ( ~ ! [SY329: $i] :
( ! [SY330: $i] :
~ ( in @ ( ordered_pair @ SV60 @ SY326 ) @ ( cartesian_product2 @ SY329 @ SY330 ) )
| ( in @ SV60 @ SY329 ) )
| ~ ! [SY331: $i,SY332: $i] :
( ~ ( in @ ( ordered_pair @ SV60 @ SY326 ) @ ( cartesian_product2 @ SY331 @ SY332 ) )
| ( in @ SY326 @ SY332 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(472,plain,
! [SV61: $i] :
( ( ! [SY333: $i] :
( ~ ( ~ ( ~ ( in @ ( sK8_C @ SY333 @ SV61 ) @ SV61 )
| ~ ( in @ ( sK8_C @ SY333 @ SV61 ) @ SY333 ) )
| ~ ( ( in @ ( sK8_C @ SY333 @ SV61 ) @ SV61 )
| ( in @ ( sK8_C @ SY333 @ SV61 ) @ SY333 ) ) )
| ( SV61 = SY333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(473,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(474,plain,
! [SV62: $i] :
( ( ( empty @ SV62 )
| ~ ( ~ ( element @ ( sK9_B @ SV62 ) @ ( powerset @ SV62 ) )
| ~ ~ ( empty @ ( sK9_B @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(475,plain,
! [SV63: $i] :
( ( ~ ( ~ ! [SY334: $i,SY335: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY334 )
| ~ ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY335 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY335 ) )
| ~ ( ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY334 )
| ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY335 ) ) ) )
| ( SY335
= ( set_intersection2 @ SV63 @ SY334 ) ) )
| ~ ! [SY336: $i,SY337: $i] :
( ( SY337
!= ( set_intersection2 @ SV63 @ SY336 ) )
| ~ ( ~ ! [SY338: $i] :
( ~ ( in @ SY338 @ SV63 )
| ~ ( in @ SY338 @ SY336 )
| ( in @ SY338 @ SY337 ) )
| ~ ~ ( ~ ! [SY339: $i] :
( ~ ( in @ SY339 @ SY337 )
| ( in @ SY339 @ SV63 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY337 )
| ( in @ SX3 @ SY336 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(476,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK26_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK26_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK26_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)],[387]) ).
thf(477,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)],[388]) ).
thf(478,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)],[389]) ).
thf(479,plain,
! [SV64: $i] :
( ( ~ ( ~ ! [SY341: $i,SY342: $i] :
( ~ ( in @ SV64 @ SY342 )
| ~ ( in @ SY341 @ SY342 )
| ( subset @ ( unordered_pair @ SV64 @ SY341 ) @ SY342 ) )
| ~ ~ ( ~ ! [SY343: $i,SY344: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY343 ) @ SY344 )
| ( in @ SV64 @ SY344 ) )
| ~ ! [SY345: $i,SY346: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY345 ) @ SY346 )
| ( in @ SY345 @ SY346 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(480,plain,
! [SV65: $i] :
( ( ~ ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY347 )
| ~ ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY348 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY348 ) )
| ~ ( ~ ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY347 )
| ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY348 ) ) ) )
| ( SY348
= ( set_difference @ SV65 @ SY347 ) ) )
| ~ ! [SY349: $i,SY350: $i] :
( ( SY350
!= ( set_difference @ SV65 @ SY349 ) )
| ~ ( ~ ! [SY351: $i] :
( ~ ( in @ SY351 @ SV65 )
| ( in @ SY351 @ SY349 )
| ( in @ SY351 @ SY350 ) )
| ~ ~ ( ~ ! [SY352: $i] :
( ~ ( in @ SY352 @ SY350 )
| ( in @ SY352 @ SV65 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY350 )
| ~ ( in @ SX3 @ SY349 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(481,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK25_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(482,plain,
! [SV66: $i] :
( ( ~ ( ~ ! [SY354: $i] :
( ~ ( subset @ SV66 @ SY354 )
| ! [SY355: $i] : ( subset @ ( cartesian_product2 @ SV66 @ SY355 ) @ ( cartesian_product2 @ SY354 @ SY355 ) ) )
| ~ ! [SY356: $i] :
( ~ ( subset @ SV66 @ SY356 )
| ! [SY357: $i] : ( subset @ ( cartesian_product2 @ SY357 @ SV66 ) @ ( cartesian_product2 @ SY357 @ SY356 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(483,plain,
! [SV67: $i] :
( ( ! [SY358: $i] :
~ ( ~ ! [SY359: $i,SY360: $i] :
( ~ ( in @ SV67 @ SY359 )
| ~ ( in @ SY358 @ SY360 )
| ( in @ ( ordered_pair @ SV67 @ SY358 ) @ ( cartesian_product2 @ SY359 @ SY360 ) ) )
| ~ ~ ( ~ ! [SY361: $i] :
( ! [SY362: $i] :
~ ( in @ ( ordered_pair @ SV67 @ SY358 ) @ ( cartesian_product2 @ SY361 @ SY362 ) )
| ( in @ SV67 @ SY361 ) )
| ~ ! [SY363: $i,SY364: $i] :
( ~ ( in @ ( ordered_pair @ SV67 @ SY358 ) @ ( cartesian_product2 @ SY363 @ SY364 ) )
| ( in @ SY358 @ SY364 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(484,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK28_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)],[395]) ).
thf(485,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(486,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK24_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK24_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)],[397]) ).
thf(487,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)],[398]) ).
thf(488,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)],[399]) ).
thf(489,plain,
! [SV68: $i] :
( ( ~ ( ~ ! [SY365: $i,SY366: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK23_D @ SY366 @ SY365 @ SV68 ) @ SY366 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
!= SV68 ) )
| ~ ( ~ ( in @ ( sK23_D @ SY366 @ SY365 @ SV68 ) @ SY366 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
!= SY365 ) ) )
| ~ ( ( in @ ( sK23_D @ SY366 @ SY365 @ SV68 ) @ SY366 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
= SV68 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
= SY365 ) ) )
| ( SY366
= ( unordered_pair @ SV68 @ SY365 ) ) )
| ~ ! [SY367: $i,SY368: $i] :
( ( SY368
!= ( unordered_pair @ SV68 @ SY367 ) )
| ~ ( ~ ! [SY369: $i] :
( ~ ( in @ SY369 @ SY368 )
| ( SY369 = SV68 )
| ( SY369 = SY367 ) )
| ~ ~ ( ~ ! [SY370: $i] :
( ( SY370 != SV68 )
| ( in @ SY370 @ SY368 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY367 )
| ( in @ SX3 @ SY368 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(490,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY232 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_SY232 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK13_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 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(491,plain,
! [SV69: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV69 )
| ( ( set_union2 @ ( singleton @ SV1 ) @ SV69 )
= SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(492,plain,
! [SV70: $i,SV2: $i] :
( ( ~ ( disjoint @ ( singleton @ SV2 ) @ SV70 )
| ~ ( in @ SV2 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(493,plain,
! [SV71: $i,SV3: $i] :
( ( ( in @ SV3 @ SV71 )
| ( disjoint @ ( singleton @ SV3 ) @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(494,plain,
! [SV72: $i,SV4: $i] :
( ( ~ ( in @ SV4 @ SV72 )
| ( subset @ SV4 @ ( union @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(495,plain,
! [SV73: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ SV73 )
| ( ( set_union2 @ ( singleton @ SV5 ) @ SV73 )
= SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(496,plain,
! [SV74: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV74 )
| ( subset @ SV6 @ ( union @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(497,plain,
! [SV75: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ SV75 )
| ~ ( in @ SV75 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(498,plain,
! [SV10: $i] :
( ( empty @ ( powerset @ SV10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(499,plain,
! [SV11: $i,SV76: $i] :
( ( ~ ( empty @ SV76 )
| ~ ( in @ SV11 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(500,plain,
! [SV12: $i] :
( ( ( singleton @ SV12 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(501,plain,
! [SV77: $i,SV13: $i] :
( ( ~ ( subset @ SV13 @ SV77 )
| ! [SY372: $i] :
( ( in @ SY372 @ SV13 )
| ( subset @ SV13 @ ( set_difference @ SV77 @ ( singleton @ SY372 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(502,plain,
! [SV78: $i,SV14: $i] :
( ( ! [SY373: $i,SY374: $i] :
( ( SV14 = SY374 )
| ( SV14 = SY373 )
| ( ( unordered_pair @ SV14 @ SV78 )
!= ( unordered_pair @ SY373 @ SY374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(503,plain,
! [SV79: $i,SV15: $i] :
( ( ! [SY375: $i,SY376: $i] :
( ~ ( subset @ SV15 @ SV79 )
| ~ ( subset @ SY375 @ SY376 )
| ( subset @ ( cartesian_product2 @ SV15 @ SY375 ) @ ( cartesian_product2 @ SV79 @ SY376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(504,plain,
! [SV80: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV80 )
| ( ( set_union2 @ SV16 @ SV80 )
= SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(505,plain,
! [SV81: $i,SV17: $i] :
( ( subset @ ( set_intersection2 @ SV17 @ SV81 ) @ SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(506,plain,
! [SV82: $i,SV18: $i] :
( ( ! [SY377: $i] :
( ~ ( subset @ SV18 @ SV82 )
| ~ ( subset @ SV18 @ SY377 )
| ( subset @ SV18 @ ( set_intersection2 @ SV82 @ SY377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(507,plain,
! [SV83: $i,SV19: $i] :
( ( ! [SY378: $i] :
( ~ ( subset @ SV19 @ SV83 )
| ~ ( subset @ SV83 @ SY378 )
| ( subset @ SV19 @ SY378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(508,plain,
! [SV84: $i,SV20: $i] :
( ( ~ ( subset @ SV20 @ SV84 )
| ! [SY379: $i] : ( subset @ ( set_intersection2 @ SV20 @ SY379 ) @ ( set_intersection2 @ SV84 @ SY379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(509,plain,
! [SV85: $i,SV21: $i] :
( ( ~ ( subset @ SV21 @ SV85 )
| ( ( set_intersection2 @ SV21 @ SV85 )
= SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(510,plain,
! [SV86: $i,SV23: $i] :
( ( ~ ( subset @ SV23 @ SV86 )
| ! [SY380: $i] : ( subset @ ( set_difference @ SV23 @ SY380 ) @ ( set_difference @ SV86 @ SY380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(511,plain,
! [SV87: $i,SV24: $i] :
( ( subset @ ( set_difference @ SV24 @ SV87 ) @ SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(512,plain,
! [SV88: $i,SV25: $i] :
( ( ( set_union2 @ SV25 @ ( set_difference @ SV88 @ SV25 ) )
= ( set_union2 @ SV25 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(513,plain,
! [SV26: $i] :
( ( ( ~ ( subset @ SV26 @ empty_set ) )
= $true )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(514,plain,
! [SV89: $i,SV27: $i] :
( ( ( set_difference @ ( set_union2 @ SV27 @ SV89 ) @ SV89 )
= ( set_difference @ SV27 @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(515,plain,
! [SV90: $i,SV28: $i] :
( ( ~ ( subset @ SV28 @ SV90 )
| ( SV90
= ( set_union2 @ SV28 @ ( set_difference @ SV90 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(516,plain,
! [SV91: $i,SV29: $i] :
( ( ( set_difference @ SV29 @ ( set_difference @ SV29 @ SV91 ) )
= ( set_intersection2 @ SV29 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(517,plain,
! [SV30: $i,SV92: $i] :
( ( ~ ( proper_subset @ SV92 @ SV30 )
| ~ ( subset @ SV30 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(518,plain,
! [SV31: $i,SV93: $i] :
( ( ! [SY381: $i] :
( ~ ( disjoint @ SV93 @ SY381 )
| ~ ( subset @ SV31 @ SV93 )
| ( disjoint @ SV31 @ SY381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(519,plain,
! [SV94: $i,SV33: $i] :
( ( ~ ( subset @ ( singleton @ SV33 ) @ ( singleton @ SV94 ) )
| ( SV33 = SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(520,plain,
! [SV95: $i,SV34: $i] :
( ( subset @ SV34 @ ( set_union2 @ SV34 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(521,plain,
! [SV96: $i,SV35: $i] :
( ( ! [SY382: $i] :
( ~ ( subset @ SV35 @ SV96 )
| ~ ( subset @ SY382 @ SV96 )
| ( subset @ ( set_union2 @ SV35 @ SY382 ) @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(522,plain,
! [SV97: $i,SV36: $i] :
( ( ! [SY383: $i] :
( ( singleton @ SV36 )
!= ( unordered_pair @ SV97 @ SY383 ) )
| ( SV36 = SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(523,plain,
! [SV98: $i,SV37: $i] :
( ( ! [SY384: $i] :
( ( ( singleton @ SV37 )
!= ( unordered_pair @ SV98 @ SY384 ) )
| ( SV98 = SY384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(524,plain,
! [SV99: $i,SV38: $i] :
( ( ( unordered_pair @ SV38 @ SV99 )
= ( unordered_pair @ SV99 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(525,plain,
! [SV100: $i,SV39: $i] :
( ( ( set_union2 @ SV39 @ SV100 )
= ( set_union2 @ SV100 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(526,plain,
! [SV101: $i,SV40: $i] :
( ( ( set_intersection2 @ SV40 @ SV101 )
= ( set_intersection2 @ SV101 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(527,plain,
! [SV102: $i,SV41: $i] :
( ( ( ordered_pair @ SV41 @ SV102 )
= ( unordered_pair @ ( unordered_pair @ SV41 @ SV102 ) @ ( singleton @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(528,plain,
! [SV103: $i,SV42: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV42 @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(529,plain,
! [SV43: $i] :
( ( ( empty @ SV43 )
= $true )
| ( ( ! [SY291: $i] :
~ ( empty @ ( set_union2 @ SV43 @ SY291 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(530,plain,
! [SV44: $i] :
( ( ( empty @ SV44 )
= $true )
| ( ( ! [SY292: $i] :
~ ( empty @ ( set_union2 @ SY292 @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(531,plain,
! [SV104: $i,SV48: $i] :
( ( ~ ( disjoint @ SV48 @ SV104 )
| ( disjoint @ SV104 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(532,plain,
! [SV53: $i] :
( ( ( ~ ( empty @ SV53 ) )
= $true )
| ( ( SV53 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(533,plain,
! [SV105: $i,SV54: $i] :
( ( ( SV54 = SV105 )
| ~ ( empty @ SV54 )
| ~ ( empty @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(534,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(535,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(536,plain,
! [SV55: $i] :
( ( ~ ! [SY295: $i] :
( ~ ( subset @ SY295 @ ( sK29_B @ SV55 ) )
| ( are_equipotent @ SY295 @ ( sK29_B @ SV55 ) )
| ( in @ SY295 @ ( sK29_B @ SV55 ) ) )
| ~ ~ ( ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ ( sK29_B @ SV55 ) )
| ( in @ ( powerset @ SY296 ) @ ( sK29_B @ SV55 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( in @ SY297 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SY298 @ SY297 )
| ( in @ SY298 @ ( sK29_B @ SV55 ) ) )
| ~ ( in @ SV55 @ ( sK29_B @ SV55 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(537,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(538,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(539,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(540,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(541,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(542,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(543,plain,
! [SV56: $i] :
( ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( ~ ( ! [SY301: $i,SY302: $i] :
( ~ ( in @ SY301 @ SV56 )
| ~ ( in @ SY302 @ SY299 )
| ( ( sK19_D @ SY300 @ SY299 @ SV56 )
!= ( ordered_pair @ SY301 @ SY302 ) ) )
| ~ ( in @ ( sK19_D @ SY300 @ SY299 @ SV56 ) @ SY300 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SY300 @ SY299 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SY300 @ SY299 @ SV56 ) @ SY299 ) )
| ( ( sK19_D @ SY300 @ SY299 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SY300 @ SY299 @ SV56 ) @ ( sK21_SY238 @ SY300 @ SY299 @ SV56 ) ) ) )
| ( in @ ( sK19_D @ SY300 @ SY299 @ SV56 ) @ SY300 ) ) )
| ( SY300
= ( cartesian_product2 @ SV56 @ SY299 ) ) )
| ~ ! [SY303: $i,SY304: $i] :
( ( SY304
!= ( cartesian_product2 @ SV56 @ SY303 ) )
| ~ ( ~ ! [SY305: $i] :
( ! [SY306: $i,SY307: $i] :
( ~ ( in @ SY306 @ SV56 )
| ~ ( in @ SY307 @ SY303 )
| ( SY305
!= ( ordered_pair @ SY306 @ SY307 ) ) )
| ( in @ SY305 @ SY304 ) )
| ~ ! [SY308: $i] :
( ~ ( in @ SY308 @ SY304 )
| ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SY308 @ SY304 @ SY303 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SY308 @ SY304 @ SY303 @ SV56 ) @ SY303 ) )
| ( SY308
!= ( ordered_pair @ ( sK17_E @ SY308 @ SY304 @ SY303 @ SV56 ) @ ( sK18_SY233 @ SY308 @ SY304 @ SY303 @ SV56 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(544,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK27_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(545,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(546,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(547,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)],[464]) ).
thf(548,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(549,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(550,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[466]) ).
thf(551,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)],[466]) ).
thf(552,plain,
( ( ~ ( in @ sK3_SY223 @ sK2_SY221 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(553,plain,
( ( ~ ~ ( in @ sK3_SY223 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[467]) ).
thf(554,plain,
! [SV57: $i] :
( ( ~ ! [SY309: $i] :
( ~ ( subset @ SY309 @ ( sK6_B @ SV57 ) )
| ( are_equipotent @ SY309 @ ( sK6_B @ SV57 ) )
| ( in @ SY309 @ ( sK6_B @ SV57 ) ) )
| ~ ~ ( ~ ! [SY310: $i] :
( ~ ( ~ ! [SY311: $i] :
( ~ ( subset @ SY311 @ SY310 )
| ( in @ SY311 @ ( sK7_SY226 @ SY310 @ SV57 ) ) )
| ~ ( in @ ( sK7_SY226 @ SY310 @ SV57 ) @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SY310 @ ( sK6_B @ SV57 ) ) )
| ~ ~ ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ SY312 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SV57 @ ( sK6_B @ SV57 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(555,plain,
! [SV106: $i,SV58: $i] :
( ( ~ ( ~ ! [SY385: $i] :
( ! [SY386: $i] :
( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SY385 @ SY386 ) )
| ( SV58 = SY385 ) )
| ~ ! [SY387: $i,SY388: $i] :
( ( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SY387 @ SY388 ) )
| ( SV106 = SY388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(556,plain,
! [SV59: $i] :
( ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY320 )
| ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SV59 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY320 )
| ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY319 ) ) )
| ~ ( ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY320 )
| ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SV59 )
| ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY319 ) ) )
| ( SY320
= ( set_union2 @ SV59 @ SY319 ) ) )
| ~ ! [SY321: $i,SY322: $i] :
( ( SY322
!= ( set_union2 @ SV59 @ SY321 ) )
| ~ ( ~ ! [SY323: $i] :
( ~ ( in @ SY323 @ SY322 )
| ( in @ SY323 @ SV59 )
| ( in @ SY323 @ SY321 ) )
| ~ ~ ( ~ ! [SY324: $i] :
( ~ ( in @ SY324 @ SV59 )
| ( in @ SY324 @ SY322 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY321 )
| ( in @ SX3 @ SY322 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(557,plain,
! [SV107: $i,SV60: $i] :
( ( ~ ( ~ ! [SY389: $i,SY390: $i] :
( ~ ( in @ SV60 @ SY389 )
| ~ ( in @ SV107 @ SY390 )
| ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY389 @ SY390 ) ) )
| ~ ~ ( ~ ! [SY391: $i] :
( ! [SY392: $i] :
~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY391 @ SY392 ) )
| ( in @ SV60 @ SY391 ) )
| ~ ! [SY393: $i,SY394: $i] :
( ~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY393 @ SY394 ) )
| ( in @ SV107 @ SY394 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(558,plain,
! [SV61: $i,SV108: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
| ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 ) )
| ~ ( ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
| ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 ) ) )
| ( SV61 = SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(559,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[473]) ).
thf(560,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[473]) ).
thf(561,plain,
! [SV62: $i] :
( ( ( empty @ SV62 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK9_B @ SV62 ) @ ( powerset @ SV62 ) )
| ~ ~ ( empty @ ( sK9_B @ SV62 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(562,plain,
! [SV63: $i] :
( ( ~ ! [SY334: $i,SY335: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY334 )
| ~ ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY335 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY335 ) )
| ~ ( ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY334 )
| ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY335 ) ) ) )
| ( SY335
= ( set_intersection2 @ SV63 @ SY334 ) ) )
| ~ ! [SY336: $i,SY337: $i] :
( ( SY337
!= ( set_intersection2 @ SV63 @ SY336 ) )
| ~ ( ~ ! [SY338: $i] :
( ~ ( in @ SY338 @ SV63 )
| ~ ( in @ SY338 @ SY336 )
| ( in @ SY338 @ SY337 ) )
| ~ ~ ( ~ ! [SY339: $i] :
( ~ ( in @ SY339 @ SY337 )
| ( in @ SY339 @ SV63 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY337 )
| ( in @ SX3 @ SY336 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(563,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK26_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK26_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(564,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)],[476]) ).
thf(565,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(566,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(567,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(568,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(569,plain,
! [SV64: $i] :
( ( ~ ! [SY341: $i,SY342: $i] :
( ~ ( in @ SV64 @ SY342 )
| ~ ( in @ SY341 @ SY342 )
| ( subset @ ( unordered_pair @ SV64 @ SY341 ) @ SY342 ) )
| ~ ~ ( ~ ! [SY343: $i,SY344: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY343 ) @ SY344 )
| ( in @ SV64 @ SY344 ) )
| ~ ! [SY345: $i,SY346: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY345 ) @ SY346 )
| ( in @ SY345 @ SY346 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(570,plain,
! [SV65: $i] :
( ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY347 )
| ~ ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY348 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY348 ) )
| ~ ( ~ ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY347 )
| ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY348 ) ) ) )
| ( SY348
= ( set_difference @ SV65 @ SY347 ) ) )
| ~ ! [SY349: $i,SY350: $i] :
( ( SY350
!= ( set_difference @ SV65 @ SY349 ) )
| ~ ( ~ ! [SY351: $i] :
( ~ ( in @ SY351 @ SV65 )
| ( in @ SY351 @ SY349 )
| ( in @ SY351 @ SY350 ) )
| ~ ~ ( ~ ! [SY352: $i] :
( ~ ( in @ SY352 @ SY350 )
| ( in @ SY352 @ SV65 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY350 )
| ~ ( in @ SX3 @ SY349 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(571,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK25_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(572,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(573,plain,
! [SV66: $i] :
( ( ~ ! [SY354: $i] :
( ~ ( subset @ SV66 @ SY354 )
| ! [SY355: $i] : ( subset @ ( cartesian_product2 @ SV66 @ SY355 ) @ ( cartesian_product2 @ SY354 @ SY355 ) ) )
| ~ ! [SY356: $i] :
( ~ ( subset @ SV66 @ SY356 )
| ! [SY357: $i] : ( subset @ ( cartesian_product2 @ SY357 @ SV66 ) @ ( cartesian_product2 @ SY357 @ SY356 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(574,plain,
! [SV109: $i,SV67: $i] :
( ( ~ ( ~ ! [SY395: $i,SY396: $i] :
( ~ ( in @ SV67 @ SY395 )
| ~ ( in @ SV109 @ SY396 )
| ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY395 @ SY396 ) ) )
| ~ ~ ( ~ ! [SY397: $i] :
( ! [SY398: $i] :
~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY397 @ SY398 ) )
| ( in @ SV67 @ SY397 ) )
| ~ ! [SY399: $i,SY400: $i] :
( ~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY399 @ SY400 ) )
| ( in @ SV109 @ SY400 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(575,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(576,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(577,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(578,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(579,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK24_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK24_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(580,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)],[486]) ).
thf(581,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[487]) ).
thf(582,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)],[487]) ).
thf(583,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(584,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)],[488]) ).
thf(585,plain,
! [SV68: $i] :
( ( ~ ! [SY365: $i,SY366: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK23_D @ SY366 @ SY365 @ SV68 ) @ SY366 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
!= SV68 ) )
| ~ ( ~ ( in @ ( sK23_D @ SY366 @ SY365 @ SV68 ) @ SY366 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
!= SY365 ) ) )
| ~ ( ( in @ ( sK23_D @ SY366 @ SY365 @ SV68 ) @ SY366 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
= SV68 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
= SY365 ) ) )
| ( SY366
= ( unordered_pair @ SV68 @ SY365 ) ) )
| ~ ! [SY367: $i,SY368: $i] :
( ( SY368
!= ( unordered_pair @ SV68 @ SY367 ) )
| ~ ( ~ ! [SY369: $i] :
( ~ ( in @ SY369 @ SY368 )
| ( SY369 = SV68 )
| ( SY369 = SY367 ) )
| ~ ~ ( ~ ! [SY370: $i] :
( ( SY370 != SV68 )
| ( in @ SY370 @ SY368 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY367 )
| ( in @ SX3 @ SY368 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(586,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY232 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_SY232 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(587,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 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(588,plain,
! [SV69: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV69 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV1 ) @ SV69 )
= SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(589,plain,
! [SV70: $i,SV2: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV2 ) @ SV70 ) )
= $true )
| ( ( ~ ( in @ SV2 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(590,plain,
! [SV71: $i,SV3: $i] :
( ( ( in @ SV3 @ SV71 )
= $true )
| ( ( disjoint @ ( singleton @ SV3 ) @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(591,plain,
! [SV72: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV72 ) )
= $true )
| ( ( subset @ SV4 @ ( union @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(592,plain,
! [SV73: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV73 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV5 ) @ SV73 )
= SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(593,plain,
! [SV74: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV74 ) )
= $true )
| ( ( subset @ SV6 @ ( union @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(594,plain,
! [SV75: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV75 ) )
= $true )
| ( ( ~ ( in @ SV75 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(595,plain,
! [SV11: $i,SV76: $i] :
( ( ( ~ ( empty @ SV76 ) )
= $true )
| ( ( ~ ( in @ SV11 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(596,plain,
! [SV77: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV77 ) )
= $true )
| ( ( ! [SY372: $i] :
( ( in @ SY372 @ SV13 )
| ( subset @ SV13 @ ( set_difference @ SV77 @ ( singleton @ SY372 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(597,plain,
! [SV78: $i,SV110: $i,SV14: $i] :
( ( ! [SY401: $i] :
( ( SV14 = SY401 )
| ( SV14 = SV110 )
| ( ( unordered_pair @ SV14 @ SV78 )
!= ( unordered_pair @ SV110 @ SY401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(598,plain,
! [SV111: $i,SV79: $i,SV15: $i] :
( ( ! [SY402: $i] :
( ~ ( subset @ SV15 @ SV79 )
| ~ ( subset @ SV111 @ SY402 )
| ( subset @ ( cartesian_product2 @ SV15 @ SV111 ) @ ( cartesian_product2 @ SV79 @ SY402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(599,plain,
! [SV80: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV80 ) )
= $true )
| ( ( ( set_union2 @ SV16 @ SV80 )
= SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(600,plain,
! [SV112: $i,SV82: $i,SV18: $i] :
( ( ~ ( subset @ SV18 @ SV82 )
| ~ ( subset @ SV18 @ SV112 )
| ( subset @ SV18 @ ( set_intersection2 @ SV82 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(601,plain,
! [SV113: $i,SV83: $i,SV19: $i] :
( ( ~ ( subset @ SV19 @ SV83 )
| ~ ( subset @ SV83 @ SV113 )
| ( subset @ SV19 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(602,plain,
! [SV84: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV84 ) )
= $true )
| ( ( ! [SY379: $i] : ( subset @ ( set_intersection2 @ SV20 @ SY379 ) @ ( set_intersection2 @ SV84 @ SY379 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(603,plain,
! [SV85: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV85 ) )
= $true )
| ( ( ( set_intersection2 @ SV21 @ SV85 )
= SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(604,plain,
! [SV86: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV86 ) )
= $true )
| ( ( ! [SY380: $i] : ( subset @ ( set_difference @ SV23 @ SY380 ) @ ( set_difference @ SV86 @ SY380 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(605,plain,
! [SV26: $i] :
( ( ( subset @ SV26 @ empty_set )
= $false )
| ( ( SV26 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(606,plain,
! [SV90: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV90 ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV28 @ ( set_difference @ SV90 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(607,plain,
! [SV30: $i,SV92: $i] :
( ( ( ~ ( proper_subset @ SV92 @ SV30 ) )
= $true )
| ( ( ~ ( subset @ SV30 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(608,plain,
! [SV31: $i,SV114: $i,SV93: $i] :
( ( ~ ( disjoint @ SV93 @ SV114 )
| ~ ( subset @ SV31 @ SV93 )
| ( disjoint @ SV31 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(609,plain,
! [SV94: $i,SV33: $i] :
( ( ( ~ ( subset @ ( singleton @ SV33 ) @ ( singleton @ SV94 ) ) )
= $true )
| ( ( SV33 = SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(610,plain,
! [SV115: $i,SV96: $i,SV35: $i] :
( ( ~ ( subset @ SV35 @ SV96 )
| ~ ( subset @ SV115 @ SV96 )
| ( subset @ ( set_union2 @ SV35 @ SV115 ) @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(611,plain,
! [SV97: $i,SV36: $i] :
( ( ( ! [SY383: $i] :
( ( singleton @ SV36 )
!= ( unordered_pair @ SV97 @ SY383 ) ) )
= $true )
| ( ( SV36 = SV97 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(612,plain,
! [SV116: $i,SV98: $i,SV37: $i] :
( ( ( ( singleton @ SV37 )
!= ( unordered_pair @ SV98 @ SV116 ) )
| ( SV98 = SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(613,plain,
! [SV103: $i,SV42: $i] :
( ( empty @ ( ordered_pair @ SV42 @ SV103 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(614,plain,
! [SV117: $i,SV43: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV43 @ SV117 ) ) )
= $true )
| ( ( empty @ SV43 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(615,plain,
! [SV44: $i,SV118: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV118 @ SV44 ) ) )
= $true )
| ( ( empty @ SV44 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(616,plain,
! [SV104: $i,SV48: $i] :
( ( ( ~ ( disjoint @ SV48 @ SV104 ) )
= $true )
| ( ( disjoint @ SV104 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(617,plain,
! [SV53: $i] :
( ( ( empty @ SV53 )
= $false )
| ( ( SV53 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(618,plain,
! [SV105: $i,SV54: $i] :
( ( ( ( SV54 = SV105 )
| ~ ( empty @ SV54 ) )
= $true )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(619,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(620,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(621,plain,
! [SV55: $i] :
( ( ~ ! [SY295: $i] :
( ~ ( subset @ SY295 @ ( sK29_B @ SV55 ) )
| ( are_equipotent @ SY295 @ ( sK29_B @ SV55 ) )
| ( in @ SY295 @ ( sK29_B @ SV55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(622,plain,
! [SV55: $i] :
( ( ~ ~ ( ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ ( sK29_B @ SV55 ) )
| ( in @ ( powerset @ SY296 ) @ ( sK29_B @ SV55 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( in @ SY297 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SY298 @ SY297 )
| ( in @ SY298 @ ( sK29_B @ SV55 ) ) )
| ~ ( in @ SV55 @ ( sK29_B @ SV55 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(623,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(624,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(625,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(626,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(627,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK16_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(628,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(629,plain,
! [SV56: $i] :
( ( ~ ! [SY299: $i,SY300: $i] :
( ~ ( ~ ( ! [SY301: $i,SY302: $i] :
( ~ ( in @ SY301 @ SV56 )
| ~ ( in @ SY302 @ SY299 )
| ( ( sK19_D @ SY300 @ SY299 @ SV56 )
!= ( ordered_pair @ SY301 @ SY302 ) ) )
| ~ ( in @ ( sK19_D @ SY300 @ SY299 @ SV56 ) @ SY300 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SY300 @ SY299 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SY300 @ SY299 @ SV56 ) @ SY299 ) )
| ( ( sK19_D @ SY300 @ SY299 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SY300 @ SY299 @ SV56 ) @ ( sK21_SY238 @ SY300 @ SY299 @ SV56 ) ) ) )
| ( in @ ( sK19_D @ SY300 @ SY299 @ SV56 ) @ SY300 ) ) )
| ( SY300
= ( cartesian_product2 @ SV56 @ SY299 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(630,plain,
! [SV56: $i] :
( ( ~ ! [SY303: $i,SY304: $i] :
( ( SY304
!= ( cartesian_product2 @ SV56 @ SY303 ) )
| ~ ( ~ ! [SY305: $i] :
( ! [SY306: $i,SY307: $i] :
( ~ ( in @ SY306 @ SV56 )
| ~ ( in @ SY307 @ SY303 )
| ( SY305
!= ( ordered_pair @ SY306 @ SY307 ) ) )
| ( in @ SY305 @ SY304 ) )
| ~ ! [SY308: $i] :
( ~ ( in @ SY308 @ SY304 )
| ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SY308 @ SY304 @ SY303 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SY308 @ SY304 @ SY303 @ SV56 ) @ SY303 ) )
| ( SY308
!= ( ordered_pair @ ( sK17_E @ SY308 @ SY304 @ SY303 @ SV56 ) @ ( sK18_SY233 @ SY308 @ SY304 @ SY303 @ SV56 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(631,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK27_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(632,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(633,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(634,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)],[547]) ).
thf(635,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(636,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[549]) ).
thf(637,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(638,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)],[551]) ).
thf(639,plain,
( ( in @ sK3_SY223 @ sK2_SY221 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(640,plain,
( ( ~ ( in @ sK3_SY223 @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(641,plain,
! [SV57: $i] :
( ( ~ ! [SY309: $i] :
( ~ ( subset @ SY309 @ ( sK6_B @ SV57 ) )
| ( are_equipotent @ SY309 @ ( sK6_B @ SV57 ) )
| ( in @ SY309 @ ( sK6_B @ SV57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[554]) ).
thf(642,plain,
! [SV57: $i] :
( ( ~ ~ ( ~ ! [SY310: $i] :
( ~ ( ~ ! [SY311: $i] :
( ~ ( subset @ SY311 @ SY310 )
| ( in @ SY311 @ ( sK7_SY226 @ SY310 @ SV57 ) ) )
| ~ ( in @ ( sK7_SY226 @ SY310 @ SV57 ) @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SY310 @ ( sK6_B @ SV57 ) ) )
| ~ ~ ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ SY312 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SV57 @ ( sK6_B @ SV57 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[554]) ).
thf(643,plain,
! [SV106: $i,SV58: $i] :
( ( ~ ! [SY385: $i] :
( ! [SY386: $i] :
( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SY385 @ SY386 ) )
| ( SV58 = SY385 ) )
| ~ ! [SY387: $i,SY388: $i] :
( ( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SY387 @ SY388 ) )
| ( SV106 = SY388 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(644,plain,
! [SV59: $i] :
( ( ~ ! [SY319: $i,SY320: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY320 )
| ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SV59 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY320 )
| ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY319 ) ) )
| ~ ( ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY320 )
| ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SV59 )
| ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY319 ) ) )
| ( SY320
= ( set_union2 @ SV59 @ SY319 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(645,plain,
! [SV59: $i] :
( ( ~ ! [SY321: $i,SY322: $i] :
( ( SY322
!= ( set_union2 @ SV59 @ SY321 ) )
| ~ ( ~ ! [SY323: $i] :
( ~ ( in @ SY323 @ SY322 )
| ( in @ SY323 @ SV59 )
| ( in @ SY323 @ SY321 ) )
| ~ ~ ( ~ ! [SY324: $i] :
( ~ ( in @ SY324 @ SV59 )
| ( in @ SY324 @ SY322 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY321 )
| ( in @ SX3 @ SY322 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[556]) ).
thf(646,plain,
! [SV107: $i,SV60: $i] :
( ( ~ ! [SY389: $i,SY390: $i] :
( ~ ( in @ SV60 @ SY389 )
| ~ ( in @ SV107 @ SY390 )
| ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY389 @ SY390 ) ) )
| ~ ~ ( ~ ! [SY391: $i] :
( ! [SY392: $i] :
~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY391 @ SY392 ) )
| ( in @ SV60 @ SY391 ) )
| ~ ! [SY393: $i,SY394: $i] :
( ~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY393 @ SY394 ) )
| ( in @ SV107 @ SY394 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(647,plain,
! [SV61: $i,SV108: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
| ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 ) )
| ~ ( ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
| ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 ) ) ) )
= $true )
| ( ( SV61 = SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(648,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(649,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(650,plain,
! [SV62: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV62 ) @ ( powerset @ SV62 ) )
| ~ ~ ( empty @ ( sK9_B @ SV62 ) ) )
= $false )
| ( ( empty @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(651,plain,
! [SV63: $i] :
( ( ~ ! [SY334: $i,SY335: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY334 )
| ~ ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY335 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY335 ) )
| ~ ( ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY334 )
| ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY335 ) ) ) )
| ( SY335
= ( set_intersection2 @ SV63 @ SY334 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[562]) ).
thf(652,plain,
! [SV63: $i] :
( ( ~ ! [SY336: $i,SY337: $i] :
( ( SY337
!= ( set_intersection2 @ SV63 @ SY336 ) )
| ~ ( ~ ! [SY338: $i] :
( ~ ( in @ SY338 @ SV63 )
| ~ ( in @ SY338 @ SY336 )
| ( in @ SY338 @ SY337 ) )
| ~ ~ ( ~ ! [SY339: $i] :
( ~ ( in @ SY339 @ SY337 )
| ( in @ SY339 @ SV63 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY337 )
| ( in @ SX3 @ SY336 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[562]) ).
thf(653,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK26_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK26_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK26_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(654,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)],[564]) ).
thf(655,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(656,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(657,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(658,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(659,plain,
! [SV64: $i] :
( ( ~ ! [SY341: $i,SY342: $i] :
( ~ ( in @ SV64 @ SY342 )
| ~ ( in @ SY341 @ SY342 )
| ( subset @ ( unordered_pair @ SV64 @ SY341 ) @ SY342 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(660,plain,
! [SV64: $i] :
( ( ~ ~ ( ~ ! [SY343: $i,SY344: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY343 ) @ SY344 )
| ( in @ SV64 @ SY344 ) )
| ~ ! [SY345: $i,SY346: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY345 ) @ SY346 )
| ( in @ SY345 @ SY346 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[569]) ).
thf(661,plain,
! [SV65: $i] :
( ( ~ ! [SY347: $i,SY348: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY347 )
| ~ ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY348 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY348 ) )
| ~ ( ~ ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY347 )
| ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY348 ) ) ) )
| ( SY348
= ( set_difference @ SV65 @ SY347 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[570]) ).
thf(662,plain,
! [SV65: $i] :
( ( ~ ! [SY349: $i,SY350: $i] :
( ( SY350
!= ( set_difference @ SV65 @ SY349 ) )
| ~ ( ~ ! [SY351: $i] :
( ~ ( in @ SY351 @ SV65 )
| ( in @ SY351 @ SY349 )
| ( in @ SY351 @ SY350 ) )
| ~ ~ ( ~ ! [SY352: $i] :
( ~ ( in @ SY352 @ SY350 )
| ( in @ SY352 @ SV65 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY350 )
| ~ ( in @ SX3 @ SY349 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[570]) ).
thf(663,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK25_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[571]) ).
thf(664,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(665,plain,
! [SV66: $i] :
( ( ~ ! [SY354: $i] :
( ~ ( subset @ SV66 @ SY354 )
| ! [SY355: $i] : ( subset @ ( cartesian_product2 @ SV66 @ SY355 ) @ ( cartesian_product2 @ SY354 @ SY355 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[573]) ).
thf(666,plain,
! [SV66: $i] :
( ( ~ ! [SY356: $i] :
( ~ ( subset @ SV66 @ SY356 )
| ! [SY357: $i] : ( subset @ ( cartesian_product2 @ SY357 @ SV66 ) @ ( cartesian_product2 @ SY357 @ SY356 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[573]) ).
thf(667,plain,
! [SV109: $i,SV67: $i] :
( ( ~ ! [SY395: $i,SY396: $i] :
( ~ ( in @ SV67 @ SY395 )
| ~ ( in @ SV109 @ SY396 )
| ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY395 @ SY396 ) ) )
| ~ ~ ( ~ ! [SY397: $i] :
( ! [SY398: $i] :
~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY397 @ SY398 ) )
| ( in @ SV67 @ SY397 ) )
| ~ ! [SY399: $i,SY400: $i] :
( ~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY399 @ SY400 ) )
| ( in @ SV109 @ SY400 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(668,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK28_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(669,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(670,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
!= SX0 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(671,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( in @ SX1 @ SX0 )
| ( ( set_difference @ SX0 @ ( singleton @ SX1 ) )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(672,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK24_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK24_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK24_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(673,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)],[580]) ).
thf(674,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(675,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)],[582]) ).
thf(676,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(677,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)],[584]) ).
thf(678,plain,
! [SV68: $i] :
( ( ~ ! [SY365: $i,SY366: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK23_D @ SY366 @ SY365 @ SV68 ) @ SY366 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
!= SV68 ) )
| ~ ( ~ ( in @ ( sK23_D @ SY366 @ SY365 @ SV68 ) @ SY366 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
!= SY365 ) ) )
| ~ ( ( in @ ( sK23_D @ SY366 @ SY365 @ SV68 ) @ SY366 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
= SV68 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
= SY365 ) ) )
| ( SY366
= ( unordered_pair @ SV68 @ SY365 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[585]) ).
thf(679,plain,
! [SV68: $i] :
( ( ~ ! [SY367: $i,SY368: $i] :
( ( SY368
!= ( unordered_pair @ SV68 @ SY367 ) )
| ~ ( ~ ! [SY369: $i] :
( ~ ( in @ SY369 @ SY368 )
| ( SY369 = SV68 )
| ( SY369 = SY367 ) )
| ~ ~ ( ~ ! [SY370: $i] :
( ( SY370 != SV68 )
| ( in @ SY370 @ SY368 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY367 )
| ( in @ SX3 @ SY368 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[585]) ).
thf(680,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ ( sK14_SY232 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK14_SY232 @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[586]) ).
thf(681,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 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(682,plain,
! [SV69: $i,SV1: $i] :
( ( ( in @ SV1 @ SV69 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV1 ) @ SV69 )
= SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(683,plain,
! [SV70: $i,SV2: $i] :
( ( ( disjoint @ ( singleton @ SV2 ) @ SV70 )
= $false )
| ( ( ~ ( in @ SV2 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(684,plain,
! [SV72: $i,SV4: $i] :
( ( ( in @ SV4 @ SV72 )
= $false )
| ( ( subset @ SV4 @ ( union @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(685,plain,
! [SV73: $i,SV5: $i] :
( ( ( in @ SV5 @ SV73 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV5 ) @ SV73 )
= SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(686,plain,
! [SV74: $i,SV6: $i] :
( ( ( in @ SV6 @ SV74 )
= $false )
| ( ( subset @ SV6 @ ( union @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(687,plain,
! [SV75: $i,SV8: $i] :
( ( ( in @ SV8 @ SV75 )
= $false )
| ( ( ~ ( in @ SV75 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(688,plain,
! [SV11: $i,SV76: $i] :
( ( ( empty @ SV76 )
= $false )
| ( ( ~ ( in @ SV11 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(689,plain,
! [SV77: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV77 )
= $false )
| ( ( ! [SY372: $i] :
( ( in @ SY372 @ SV13 )
| ( subset @ SV13 @ ( set_difference @ SV77 @ ( singleton @ SY372 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(690,plain,
! [SV78: $i,SV110: $i,SV119: $i,SV14: $i] :
( ( ( SV14 = SV119 )
| ( SV14 = SV110 )
| ( ( unordered_pair @ SV14 @ SV78 )
!= ( unordered_pair @ SV110 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(691,plain,
! [SV120: $i,SV111: $i,SV79: $i,SV15: $i] :
( ( ~ ( subset @ SV15 @ SV79 )
| ~ ( subset @ SV111 @ SV120 )
| ( subset @ ( cartesian_product2 @ SV15 @ SV111 ) @ ( cartesian_product2 @ SV79 @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(692,plain,
! [SV80: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV80 )
= $false )
| ( ( ( set_union2 @ SV16 @ SV80 )
= SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(693,plain,
! [SV112: $i,SV82: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV82 )
| ~ ( subset @ SV18 @ SV112 ) )
= $true )
| ( ( subset @ SV18 @ ( set_intersection2 @ SV82 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(694,plain,
! [SV113: $i,SV83: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV83 )
| ~ ( subset @ SV83 @ SV113 ) )
= $true )
| ( ( subset @ SV19 @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(695,plain,
! [SV84: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV84 )
= $false )
| ( ( ! [SY379: $i] : ( subset @ ( set_intersection2 @ SV20 @ SY379 ) @ ( set_intersection2 @ SV84 @ SY379 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(696,plain,
! [SV85: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV85 )
= $false )
| ( ( ( set_intersection2 @ SV21 @ SV85 )
= SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(697,plain,
! [SV86: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV86 )
= $false )
| ( ( ! [SY380: $i] : ( subset @ ( set_difference @ SV23 @ SY380 ) @ ( set_difference @ SV86 @ SY380 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(698,plain,
! [SV90: $i,SV28: $i] :
( ( ( subset @ SV28 @ SV90 )
= $false )
| ( ( SV90
= ( set_union2 @ SV28 @ ( set_difference @ SV90 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(699,plain,
! [SV30: $i,SV92: $i] :
( ( ( proper_subset @ SV92 @ SV30 )
= $false )
| ( ( ~ ( subset @ SV30 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(700,plain,
! [SV31: $i,SV114: $i,SV93: $i] :
( ( ( ~ ( disjoint @ SV93 @ SV114 )
| ~ ( subset @ SV31 @ SV93 ) )
= $true )
| ( ( disjoint @ SV31 @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(701,plain,
! [SV94: $i,SV33: $i] :
( ( ( subset @ ( singleton @ SV33 ) @ ( singleton @ SV94 ) )
= $false )
| ( ( SV33 = SV94 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(702,plain,
! [SV115: $i,SV96: $i,SV35: $i] :
( ( ( ~ ( subset @ SV35 @ SV96 )
| ~ ( subset @ SV115 @ SV96 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV35 @ SV115 ) @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(703,plain,
! [SV121: $i,SV97: $i,SV36: $i] :
( ( ( ( ( singleton @ SV36 )
!= ( unordered_pair @ SV97 @ SV121 ) ) )
= $true )
| ( ( SV36 = SV97 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(704,plain,
! [SV116: $i,SV98: $i,SV37: $i] :
( ( ( ( ( singleton @ SV37 )
!= ( unordered_pair @ SV98 @ SV116 ) ) )
= $true )
| ( ( SV98 = SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(705,plain,
! [SV117: $i,SV43: $i] :
( ( ( empty @ ( set_union2 @ SV43 @ SV117 ) )
= $false )
| ( ( empty @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(706,plain,
! [SV44: $i,SV118: $i] :
( ( ( empty @ ( set_union2 @ SV118 @ SV44 ) )
= $false )
| ( ( empty @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(707,plain,
! [SV104: $i,SV48: $i] :
( ( ( disjoint @ SV48 @ SV104 )
= $false )
| ( ( disjoint @ SV104 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(708,plain,
! [SV105: $i,SV54: $i] :
( ( ( SV54 = SV105 )
= $true )
| ( ( ~ ( empty @ SV54 ) )
= $true )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(709,plain,
! [SV122: $i] :
( ( ! [SY403: $i] :
( ( ( set_difference @ SV122 @ SY403 )
!= empty_set )
| ( subset @ SV122 @ SY403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(710,plain,
! [SV123: $i] :
( ( ! [SY404: $i] :
( ~ ( subset @ SV123 @ SY404 )
| ( ( set_difference @ SV123 @ SY404 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(711,plain,
! [SV55: $i] :
( ( ! [SY295: $i] :
( ~ ( subset @ SY295 @ ( sK29_B @ SV55 ) )
| ( are_equipotent @ SY295 @ ( sK29_B @ SV55 ) )
| ( in @ SY295 @ ( sK29_B @ SV55 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(712,plain,
! [SV55: $i] :
( ( ~ ( ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ ( sK29_B @ SV55 ) )
| ( in @ ( powerset @ SY296 ) @ ( sK29_B @ SV55 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( in @ SY297 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SY298 @ SY297 )
| ( in @ SY298 @ ( sK29_B @ SV55 ) ) )
| ~ ( in @ SV55 @ ( sK29_B @ SV55 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(713,plain,
! [SV124: $i] :
( ( ! [SY405: $i] :
( ( ( set_difference @ SV124 @ SY405 )
!= empty_set )
| ( subset @ SV124 @ SY405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(714,plain,
! [SV125: $i] :
( ( ! [SY406: $i] :
( ~ ( subset @ SV125 @ SY406 )
| ( ( set_difference @ SV125 @ SY406 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(715,plain,
! [SV126: $i] :
( ( ! [SY407: $i] :
( ~ ( in @ SV126 @ SY407 )
| ( subset @ ( singleton @ SV126 ) @ SY407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(716,plain,
! [SV127: $i] :
( ( ! [SY408: $i] :
( ~ ( subset @ ( singleton @ SV127 ) @ SY408 )
| ( in @ SV127 @ SY408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(717,plain,
! [SV128: $i] :
( ( ! [SY409: $i] :
( ~ ( ~ ( in @ ( sK16_C @ SY409 @ SV128 ) @ SV128 )
| ~ ~ ( in @ ( sK16_C @ SY409 @ SV128 ) @ SY409 ) )
| ( subset @ SV128 @ SY409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(718,plain,
! [SV129: $i] :
( ( ! [SY410: $i] :
( ~ ( subset @ SV129 @ SY410 )
| ! [SY411: $i] :
( ~ ( in @ SY411 @ SV129 )
| ( in @ SY411 @ SY410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(719,plain,
! [SV56: $i] :
( ( ! [SY299: $i,SY300: $i] :
( ~ ( ~ ( ! [SY301: $i,SY302: $i] :
( ~ ( in @ SY301 @ SV56 )
| ~ ( in @ SY302 @ SY299 )
| ( ( sK19_D @ SY300 @ SY299 @ SV56 )
!= ( ordered_pair @ SY301 @ SY302 ) ) )
| ~ ( in @ ( sK19_D @ SY300 @ SY299 @ SV56 ) @ SY300 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SY300 @ SY299 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SY300 @ SY299 @ SV56 ) @ SY299 ) )
| ( ( sK19_D @ SY300 @ SY299 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SY300 @ SY299 @ SV56 ) @ ( sK21_SY238 @ SY300 @ SY299 @ SV56 ) ) ) )
| ( in @ ( sK19_D @ SY300 @ SY299 @ SV56 ) @ SY300 ) ) )
| ( SY300
= ( cartesian_product2 @ SV56 @ SY299 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[629]) ).
thf(720,plain,
! [SV56: $i] :
( ( ! [SY303: $i,SY304: $i] :
( ( SY304
!= ( cartesian_product2 @ SV56 @ SY303 ) )
| ~ ( ~ ! [SY305: $i] :
( ! [SY306: $i,SY307: $i] :
( ~ ( in @ SY306 @ SV56 )
| ~ ( in @ SY307 @ SY303 )
| ( SY305
!= ( ordered_pair @ SY306 @ SY307 ) ) )
| ( in @ SY305 @ SY304 ) )
| ~ ! [SY308: $i] :
( ~ ( in @ SY308 @ SY304 )
| ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SY308 @ SY304 @ SY303 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SY308 @ SY304 @ SY303 @ SV56 ) @ SY303 ) )
| ( SY308
!= ( ordered_pair @ ( sK17_E @ SY308 @ SY304 @ SY303 @ SV56 ) @ ( sK18_SY233 @ SY308 @ SY304 @ SY303 @ SV56 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[630]) ).
thf(721,plain,
! [SV130: $i] :
( ( ! [SY412: $i] :
( ( disjoint @ SV130 @ SY412 )
| ( in @ ( sK27_C @ SY412 @ SV130 ) @ ( set_intersection2 @ SV130 @ SY412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(722,plain,
! [SV131: $i] :
( ( ! [SY413: $i] :
( ! [SY414: $i] :
~ ( in @ SY414 @ ( set_intersection2 @ SV131 @ SY413 ) )
| ~ ( disjoint @ SV131 @ SY413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(723,plain,
! [SV132: $i] :
( ( ! [SY415: $i] :
( ~ ( subset @ SV132 @ SY415 )
| ~ ( subset @ SY415 @ SV132 )
| ( SV132 = SY415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(724,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)],[634]) ).
thf(725,plain,
! [SV133: $i] :
( ( ! [SY416: $i] :
( ~ ( in @ SV133 @ SY416 )
| ( subset @ ( singleton @ SV133 ) @ SY416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(726,plain,
! [SV134: $i] :
( ( ! [SY417: $i] :
( ~ ( subset @ ( singleton @ SV134 ) @ SY417 )
| ( in @ SV134 @ SY417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(727,plain,
! [SV135: $i] :
( ( ! [SY418: $i] :
( ~ ( subset @ SV135 @ ( singleton @ SY418 ) )
| ( SV135 = empty_set )
| ( SV135
= ( singleton @ SY418 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(728,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)],[638]) ).
thf(729,plain,
( ( in @ sK3_SY223 @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(730,plain,
! [SV57: $i] :
( ( ! [SY309: $i] :
( ~ ( subset @ SY309 @ ( sK6_B @ SV57 ) )
| ( are_equipotent @ SY309 @ ( sK6_B @ SV57 ) )
| ( in @ SY309 @ ( sK6_B @ SV57 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(731,plain,
! [SV57: $i] :
( ( ~ ( ~ ! [SY310: $i] :
( ~ ( ~ ! [SY311: $i] :
( ~ ( subset @ SY311 @ SY310 )
| ( in @ SY311 @ ( sK7_SY226 @ SY310 @ SV57 ) ) )
| ~ ( in @ ( sK7_SY226 @ SY310 @ SV57 ) @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SY310 @ ( sK6_B @ SV57 ) ) )
| ~ ~ ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ SY312 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SV57 @ ( sK6_B @ SV57 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(732,plain,
! [SV106: $i,SV58: $i] :
( ( ~ ! [SY385: $i] :
( ! [SY386: $i] :
( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SY385 @ SY386 ) )
| ( SV58 = SY385 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(733,plain,
! [SV106: $i,SV58: $i] :
( ( ~ ! [SY387: $i,SY388: $i] :
( ( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SY387 @ SY388 ) )
| ( SV106 = SY388 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(734,plain,
! [SV59: $i] :
( ( ! [SY319: $i,SY320: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY320 )
| ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SV59 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY320 )
| ~ ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY319 ) ) )
| ~ ( ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY320 )
| ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SV59 )
| ( in @ ( sK22_D @ SY320 @ SY319 @ SV59 ) @ SY319 ) ) )
| ( SY320
= ( set_union2 @ SV59 @ SY319 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(735,plain,
! [SV59: $i] :
( ( ! [SY321: $i,SY322: $i] :
( ( SY322
!= ( set_union2 @ SV59 @ SY321 ) )
| ~ ( ~ ! [SY323: $i] :
( ~ ( in @ SY323 @ SY322 )
| ( in @ SY323 @ SV59 )
| ( in @ SY323 @ SY321 ) )
| ~ ~ ( ~ ! [SY324: $i] :
( ~ ( in @ SY324 @ SV59 )
| ( in @ SY324 @ SY322 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY321 )
| ( in @ SX3 @ SY322 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(736,plain,
! [SV107: $i,SV60: $i] :
( ( ~ ! [SY389: $i,SY390: $i] :
( ~ ( in @ SV60 @ SY389 )
| ~ ( in @ SV107 @ SY390 )
| ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY389 @ SY390 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(737,plain,
! [SV107: $i,SV60: $i] :
( ( ~ ~ ( ~ ! [SY391: $i] :
( ! [SY392: $i] :
~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY391 @ SY392 ) )
| ( in @ SV60 @ SY391 ) )
| ~ ! [SY393: $i,SY394: $i] :
( ~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY393 @ SY394 ) )
| ( in @ SV107 @ SY394 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(738,plain,
! [SV61: $i,SV108: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
| ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 ) )
| ~ ( ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
| ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 ) ) )
= $false )
| ( ( SV61 = SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(739,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(740,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(741,plain,
! [SV62: $i] :
( ( ( ~ ( element @ ( sK9_B @ SV62 ) @ ( powerset @ SV62 ) ) )
= $false )
| ( ( empty @ SV62 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[650]) ).
thf(742,plain,
! [SV62: $i] :
( ( ( ~ ~ ( empty @ ( sK9_B @ SV62 ) ) )
= $false )
| ( ( empty @ SV62 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[650]) ).
thf(743,plain,
! [SV63: $i] :
( ( ! [SY334: $i,SY335: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY334 )
| ~ ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY335 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY335 ) )
| ~ ( ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY334 )
| ( in @ ( sK15_D @ SY335 @ SY334 @ SV63 ) @ SY335 ) ) ) )
| ( SY335
= ( set_intersection2 @ SV63 @ SY334 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(744,plain,
! [SV63: $i] :
( ( ! [SY336: $i,SY337: $i] :
( ( SY337
!= ( set_intersection2 @ SV63 @ SY336 ) )
| ~ ( ~ ! [SY338: $i] :
( ~ ( in @ SY338 @ SV63 )
| ~ ( in @ SY338 @ SY336 )
| ( in @ SY338 @ SY337 ) )
| ~ ~ ( ~ ! [SY339: $i] :
( ~ ( in @ SY339 @ SY337 )
| ( in @ SY339 @ SV63 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY337 )
| ( in @ SX3 @ SY336 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[652]) ).
thf(745,plain,
! [SV136: $i] :
( ( ! [SY419: $i] :
( ~ ( ~ ( ( ( sK26_C @ SY419 @ SV136 )
!= SV136 )
| ~ ( in @ ( sK26_C @ SY419 @ SV136 ) @ SY419 ) )
| ~ ( ( ( sK26_C @ SY419 @ SV136 )
= SV136 )
| ( in @ ( sK26_C @ SY419 @ SV136 ) @ SY419 ) ) )
| ( SY419
= ( singleton @ SV136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(746,plain,
! [SV137: $i] :
( ( ! [SY420: $i] :
( ( SY420
!= ( singleton @ SV137 ) )
| ~ ( ~ ! [SY421: $i] :
( ( SY421 != SV137 )
| ( in @ SY421 @ SY420 ) )
| ~ ! [SY422: $i] :
( ~ ( in @ SY422 @ SY420 )
| ( SY422 = SV137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(747,plain,
! [SV138: $i] :
( ( ! [SY423: $i] :
( ( ( set_intersection2 @ SV138 @ SY423 )
!= empty_set )
| ( disjoint @ SV138 @ SY423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(748,plain,
! [SV139: $i] :
( ( ! [SY424: $i] :
( ~ ( disjoint @ SV139 @ SY424 )
| ( ( set_intersection2 @ SV139 @ SY424 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(749,plain,
! [SV140: $i] :
( ( ! [SY425: $i] :
( ( ( set_difference @ SV140 @ SY425 )
!= SV140 )
| ( disjoint @ SV140 @ SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(750,plain,
! [SV141: $i] :
( ( ! [SY426: $i] :
( ~ ( disjoint @ SV141 @ SY426 )
| ( ( set_difference @ SV141 @ SY426 )
= SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(751,plain,
! [SV64: $i] :
( ( ! [SY341: $i,SY342: $i] :
( ~ ( in @ SV64 @ SY342 )
| ~ ( in @ SY341 @ SY342 )
| ( subset @ ( unordered_pair @ SV64 @ SY341 ) @ SY342 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[659]) ).
thf(752,plain,
! [SV64: $i] :
( ( ~ ( ~ ! [SY343: $i,SY344: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY343 ) @ SY344 )
| ( in @ SV64 @ SY344 ) )
| ~ ! [SY345: $i,SY346: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY345 ) @ SY346 )
| ( in @ SY345 @ SY346 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[660]) ).
thf(753,plain,
! [SV65: $i] :
( ( ! [SY347: $i,SY348: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY347 )
| ~ ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY348 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY348 ) )
| ~ ( ~ ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY347 )
| ( in @ ( sK11_D @ SY348 @ SY347 @ SV65 ) @ SY348 ) ) ) )
| ( SY348
= ( set_difference @ SV65 @ SY347 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[661]) ).
thf(754,plain,
! [SV65: $i] :
( ( ! [SY349: $i,SY350: $i] :
( ( SY350
!= ( set_difference @ SV65 @ SY349 ) )
| ~ ( ~ ! [SY351: $i] :
( ~ ( in @ SY351 @ SV65 )
| ( in @ SY351 @ SY349 )
| ( in @ SY351 @ SY350 ) )
| ~ ~ ( ~ ! [SY352: $i] :
( ~ ( in @ SY352 @ SY350 )
| ( in @ SY352 @ SV65 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY350 )
| ~ ( in @ SX3 @ SY349 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[662]) ).
thf(755,plain,
! [SV142: $i] :
( ( ( in @ ( sK25_B @ SV142 ) @ SV142 )
| ( SV142 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(756,plain,
! [SV143: $i] :
( ( ( SV143 != empty_set )
| ! [SY427: $i] :
~ ( in @ SY427 @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(757,plain,
! [SV66: $i] :
( ( ! [SY354: $i] :
( ~ ( subset @ SV66 @ SY354 )
| ! [SY355: $i] : ( subset @ ( cartesian_product2 @ SV66 @ SY355 ) @ ( cartesian_product2 @ SY354 @ SY355 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[665]) ).
thf(758,plain,
! [SV66: $i] :
( ( ! [SY356: $i] :
( ~ ( subset @ SV66 @ SY356 )
| ! [SY357: $i] : ( subset @ ( cartesian_product2 @ SY357 @ SV66 ) @ ( cartesian_product2 @ SY357 @ SY356 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[666]) ).
thf(759,plain,
! [SV109: $i,SV67: $i] :
( ( ~ ! [SY395: $i,SY396: $i] :
( ~ ( in @ SV67 @ SY395 )
| ~ ( in @ SV109 @ SY396 )
| ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY395 @ SY396 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(760,plain,
! [SV109: $i,SV67: $i] :
( ( ~ ~ ( ~ ! [SY397: $i] :
( ! [SY398: $i] :
~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY397 @ SY398 ) )
| ( in @ SV67 @ SY397 ) )
| ~ ! [SY399: $i,SY400: $i] :
( ~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY399 @ SY400 ) )
| ( in @ SV109 @ SY400 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(761,plain,
! [SV144: $i] :
( ( ! [SY428: $i] :
( ( disjoint @ SV144 @ SY428 )
| ~ ( ~ ( in @ ( sK28_C @ SY428 @ SV144 ) @ SV144 )
| ~ ( in @ ( sK28_C @ SY428 @ SV144 ) @ SY428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(762,plain,
! [SV145: $i] :
( ( ! [SY429: $i] :
( ! [SY430: $i] :
( ~ ( in @ SY430 @ SV145 )
| ~ ( in @ SY430 @ SY429 ) )
| ~ ( disjoint @ SV145 @ SY429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(763,plain,
! [SV146: $i] :
( ( ! [SY431: $i] :
( ( ( set_difference @ SV146 @ ( singleton @ SY431 ) )
!= SV146 )
| ~ ( in @ SY431 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(764,plain,
! [SV147: $i] :
( ( ! [SY432: $i] :
( ( in @ SY432 @ SV147 )
| ( ( set_difference @ SV147 @ ( singleton @ SY432 ) )
= SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(765,plain,
! [SV148: $i] :
( ( ! [SY433: $i] :
( ~ ( ~ ( ~ ( in @ ( sK24_C @ SY433 @ SV148 ) @ SY433 )
| ~ ( subset @ ( sK24_C @ SY433 @ SV148 ) @ SV148 ) )
| ~ ( ( in @ ( sK24_C @ SY433 @ SV148 ) @ SY433 )
| ( subset @ ( sK24_C @ SY433 @ SV148 ) @ SV148 ) ) )
| ( SY433
= ( powerset @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(766,plain,
! [SV149: $i] :
( ( ! [SY434: $i] :
( ( SY434
!= ( powerset @ SV149 ) )
| ~ ( ~ ! [SY435: $i] :
( ~ ( in @ SY435 @ SY434 )
| ( subset @ SY435 @ SV149 ) )
| ~ ! [SY436: $i] :
( ~ ( subset @ SY436 @ SV149 )
| ( in @ SY436 @ SY434 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(767,plain,
! [SV150: $i] :
( ( ! [SY437: $i] :
( ~ ( subset @ SV150 @ ( singleton @ SY437 ) )
| ( SV150 = empty_set )
| ( SV150
= ( singleton @ SY437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(768,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)],[675]) ).
thf(769,plain,
! [SV151: $i] :
( ( ! [SY438: $i] :
( ( SV151 = SY438 )
| ~ ( subset @ SV151 @ SY438 )
| ( proper_subset @ SV151 @ SY438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(770,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)],[677]) ).
thf(771,plain,
! [SV68: $i] :
( ( ! [SY365: $i,SY366: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK23_D @ SY366 @ SY365 @ SV68 ) @ SY366 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
!= SV68 ) )
| ~ ( ~ ( in @ ( sK23_D @ SY366 @ SY365 @ SV68 ) @ SY366 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
!= SY365 ) ) )
| ~ ( ( in @ ( sK23_D @ SY366 @ SY365 @ SV68 ) @ SY366 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
= SV68 )
| ( ( sK23_D @ SY366 @ SY365 @ SV68 )
= SY365 ) ) )
| ( SY366
= ( unordered_pair @ SV68 @ SY365 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[678]) ).
thf(772,plain,
! [SV68: $i] :
( ( ! [SY367: $i,SY368: $i] :
( ( SY368
!= ( unordered_pair @ SV68 @ SY367 ) )
| ~ ( ~ ! [SY369: $i] :
( ~ ( in @ SY369 @ SY368 )
| ( SY369 = SV68 )
| ( SY369 = SY367 ) )
| ~ ~ ( ~ ! [SY370: $i] :
( ( SY370 != SV68 )
| ( in @ SY370 @ SY368 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY367 )
| ( in @ SX3 @ SY368 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[679]) ).
thf(773,plain,
! [SV152: $i] :
( ( ! [SY439: $i] :
( ~ ( ~ ( ! [SY440: $i] :
( ~ ( in @ ( sK13_C @ SY439 @ SV152 ) @ SY440 )
| ~ ( in @ SY440 @ SV152 ) )
| ~ ( in @ ( sK13_C @ SY439 @ SV152 ) @ SY439 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SY439 @ SV152 ) @ ( sK14_SY232 @ SY439 @ SV152 ) )
| ~ ( in @ ( sK14_SY232 @ SY439 @ SV152 ) @ SV152 ) )
| ( in @ ( sK13_C @ SY439 @ SV152 ) @ SY439 ) ) )
| ( SY439
= ( union @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(774,plain,
! [SV153: $i] :
( ( ! [SY441: $i] :
( ( SY441
!= ( union @ SV153 ) )
| ~ ( ~ ! [SY442: $i] :
( ! [SY443: $i] :
( ~ ( in @ SY442 @ SY443 )
| ~ ( in @ SY443 @ SV153 ) )
| ( in @ SY442 @ SY441 ) )
| ~ ! [SY444: $i] :
( ~ ( in @ SY444 @ SY441 )
| ~ ( ~ ( in @ SY444 @ ( sK12_D @ SY444 @ SY441 @ SV153 ) )
| ~ ( in @ ( sK12_D @ SY444 @ SY441 @ SV153 ) @ SV153 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(775,plain,
! [SV70: $i,SV2: $i] :
( ( ( in @ SV2 @ SV70 )
= $false )
| ( ( disjoint @ ( singleton @ SV2 ) @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(776,plain,
! [SV8: $i,SV75: $i] :
( ( ( in @ SV75 @ SV8 )
= $false )
| ( ( in @ SV8 @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(777,plain,
! [SV76: $i,SV11: $i] :
( ( ( in @ SV11 @ SV76 )
= $false )
| ( ( empty @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(778,plain,
! [SV77: $i,SV13: $i,SV154: $i] :
( ( ( ( in @ SV154 @ SV13 )
| ( subset @ SV13 @ ( set_difference @ SV77 @ ( singleton @ SV154 ) ) ) )
= $true )
| ( ( subset @ SV13 @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(779,plain,
! [SV78: $i,SV110: $i,SV119: $i,SV14: $i] :
( ( ( SV14 = SV119 )
= $true )
| ( ( ( SV14 = SV110 )
| ( ( unordered_pair @ SV14 @ SV78 )
!= ( unordered_pair @ SV110 @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[690]) ).
thf(780,plain,
! [SV120: $i,SV111: $i,SV79: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV79 )
| ~ ( subset @ SV111 @ SV120 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV15 @ SV111 ) @ ( cartesian_product2 @ SV79 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(781,plain,
! [SV112: $i,SV82: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV82 ) )
= $true )
| ( ( ~ ( subset @ SV18 @ SV112 ) )
= $true )
| ( ( subset @ SV18 @ ( set_intersection2 @ SV82 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[693]) ).
thf(782,plain,
! [SV113: $i,SV83: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV83 ) )
= $true )
| ( ( ~ ( subset @ SV83 @ SV113 ) )
= $true )
| ( ( subset @ SV19 @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(783,plain,
! [SV84: $i,SV155: $i,SV20: $i] :
( ( ( subset @ ( set_intersection2 @ SV20 @ SV155 ) @ ( set_intersection2 @ SV84 @ SV155 ) )
= $true )
| ( ( subset @ SV20 @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(784,plain,
! [SV86: $i,SV156: $i,SV23: $i] :
( ( ( subset @ ( set_difference @ SV23 @ SV156 ) @ ( set_difference @ SV86 @ SV156 ) )
= $true )
| ( ( subset @ SV23 @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(785,plain,
! [SV92: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV92 )
= $false )
| ( ( proper_subset @ SV92 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(786,plain,
! [SV31: $i,SV114: $i,SV93: $i] :
( ( ( ~ ( disjoint @ SV93 @ SV114 ) )
= $true )
| ( ( ~ ( subset @ SV31 @ SV93 ) )
= $true )
| ( ( disjoint @ SV31 @ SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(787,plain,
! [SV115: $i,SV96: $i,SV35: $i] :
( ( ( ~ ( subset @ SV35 @ SV96 ) )
= $true )
| ( ( ~ ( subset @ SV115 @ SV96 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV35 @ SV115 ) @ SV96 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(788,plain,
! [SV121: $i,SV97: $i,SV36: $i] :
( ( ( ( singleton @ SV36 )
= ( unordered_pair @ SV97 @ SV121 ) )
= $false )
| ( ( SV36 = SV97 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(789,plain,
! [SV116: $i,SV98: $i,SV37: $i] :
( ( ( ( singleton @ SV37 )
= ( unordered_pair @ SV98 @ SV116 ) )
= $false )
| ( ( SV98 = SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(790,plain,
! [SV105: $i,SV54: $i] :
( ( ( empty @ SV54 )
= $false )
| ( ( SV54 = SV105 )
= $true )
| ( ( ~ ( empty @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(791,plain,
! [SV157: $i,SV122: $i] :
( ( ( ( set_difference @ SV122 @ SV157 )
!= empty_set )
| ( subset @ SV122 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(792,plain,
! [SV158: $i,SV123: $i] :
( ( ~ ( subset @ SV123 @ SV158 )
| ( ( set_difference @ SV123 @ SV158 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(793,plain,
! [SV55: $i,SV159: $i] :
( ( ~ ( subset @ SV159 @ ( sK29_B @ SV55 ) )
| ( are_equipotent @ SV159 @ ( sK29_B @ SV55 ) )
| ( in @ SV159 @ ( sK29_B @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(794,plain,
! [SV55: $i] :
( ( ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ ( sK29_B @ SV55 ) )
| ( in @ ( powerset @ SY296 ) @ ( sK29_B @ SV55 ) ) )
| ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( in @ SY297 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SY298 @ SY297 )
| ( in @ SY298 @ ( sK29_B @ SV55 ) ) )
| ~ ( in @ SV55 @ ( sK29_B @ SV55 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(795,plain,
! [SV160: $i,SV124: $i] :
( ( ( ( set_difference @ SV124 @ SV160 )
!= empty_set )
| ( subset @ SV124 @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(796,plain,
! [SV161: $i,SV125: $i] :
( ( ~ ( subset @ SV125 @ SV161 )
| ( ( set_difference @ SV125 @ SV161 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(797,plain,
! [SV162: $i,SV126: $i] :
( ( ~ ( in @ SV126 @ SV162 )
| ( subset @ ( singleton @ SV126 ) @ SV162 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(798,plain,
! [SV163: $i,SV127: $i] :
( ( ~ ( subset @ ( singleton @ SV127 ) @ SV163 )
| ( in @ SV127 @ SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(799,plain,
! [SV128: $i,SV164: $i] :
( ( ~ ( ~ ( in @ ( sK16_C @ SV164 @ SV128 ) @ SV128 )
| ~ ~ ( in @ ( sK16_C @ SV164 @ SV128 ) @ SV164 ) )
| ( subset @ SV128 @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(800,plain,
! [SV165: $i,SV129: $i] :
( ( ~ ( subset @ SV129 @ SV165 )
| ! [SY445: $i] :
( ~ ( in @ SY445 @ SV129 )
| ( in @ SY445 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(801,plain,
! [SV166: $i,SV56: $i] :
( ( ! [SY446: $i] :
( ~ ( ~ ( ! [SY447: $i,SY448: $i] :
( ~ ( in @ SY447 @ SV56 )
| ~ ( in @ SY448 @ SV166 )
| ( ( sK19_D @ SY446 @ SV166 @ SV56 )
!= ( ordered_pair @ SY447 @ SY448 ) ) )
| ~ ( in @ ( sK19_D @ SY446 @ SV166 @ SV56 ) @ SY446 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SY446 @ SV166 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SY446 @ SV166 @ SV56 ) @ SV166 ) )
| ( ( sK19_D @ SY446 @ SV166 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SY446 @ SV166 @ SV56 ) @ ( sK21_SY238 @ SY446 @ SV166 @ SV56 ) ) ) )
| ( in @ ( sK19_D @ SY446 @ SV166 @ SV56 ) @ SY446 ) ) )
| ( SY446
= ( cartesian_product2 @ SV56 @ SV166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(802,plain,
! [SV167: $i,SV56: $i] :
( ( ! [SY449: $i] :
( ( SY449
!= ( cartesian_product2 @ SV56 @ SV167 ) )
| ~ ( ~ ! [SY450: $i] :
( ! [SY451: $i,SY452: $i] :
( ~ ( in @ SY451 @ SV56 )
| ~ ( in @ SY452 @ SV167 )
| ( SY450
!= ( ordered_pair @ SY451 @ SY452 ) ) )
| ( in @ SY450 @ SY449 ) )
| ~ ! [SY453: $i] :
( ~ ( in @ SY453 @ SY449 )
| ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SY453 @ SY449 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SY453 @ SY449 @ SV167 @ SV56 ) @ SV167 ) )
| ( SY453
!= ( ordered_pair @ ( sK17_E @ SY453 @ SY449 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SY453 @ SY449 @ SV167 @ SV56 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(803,plain,
! [SV168: $i,SV130: $i] :
( ( ( disjoint @ SV130 @ SV168 )
| ( in @ ( sK27_C @ SV168 @ SV130 ) @ ( set_intersection2 @ SV130 @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(804,plain,
! [SV169: $i,SV131: $i] :
( ( ! [SY454: $i] :
~ ( in @ SY454 @ ( set_intersection2 @ SV131 @ SV169 ) )
| ~ ( disjoint @ SV131 @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(805,plain,
! [SV170: $i,SV132: $i] :
( ( ~ ( subset @ SV132 @ SV170 )
| ~ ( subset @ SV170 @ SV132 )
| ( SV132 = SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(806,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[724]) ).
thf(807,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[724]) ).
thf(808,plain,
! [SV171: $i,SV133: $i] :
( ( ~ ( in @ SV133 @ SV171 )
| ( subset @ ( singleton @ SV133 ) @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(809,plain,
! [SV172: $i,SV134: $i] :
( ( ~ ( subset @ ( singleton @ SV134 ) @ SV172 )
| ( in @ SV134 @ SV172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(810,plain,
! [SV173: $i,SV135: $i] :
( ( ~ ( subset @ SV135 @ ( singleton @ SV173 ) )
| ( SV135 = empty_set )
| ( SV135
= ( singleton @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(811,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(812,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[728]) ).
thf(813,plain,
! [SV57: $i,SV174: $i] :
( ( ~ ( subset @ SV174 @ ( sK6_B @ SV57 ) )
| ( are_equipotent @ SV174 @ ( sK6_B @ SV57 ) )
| ( in @ SV174 @ ( sK6_B @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(814,plain,
! [SV57: $i] :
( ( ~ ! [SY310: $i] :
( ~ ( ~ ! [SY311: $i] :
( ~ ( subset @ SY311 @ SY310 )
| ( in @ SY311 @ ( sK7_SY226 @ SY310 @ SV57 ) ) )
| ~ ( in @ ( sK7_SY226 @ SY310 @ SV57 ) @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SY310 @ ( sK6_B @ SV57 ) ) )
| ~ ~ ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ SY312 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SV57 @ ( sK6_B @ SV57 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(815,plain,
! [SV106: $i,SV58: $i] :
( ( ! [SY385: $i] :
( ! [SY386: $i] :
( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SY385 @ SY386 ) )
| ( SV58 = SY385 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[732]) ).
thf(816,plain,
! [SV106: $i,SV58: $i] :
( ( ! [SY387: $i,SY388: $i] :
( ( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SY387 @ SY388 ) )
| ( SV106 = SY388 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[733]) ).
thf(817,plain,
! [SV59: $i,SV175: $i] :
( ( ! [SY455: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SY455 @ SV175 @ SV59 ) @ SY455 )
| ~ ( in @ ( sK22_D @ SY455 @ SV175 @ SV59 ) @ SV59 ) )
| ~ ( ~ ( in @ ( sK22_D @ SY455 @ SV175 @ SV59 ) @ SY455 )
| ~ ( in @ ( sK22_D @ SY455 @ SV175 @ SV59 ) @ SV175 ) ) )
| ~ ( ( in @ ( sK22_D @ SY455 @ SV175 @ SV59 ) @ SY455 )
| ( in @ ( sK22_D @ SY455 @ SV175 @ SV59 ) @ SV59 )
| ( in @ ( sK22_D @ SY455 @ SV175 @ SV59 ) @ SV175 ) ) )
| ( SY455
= ( set_union2 @ SV59 @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(818,plain,
! [SV176: $i,SV59: $i] :
( ( ! [SY456: $i] :
( ( SY456
!= ( set_union2 @ SV59 @ SV176 ) )
| ~ ( ~ ! [SY457: $i] :
( ~ ( in @ SY457 @ SY456 )
| ( in @ SY457 @ SV59 )
| ( in @ SY457 @ SV176 ) )
| ~ ~ ( ~ ! [SY324: $i] :
( ~ ( in @ SY324 @ SV59 )
| ( in @ SY324 @ SY456 ) )
| ~ ! [SY459: $i] :
( ~ ( in @ SY459 @ SV176 )
| ( in @ SY459 @ SY456 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(819,plain,
! [SV107: $i,SV60: $i] :
( ( ! [SY389: $i,SY390: $i] :
( ~ ( in @ SV60 @ SY389 )
| ~ ( in @ SV107 @ SY390 )
| ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY389 @ SY390 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(820,plain,
! [SV107: $i,SV60: $i] :
( ( ~ ( ~ ! [SY391: $i] :
( ! [SY392: $i] :
~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY391 @ SY392 ) )
| ( in @ SV60 @ SY391 ) )
| ~ ! [SY393: $i,SY394: $i] :
( ~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY393 @ SY394 ) )
| ( in @ SV107 @ SY394 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(821,plain,
! [SV61: $i,SV108: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
| ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 ) ) )
= $false )
| ( ( SV61 = SV108 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[738]) ).
thf(822,plain,
! [SV61: $i,SV108: $i] :
( ( ( ~ ( ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
| ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 ) ) )
= $false )
| ( ( SV61 = SV108 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[738]) ).
thf(823,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[739]) ).
thf(824,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[739]) ).
thf(825,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(826,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(827,plain,
! [SV62: $i] :
( ( ( element @ ( sK9_B @ SV62 ) @ ( powerset @ SV62 ) )
= $true )
| ( ( empty @ SV62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(828,plain,
! [SV62: $i] :
( ( ( ~ ( empty @ ( sK9_B @ SV62 ) ) )
= $true )
| ( ( empty @ SV62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(829,plain,
! [SV63: $i,SV177: $i] :
( ( ! [SY460: $i] :
( ~ ( ~ ( ~ ( in @ ( sK15_D @ SY460 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK15_D @ SY460 @ SV177 @ SV63 ) @ SV177 )
| ~ ( in @ ( sK15_D @ SY460 @ SV177 @ SV63 ) @ SY460 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SY460 @ SV177 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SY460 @ SV177 @ SV63 ) @ SY460 ) )
| ~ ( ( in @ ( sK15_D @ SY460 @ SV177 @ SV63 ) @ SV177 )
| ( in @ ( sK15_D @ SY460 @ SV177 @ SV63 ) @ SY460 ) ) ) )
| ( SY460
= ( set_intersection2 @ SV63 @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(830,plain,
! [SV178: $i,SV63: $i] :
( ( ! [SY461: $i] :
( ( SY461
!= ( set_intersection2 @ SV63 @ SV178 ) )
| ~ ( ~ ! [SY462: $i] :
( ~ ( in @ SY462 @ SV63 )
| ~ ( in @ SY462 @ SV178 )
| ( in @ SY462 @ SY461 ) )
| ~ ~ ( ~ ! [SY339: $i] :
( ~ ( in @ SY339 @ SY461 )
| ( in @ SY339 @ SV63 ) )
| ~ ! [SY464: $i] :
( ~ ( in @ SY464 @ SY461 )
| ( in @ SY464 @ SV178 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(831,plain,
! [SV136: $i,SV179: $i] :
( ( ~ ( ~ ( ( ( sK26_C @ SV179 @ SV136 )
!= SV136 )
| ~ ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 ) )
| ~ ( ( ( sK26_C @ SV179 @ SV136 )
= SV136 )
| ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 ) ) )
| ( SV179
= ( singleton @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(832,plain,
! [SV137: $i,SV180: $i] :
( ( ( SV180
!= ( singleton @ SV137 ) )
| ~ ( ~ ! [SY465: $i] :
( ( SY465 != SV137 )
| ( in @ SY465 @ SV180 ) )
| ~ ! [SY466: $i] :
( ~ ( in @ SY466 @ SV180 )
| ( SY466 = SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(833,plain,
! [SV181: $i,SV138: $i] :
( ( ( ( set_intersection2 @ SV138 @ SV181 )
!= empty_set )
| ( disjoint @ SV138 @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(834,plain,
! [SV182: $i,SV139: $i] :
( ( ~ ( disjoint @ SV139 @ SV182 )
| ( ( set_intersection2 @ SV139 @ SV182 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(835,plain,
! [SV183: $i,SV140: $i] :
( ( ( ( set_difference @ SV140 @ SV183 )
!= SV140 )
| ( disjoint @ SV140 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(836,plain,
! [SV184: $i,SV141: $i] :
( ( ~ ( disjoint @ SV141 @ SV184 )
| ( ( set_difference @ SV141 @ SV184 )
= SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(837,plain,
! [SV185: $i,SV64: $i] :
( ( ! [SY467: $i] :
( ~ ( in @ SV64 @ SY467 )
| ~ ( in @ SV185 @ SY467 )
| ( subset @ ( unordered_pair @ SV64 @ SV185 ) @ SY467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(838,plain,
! [SV64: $i] :
( ( ~ ! [SY343: $i,SY344: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY343 ) @ SY344 )
| ( in @ SV64 @ SY344 ) )
| ~ ! [SY345: $i,SY346: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY345 ) @ SY346 )
| ( in @ SY345 @ SY346 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(839,plain,
! [SV65: $i,SV186: $i] :
( ( ! [SY468: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_D @ SY468 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SY468 @ SV186 @ SV65 ) @ SV186 )
| ~ ( in @ ( sK11_D @ SY468 @ SV186 @ SV65 ) @ SY468 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SY468 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SY468 @ SV186 @ SV65 ) @ SY468 ) )
| ~ ( ~ ( in @ ( sK11_D @ SY468 @ SV186 @ SV65 ) @ SV186 )
| ( in @ ( sK11_D @ SY468 @ SV186 @ SV65 ) @ SY468 ) ) ) )
| ( SY468
= ( set_difference @ SV65 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(840,plain,
! [SV187: $i,SV65: $i] :
( ( ! [SY469: $i] :
( ( SY469
!= ( set_difference @ SV65 @ SV187 ) )
| ~ ( ~ ! [SY470: $i] :
( ~ ( in @ SY470 @ SV65 )
| ( in @ SY470 @ SV187 )
| ( in @ SY470 @ SY469 ) )
| ~ ~ ( ~ ! [SY352: $i] :
( ~ ( in @ SY352 @ SY469 )
| ( in @ SY352 @ SV65 ) )
| ~ ! [SY472: $i] :
( ~ ( in @ SY472 @ SY469 )
| ~ ( in @ SY472 @ SV187 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(841,plain,
! [SV142: $i] :
( ( ( in @ ( sK25_B @ SV142 ) @ SV142 )
= $true )
| ( ( SV142 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(842,plain,
! [SV143: $i] :
( ( ( ( SV143 != empty_set ) )
= $true )
| ( ( ! [SY427: $i] :
~ ( in @ SY427 @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(843,plain,
! [SV188: $i,SV66: $i] :
( ( ~ ( subset @ SV66 @ SV188 )
| ! [SY473: $i] : ( subset @ ( cartesian_product2 @ SV66 @ SY473 ) @ ( cartesian_product2 @ SV188 @ SY473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(844,plain,
! [SV189: $i,SV66: $i] :
( ( ~ ( subset @ SV66 @ SV189 )
| ! [SY474: $i] : ( subset @ ( cartesian_product2 @ SY474 @ SV66 ) @ ( cartesian_product2 @ SY474 @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(845,plain,
! [SV109: $i,SV67: $i] :
( ( ! [SY395: $i,SY396: $i] :
( ~ ( in @ SV67 @ SY395 )
| ~ ( in @ SV109 @ SY396 )
| ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY395 @ SY396 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[759]) ).
thf(846,plain,
! [SV109: $i,SV67: $i] :
( ( ~ ( ~ ! [SY397: $i] :
( ! [SY398: $i] :
~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY397 @ SY398 ) )
| ( in @ SV67 @ SY397 ) )
| ~ ! [SY399: $i,SY400: $i] :
( ~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY399 @ SY400 ) )
| ( in @ SV109 @ SY400 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(847,plain,
! [SV190: $i,SV144: $i] :
( ( ( disjoint @ SV144 @ SV190 )
| ~ ( ~ ( in @ ( sK28_C @ SV190 @ SV144 ) @ SV144 )
| ~ ( in @ ( sK28_C @ SV190 @ SV144 ) @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(848,plain,
! [SV191: $i,SV145: $i] :
( ( ! [SY475: $i] :
( ~ ( in @ SY475 @ SV145 )
| ~ ( in @ SY475 @ SV191 ) )
| ~ ( disjoint @ SV145 @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(849,plain,
! [SV192: $i,SV146: $i] :
( ( ( ( set_difference @ SV146 @ ( singleton @ SV192 ) )
!= SV146 )
| ~ ( in @ SV192 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(850,plain,
! [SV147: $i,SV193: $i] :
( ( ( in @ SV193 @ SV147 )
| ( ( set_difference @ SV147 @ ( singleton @ SV193 ) )
= SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(851,plain,
! [SV148: $i,SV194: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
| ~ ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 ) )
| ~ ( ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
| ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 ) ) )
| ( SV194
= ( powerset @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(852,plain,
! [SV149: $i,SV195: $i] :
( ( ( SV195
!= ( powerset @ SV149 ) )
| ~ ( ~ ! [SY476: $i] :
( ~ ( in @ SY476 @ SV195 )
| ( subset @ SY476 @ SV149 ) )
| ~ ! [SY477: $i] :
( ~ ( subset @ SY477 @ SV149 )
| ( in @ SY477 @ SV195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(853,plain,
! [SV196: $i,SV150: $i] :
( ( ~ ( subset @ SV150 @ ( singleton @ SV196 ) )
| ( SV150 = empty_set )
| ( SV150
= ( singleton @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(854,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[768]) ).
thf(855,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[768]) ).
thf(856,plain,
! [SV197: $i,SV151: $i] :
( ( ( SV151 = SV197 )
| ~ ( subset @ SV151 @ SV197 )
| ( proper_subset @ SV151 @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(857,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[770]) ).
thf(858,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[770]) ).
thf(859,plain,
! [SV68: $i,SV198: $i] :
( ( ! [SY478: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK23_D @ SY478 @ SV198 @ SV68 ) @ SY478 )
| ( ( sK23_D @ SY478 @ SV198 @ SV68 )
!= SV68 ) )
| ~ ( ~ ( in @ ( sK23_D @ SY478 @ SV198 @ SV68 ) @ SY478 )
| ( ( sK23_D @ SY478 @ SV198 @ SV68 )
!= SV198 ) ) )
| ~ ( ( in @ ( sK23_D @ SY478 @ SV198 @ SV68 ) @ SY478 )
| ( ( sK23_D @ SY478 @ SV198 @ SV68 )
= SV68 )
| ( ( sK23_D @ SY478 @ SV198 @ SV68 )
= SV198 ) ) )
| ( SY478
= ( unordered_pair @ SV68 @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(860,plain,
! [SV199: $i,SV68: $i] :
( ( ! [SY479: $i] :
( ( SY479
!= ( unordered_pair @ SV68 @ SV199 ) )
| ~ ( ~ ! [SY480: $i] :
( ~ ( in @ SY480 @ SY479 )
| ( SY480 = SV68 )
| ( SY480 = SV199 ) )
| ~ ~ ( ~ ! [SY370: $i] :
( ( SY370 != SV68 )
| ( in @ SY370 @ SY479 ) )
| ~ ! [SY482: $i] :
( ( SY482 != SV199 )
| ( in @ SY482 @ SY479 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(861,plain,
! [SV152: $i,SV200: $i] :
( ( ~ ( ~ ( ! [SY483: $i] :
( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SY483 )
| ~ ( in @ SY483 @ SV152 ) )
| ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ ( sK14_SY232 @ SV200 @ SV152 ) )
| ~ ( in @ ( sK14_SY232 @ SV200 @ SV152 ) @ SV152 ) )
| ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) ) )
| ( SV200
= ( union @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(862,plain,
! [SV153: $i,SV201: $i] :
( ( ( SV201
!= ( union @ SV153 ) )
| ~ ( ~ ! [SY484: $i] :
( ! [SY443: $i] :
( ~ ( in @ SY484 @ SY443 )
| ~ ( in @ SY443 @ SV153 ) )
| ( in @ SY484 @ SV201 ) )
| ~ ! [SY486: $i] :
( ~ ( in @ SY486 @ SV201 )
| ~ ( ~ ( in @ SY486 @ ( sK12_D @ SY486 @ SV201 @ SV153 ) )
| ~ ( in @ ( sK12_D @ SY486 @ SV201 @ SV153 ) @ SV153 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(863,plain,
! [SV77: $i,SV13: $i,SV154: $i] :
( ( ( in @ SV154 @ SV13 )
= $true )
| ( ( subset @ SV13 @ ( set_difference @ SV77 @ ( singleton @ SV154 ) ) )
= $true )
| ( ( subset @ SV13 @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(864,plain,
! [SV119: $i,SV78: $i,SV110: $i,SV14: $i] :
( ( ( SV14 = SV110 )
= $true )
| ( ( ( ( unordered_pair @ SV14 @ SV78 )
!= ( unordered_pair @ SV110 @ SV119 ) ) )
= $true )
| ( ( SV14 = SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(865,plain,
! [SV120: $i,SV111: $i,SV79: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV79 ) )
= $true )
| ( ( ~ ( subset @ SV111 @ SV120 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV15 @ SV111 ) @ ( cartesian_product2 @ SV79 @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(866,plain,
! [SV112: $i,SV82: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV82 )
= $false )
| ( ( ~ ( subset @ SV18 @ SV112 ) )
= $true )
| ( ( subset @ SV18 @ ( set_intersection2 @ SV82 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(867,plain,
! [SV113: $i,SV83: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV83 )
= $false )
| ( ( ~ ( subset @ SV83 @ SV113 ) )
= $true )
| ( ( subset @ SV19 @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(868,plain,
! [SV31: $i,SV114: $i,SV93: $i] :
( ( ( disjoint @ SV93 @ SV114 )
= $false )
| ( ( ~ ( subset @ SV31 @ SV93 ) )
= $true )
| ( ( disjoint @ SV31 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(869,plain,
! [SV115: $i,SV96: $i,SV35: $i] :
( ( ( subset @ SV35 @ SV96 )
= $false )
| ( ( ~ ( subset @ SV115 @ SV96 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV35 @ SV115 ) @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(870,plain,
! [SV54: $i,SV105: $i] :
( ( ( empty @ SV105 )
= $false )
| ( ( SV54 = SV105 )
= $true )
| ( ( empty @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(871,plain,
! [SV157: $i,SV122: $i] :
( ( ( ( ( set_difference @ SV122 @ SV157 )
!= empty_set ) )
= $true )
| ( ( subset @ SV122 @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[791]) ).
thf(872,plain,
! [SV158: $i,SV123: $i] :
( ( ( ~ ( subset @ SV123 @ SV158 ) )
= $true )
| ( ( ( set_difference @ SV123 @ SV158 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(873,plain,
! [SV55: $i,SV159: $i] :
( ( ( ~ ( subset @ SV159 @ ( sK29_B @ SV55 ) )
| ( are_equipotent @ SV159 @ ( sK29_B @ SV55 ) ) )
= $true )
| ( ( in @ SV159 @ ( sK29_B @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[793]) ).
thf(874,plain,
! [SV55: $i] :
( ( ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ ( sK29_B @ SV55 ) )
| ( in @ ( powerset @ SY296 ) @ ( sK29_B @ SV55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[794]) ).
thf(875,plain,
! [SV55: $i] :
( ( ~ ~ ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( in @ SY297 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SY298 @ SY297 )
| ( in @ SY298 @ ( sK29_B @ SV55 ) ) )
| ~ ( in @ SV55 @ ( sK29_B @ SV55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[794]) ).
thf(876,plain,
! [SV160: $i,SV124: $i] :
( ( ( ( ( set_difference @ SV124 @ SV160 )
!= empty_set ) )
= $true )
| ( ( subset @ SV124 @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(877,plain,
! [SV161: $i,SV125: $i] :
( ( ( ~ ( subset @ SV125 @ SV161 ) )
= $true )
| ( ( ( set_difference @ SV125 @ SV161 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(878,plain,
! [SV162: $i,SV126: $i] :
( ( ( ~ ( in @ SV126 @ SV162 ) )
= $true )
| ( ( subset @ ( singleton @ SV126 ) @ SV162 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(879,plain,
! [SV163: $i,SV127: $i] :
( ( ( ~ ( subset @ ( singleton @ SV127 ) @ SV163 ) )
= $true )
| ( ( in @ SV127 @ SV163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(880,plain,
! [SV128: $i,SV164: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_C @ SV164 @ SV128 ) @ SV128 )
| ~ ~ ( in @ ( sK16_C @ SV164 @ SV128 ) @ SV164 ) ) )
= $true )
| ( ( subset @ SV128 @ SV164 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[799]) ).
thf(881,plain,
! [SV165: $i,SV129: $i] :
( ( ( ~ ( subset @ SV129 @ SV165 ) )
= $true )
| ( ( ! [SY445: $i] :
( ~ ( in @ SY445 @ SV129 )
| ( in @ SY445 @ SV165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(882,plain,
! [SV202: $i,SV166: $i,SV56: $i] :
( ( ~ ( ~ ( ! [SY487: $i,SY488: $i] :
( ~ ( in @ SY487 @ SV56 )
| ~ ( in @ SY488 @ SV166 )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ SY487 @ SY488 ) ) )
| ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) @ SV166 ) )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) ) ) )
| ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) ) )
| ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(883,plain,
! [SV167: $i,SV56: $i,SV203: $i] :
( ( ( SV203
!= ( cartesian_product2 @ SV56 @ SV167 ) )
| ~ ( ~ ! [SY489: $i] :
( ! [SY451: $i,SY452: $i] :
( ~ ( in @ SY451 @ SV56 )
| ~ ( in @ SY452 @ SV167 )
| ( SY489
!= ( ordered_pair @ SY451 @ SY452 ) ) )
| ( in @ SY489 @ SV203 ) )
| ~ ! [SY492: $i] :
( ~ ( in @ SY492 @ SV203 )
| ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SY492 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SY492 @ SV203 @ SV167 @ SV56 ) @ SV167 ) )
| ( SY492
!= ( ordered_pair @ ( sK17_E @ SY492 @ SV203 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SY492 @ SV203 @ SV167 @ SV56 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(884,plain,
! [SV168: $i,SV130: $i] :
( ( ( disjoint @ SV130 @ SV168 )
= $true )
| ( ( in @ ( sK27_C @ SV168 @ SV130 ) @ ( set_intersection2 @ SV130 @ SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(885,plain,
! [SV169: $i,SV131: $i] :
( ( ( ! [SY454: $i] :
~ ( in @ SY454 @ ( set_intersection2 @ SV131 @ SV169 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(886,plain,
! [SV170: $i,SV132: $i] :
( ( ( ~ ( subset @ SV132 @ SV170 )
| ~ ( subset @ SV170 @ SV132 ) )
= $true )
| ( ( SV132 = SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(887,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(888,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(889,plain,
! [SV171: $i,SV133: $i] :
( ( ( ~ ( in @ SV133 @ SV171 ) )
= $true )
| ( ( subset @ ( singleton @ SV133 ) @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(890,plain,
! [SV172: $i,SV134: $i] :
( ( ( ~ ( subset @ ( singleton @ SV134 ) @ SV172 ) )
= $true )
| ( ( in @ SV134 @ SV172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[809]) ).
thf(891,plain,
! [SV173: $i,SV135: $i] :
( ( ( ~ ( subset @ SV135 @ ( singleton @ SV173 ) ) )
= $true )
| ( ( ( SV135 = empty_set )
| ( SV135
= ( singleton @ SV173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(892,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(893,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(894,plain,
! [SV57: $i,SV174: $i] :
( ( ( ~ ( subset @ SV174 @ ( sK6_B @ SV57 ) )
| ( are_equipotent @ SV174 @ ( sK6_B @ SV57 ) ) )
= $true )
| ( ( in @ SV174 @ ( sK6_B @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(895,plain,
! [SV57: $i] :
( ( ~ ! [SY310: $i] :
( ~ ( ~ ! [SY311: $i] :
( ~ ( subset @ SY311 @ SY310 )
| ( in @ SY311 @ ( sK7_SY226 @ SY310 @ SV57 ) ) )
| ~ ( in @ ( sK7_SY226 @ SY310 @ SV57 ) @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SY310 @ ( sK6_B @ SV57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(896,plain,
! [SV57: $i] :
( ( ~ ~ ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ SY312 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SV57 @ ( sK6_B @ SV57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[814]) ).
thf(897,plain,
! [SV204: $i,SV106: $i,SV58: $i] :
( ( ! [SY493: $i] :
( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SV204 @ SY493 ) )
| ( SV58 = SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(898,plain,
! [SV205: $i,SV106: $i,SV58: $i] :
( ( ! [SY494: $i] :
( ( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SV205 @ SY494 ) )
| ( SV106 = SY494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(899,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) ) )
| ~ ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 )
| ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) ) )
| ( SV206
= ( set_union2 @ SV59 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(900,plain,
! [SV176: $i,SV59: $i,SV207: $i] :
( ( ( SV207
!= ( set_union2 @ SV59 @ SV176 ) )
| ~ ( ~ ! [SY495: $i] :
( ~ ( in @ SY495 @ SV207 )
| ( in @ SY495 @ SV59 )
| ( in @ SY495 @ SV176 ) )
| ~ ~ ( ~ ! [SY496: $i] :
( ~ ( in @ SY496 @ SV59 )
| ( in @ SY496 @ SV207 ) )
| ~ ! [SY497: $i] :
( ~ ( in @ SY497 @ SV176 )
| ( in @ SY497 @ SV207 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(901,plain,
! [SV107: $i,SV208: $i,SV60: $i] :
( ( ! [SY498: $i] :
( ~ ( in @ SV60 @ SV208 )
| ~ ( in @ SV107 @ SY498 )
| ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV208 @ SY498 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(902,plain,
! [SV107: $i,SV60: $i] :
( ( ~ ! [SY391: $i] :
( ! [SY392: $i] :
~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY391 @ SY392 ) )
| ( in @ SV60 @ SY391 ) )
| ~ ! [SY393: $i,SY394: $i] :
( ~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY393 @ SY394 ) )
| ( in @ SV107 @ SY394 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(903,plain,
! [SV61: $i,SV108: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
| ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 ) )
= $true )
| ( ( SV61 = SV108 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(904,plain,
! [SV61: $i,SV108: $i] :
( ( ( ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
| ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 ) )
= $true )
| ( ( SV61 = SV108 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(905,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(906,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(907,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ SX0 )
| ( empty @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(908,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ! [SX1: $i] :
( ~ ( empty @ SX1 )
| ( element @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(909,plain,
! [SV62: $i] :
( ( ( empty @ ( sK9_B @ SV62 ) )
= $false )
| ( ( empty @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(910,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
| ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) ) ) )
| ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(911,plain,
! [SV178: $i,SV63: $i,SV210: $i] :
( ( ( SV210
!= ( set_intersection2 @ SV63 @ SV178 ) )
| ~ ( ~ ! [SY499: $i] :
( ~ ( in @ SY499 @ SV63 )
| ~ ( in @ SY499 @ SV178 )
| ( in @ SY499 @ SV210 ) )
| ~ ~ ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SV210 )
| ( in @ SY500 @ SV63 ) )
| ~ ! [SY501: $i] :
( ~ ( in @ SY501 @ SV210 )
| ( in @ SY501 @ SV178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(912,plain,
! [SV136: $i,SV179: $i] :
( ( ( ~ ( ~ ( ( ( sK26_C @ SV179 @ SV136 )
!= SV136 )
| ~ ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 ) )
| ~ ( ( ( sK26_C @ SV179 @ SV136 )
= SV136 )
| ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 ) ) ) )
= $true )
| ( ( SV179
= ( singleton @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[831]) ).
thf(913,plain,
! [SV137: $i,SV180: $i] :
( ( ( ( SV180
!= ( singleton @ SV137 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY465: $i] :
( ( SY465 != SV137 )
| ( in @ SY465 @ SV180 ) )
| ~ ! [SY466: $i] :
( ~ ( in @ SY466 @ SV180 )
| ( SY466 = SV137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[832]) ).
thf(914,plain,
! [SV181: $i,SV138: $i] :
( ( ( ( ( set_intersection2 @ SV138 @ SV181 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV138 @ SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[833]) ).
thf(915,plain,
! [SV182: $i,SV139: $i] :
( ( ( ~ ( disjoint @ SV139 @ SV182 ) )
= $true )
| ( ( ( set_intersection2 @ SV139 @ SV182 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(916,plain,
! [SV183: $i,SV140: $i] :
( ( ( ( ( set_difference @ SV140 @ SV183 )
!= SV140 ) )
= $true )
| ( ( disjoint @ SV140 @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[835]) ).
thf(917,plain,
! [SV184: $i,SV141: $i] :
( ( ( ~ ( disjoint @ SV141 @ SV184 ) )
= $true )
| ( ( ( set_difference @ SV141 @ SV184 )
= SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(918,plain,
! [SV185: $i,SV211: $i,SV64: $i] :
( ( ~ ( in @ SV64 @ SV211 )
| ~ ( in @ SV185 @ SV211 )
| ( subset @ ( unordered_pair @ SV64 @ SV185 ) @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(919,plain,
! [SV64: $i] :
( ( ~ ! [SY343: $i,SY344: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY343 ) @ SY344 )
| ( in @ SV64 @ SY344 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(920,plain,
! [SV64: $i] :
( ( ~ ! [SY345: $i,SY346: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY345 ) @ SY346 )
| ( in @ SY345 @ SY346 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[838]) ).
thf(921,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
| ~ ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) ) ) )
| ( SV212
= ( set_difference @ SV65 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(922,plain,
! [SV187: $i,SV65: $i,SV213: $i] :
( ( ( SV213
!= ( set_difference @ SV65 @ SV187 ) )
| ~ ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV65 )
| ( in @ SY502 @ SV187 )
| ( in @ SY502 @ SV213 ) )
| ~ ~ ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SV213 )
| ( in @ SY503 @ SV65 ) )
| ~ ! [SY504: $i] :
( ~ ( in @ SY504 @ SV213 )
| ~ ( in @ SY504 @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(923,plain,
! [SV143: $i] :
( ( ( SV143 = empty_set )
= $false )
| ( ( ! [SY427: $i] :
~ ( in @ SY427 @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(924,plain,
! [SV188: $i,SV66: $i] :
( ( ( ~ ( subset @ SV66 @ SV188 ) )
= $true )
| ( ( ! [SY473: $i] : ( subset @ ( cartesian_product2 @ SV66 @ SY473 ) @ ( cartesian_product2 @ SV188 @ SY473 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(925,plain,
! [SV189: $i,SV66: $i] :
( ( ( ~ ( subset @ SV66 @ SV189 ) )
= $true )
| ( ( ! [SY474: $i] : ( subset @ ( cartesian_product2 @ SY474 @ SV66 ) @ ( cartesian_product2 @ SY474 @ SV189 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(926,plain,
! [SV109: $i,SV214: $i,SV67: $i] :
( ( ! [SY505: $i] :
( ~ ( in @ SV67 @ SV214 )
| ~ ( in @ SV109 @ SY505 )
| ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV214 @ SY505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(927,plain,
! [SV109: $i,SV67: $i] :
( ( ~ ! [SY397: $i] :
( ! [SY398: $i] :
~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY397 @ SY398 ) )
| ( in @ SV67 @ SY397 ) )
| ~ ! [SY399: $i,SY400: $i] :
( ~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY399 @ SY400 ) )
| ( in @ SV109 @ SY400 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(928,plain,
! [SV190: $i,SV144: $i] :
( ( ( disjoint @ SV144 @ SV190 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK28_C @ SV190 @ SV144 ) @ SV144 )
| ~ ( in @ ( sK28_C @ SV190 @ SV144 ) @ SV190 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(929,plain,
! [SV191: $i,SV145: $i] :
( ( ( ! [SY475: $i] :
( ~ ( in @ SY475 @ SV145 )
| ~ ( in @ SY475 @ SV191 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV145 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(930,plain,
! [SV192: $i,SV146: $i] :
( ( ( ( ( set_difference @ SV146 @ ( singleton @ SV192 ) )
!= SV146 ) )
= $true )
| ( ( ~ ( in @ SV192 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(931,plain,
! [SV147: $i,SV193: $i] :
( ( ( in @ SV193 @ SV147 )
= $true )
| ( ( ( set_difference @ SV147 @ ( singleton @ SV193 ) )
= SV147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(932,plain,
! [SV148: $i,SV194: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
| ~ ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 ) )
| ~ ( ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
| ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 ) ) ) )
= $true )
| ( ( SV194
= ( powerset @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(933,plain,
! [SV149: $i,SV195: $i] :
( ( ( ( SV195
!= ( powerset @ SV149 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY476: $i] :
( ~ ( in @ SY476 @ SV195 )
| ( subset @ SY476 @ SV149 ) )
| ~ ! [SY477: $i] :
( ~ ( subset @ SY477 @ SV149 )
| ( in @ SY477 @ SV195 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(934,plain,
! [SV196: $i,SV150: $i] :
( ( ( ~ ( subset @ SV150 @ ( singleton @ SV196 ) ) )
= $true )
| ( ( ( SV150 = empty_set )
| ( SV150
= ( singleton @ SV196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(935,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(936,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[855]) ).
thf(937,plain,
! [SV197: $i,SV151: $i] :
( ( ( ( SV151 = SV197 )
| ~ ( subset @ SV151 @ SV197 ) )
= $true )
| ( ( proper_subset @ SV151 @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[856]) ).
thf(938,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(939,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[858]) ).
thf(940,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV68 ) )
| ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV198 ) ) )
| ~ ( ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV68 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV198 ) ) )
| ( SV215
= ( unordered_pair @ SV68 @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(941,plain,
! [SV199: $i,SV68: $i,SV216: $i] :
( ( ( SV216
!= ( unordered_pair @ SV68 @ SV199 ) )
| ~ ( ~ ! [SY506: $i] :
( ~ ( in @ SY506 @ SV216 )
| ( SY506 = SV68 )
| ( SY506 = SV199 ) )
| ~ ~ ( ~ ! [SY507: $i] :
( ( SY507 != SV68 )
| ( in @ SY507 @ SV216 ) )
| ~ ! [SY508: $i] :
( ( SY508 != SV199 )
| ( in @ SY508 @ SV216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(942,plain,
! [SV152: $i,SV200: $i] :
( ( ( ~ ( ~ ( ! [SY483: $i] :
( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SY483 )
| ~ ( in @ SY483 @ SV152 ) )
| ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ ( sK14_SY232 @ SV200 @ SV152 ) )
| ~ ( in @ ( sK14_SY232 @ SV200 @ SV152 ) @ SV152 ) )
| ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) ) ) )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(943,plain,
! [SV153: $i,SV201: $i] :
( ( ( ( SV201
!= ( union @ SV153 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY484: $i] :
( ! [SY443: $i] :
( ~ ( in @ SY484 @ SY443 )
| ~ ( in @ SY443 @ SV153 ) )
| ( in @ SY484 @ SV201 ) )
| ~ ! [SY486: $i] :
( ~ ( in @ SY486 @ SV201 )
| ~ ( ~ ( in @ SY486 @ ( sK12_D @ SY486 @ SV201 @ SV153 ) )
| ~ ( in @ ( sK12_D @ SY486 @ SV201 @ SV153 ) @ SV153 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(944,plain,
! [SV119: $i,SV110: $i,SV78: $i,SV14: $i] :
( ( ( ( unordered_pair @ SV14 @ SV78 )
= ( unordered_pair @ SV110 @ SV119 ) )
= $false )
| ( ( SV14 = SV110 )
= $true )
| ( ( SV14 = SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(945,plain,
! [SV120: $i,SV111: $i,SV79: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV79 )
= $false )
| ( ( ~ ( subset @ SV111 @ SV120 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV15 @ SV111 ) @ ( cartesian_product2 @ SV79 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(946,plain,
! [SV82: $i,SV112: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV112 )
= $false )
| ( ( subset @ SV18 @ SV82 )
= $false )
| ( ( subset @ SV18 @ ( set_intersection2 @ SV82 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(947,plain,
! [SV19: $i,SV113: $i,SV83: $i] :
( ( ( subset @ SV83 @ SV113 )
= $false )
| ( ( subset @ SV19 @ SV83 )
= $false )
| ( ( subset @ SV19 @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(948,plain,
! [SV114: $i,SV93: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV93 )
= $false )
| ( ( disjoint @ SV93 @ SV114 )
= $false )
| ( ( disjoint @ SV31 @ SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(949,plain,
! [SV35: $i,SV96: $i,SV115: $i] :
( ( ( subset @ SV115 @ SV96 )
= $false )
| ( ( subset @ SV35 @ SV96 )
= $false )
| ( ( subset @ ( set_union2 @ SV35 @ SV115 ) @ SV96 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(950,plain,
! [SV157: $i,SV122: $i] :
( ( ( ( set_difference @ SV122 @ SV157 )
= empty_set )
= $false )
| ( ( subset @ SV122 @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(951,plain,
! [SV158: $i,SV123: $i] :
( ( ( subset @ SV123 @ SV158 )
= $false )
| ( ( ( set_difference @ SV123 @ SV158 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(952,plain,
! [SV55: $i,SV159: $i] :
( ( ( ~ ( subset @ SV159 @ ( sK29_B @ SV55 ) ) )
= $true )
| ( ( are_equipotent @ SV159 @ ( sK29_B @ SV55 ) )
= $true )
| ( ( in @ SV159 @ ( sK29_B @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(953,plain,
! [SV55: $i] :
( ( ! [SY296: $i] :
( ~ ( in @ SY296 @ ( sK29_B @ SV55 ) )
| ( in @ ( powerset @ SY296 ) @ ( sK29_B @ SV55 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[874]) ).
thf(954,plain,
! [SV55: $i] :
( ( ~ ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( in @ SY297 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SY298 @ SY297 )
| ( in @ SY298 @ ( sK29_B @ SV55 ) ) )
| ~ ( in @ SV55 @ ( sK29_B @ SV55 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(955,plain,
! [SV160: $i,SV124: $i] :
( ( ( ( set_difference @ SV124 @ SV160 )
= empty_set )
= $false )
| ( ( subset @ SV124 @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(956,plain,
! [SV161: $i,SV125: $i] :
( ( ( subset @ SV125 @ SV161 )
= $false )
| ( ( ( set_difference @ SV125 @ SV161 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(957,plain,
! [SV162: $i,SV126: $i] :
( ( ( in @ SV126 @ SV162 )
= $false )
| ( ( subset @ ( singleton @ SV126 ) @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(958,plain,
! [SV163: $i,SV127: $i] :
( ( ( subset @ ( singleton @ SV127 ) @ SV163 )
= $false )
| ( ( in @ SV127 @ SV163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(959,plain,
! [SV128: $i,SV164: $i] :
( ( ( ~ ( in @ ( sK16_C @ SV164 @ SV128 ) @ SV128 )
| ~ ~ ( in @ ( sK16_C @ SV164 @ SV128 ) @ SV164 ) )
= $false )
| ( ( subset @ SV128 @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(960,plain,
! [SV165: $i,SV129: $i] :
( ( ( subset @ SV129 @ SV165 )
= $false )
| ( ( ! [SY445: $i] :
( ~ ( in @ SY445 @ SV129 )
| ( in @ SY445 @ SV165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(961,plain,
! [SV202: $i,SV166: $i,SV56: $i] :
( ( ( ~ ( ~ ( ! [SY487: $i,SY488: $i] :
( ~ ( in @ SY487 @ SV56 )
| ~ ( in @ SY488 @ SV166 )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ SY487 @ SY488 ) ) )
| ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) @ SV166 ) )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) ) ) )
| ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) ) ) )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[882]) ).
thf(962,plain,
! [SV167: $i,SV56: $i,SV203: $i] :
( ( ( ( SV203
!= ( cartesian_product2 @ SV56 @ SV167 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY489: $i] :
( ! [SY451: $i,SY452: $i] :
( ~ ( in @ SY451 @ SV56 )
| ~ ( in @ SY452 @ SV167 )
| ( SY489
!= ( ordered_pair @ SY451 @ SY452 ) ) )
| ( in @ SY489 @ SV203 ) )
| ~ ! [SY492: $i] :
( ~ ( in @ SY492 @ SV203 )
| ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SY492 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SY492 @ SV203 @ SV167 @ SV56 ) @ SV167 ) )
| ( SY492
!= ( ordered_pair @ ( sK17_E @ SY492 @ SV203 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SY492 @ SV203 @ SV167 @ SV56 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(963,plain,
! [SV169: $i,SV131: $i,SV217: $i] :
( ( ( ~ ( in @ SV217 @ ( set_intersection2 @ SV131 @ SV169 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(964,plain,
! [SV170: $i,SV132: $i] :
( ( ( ~ ( subset @ SV132 @ SV170 ) )
= $true )
| ( ( ~ ( subset @ SV170 @ SV132 ) )
= $true )
| ( ( SV132 = SV170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[886]) ).
thf(965,plain,
! [SV218: $i] :
( ( ! [SY509: $i] :
( ( SV218 != SY509 )
| ( subset @ SV218 @ SY509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(966,plain,
! [SV219: $i] :
( ( ! [SY510: $i] :
( ( SV219 != SY510 )
| ( subset @ SY510 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(967,plain,
! [SV171: $i,SV133: $i] :
( ( ( in @ SV133 @ SV171 )
= $false )
| ( ( subset @ ( singleton @ SV133 ) @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(968,plain,
! [SV172: $i,SV134: $i] :
( ( ( subset @ ( singleton @ SV134 ) @ SV172 )
= $false )
| ( ( in @ SV134 @ SV172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(969,plain,
! [SV173: $i,SV135: $i] :
( ( ( subset @ SV135 @ ( singleton @ SV173 ) )
= $false )
| ( ( ( SV135 = empty_set )
| ( SV135
= ( singleton @ SV173 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(970,plain,
! [SV220: $i] :
( ( ( SV220 != empty_set )
| ! [SY511: $i] : ( subset @ SV220 @ ( singleton @ SY511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(971,plain,
! [SV221: $i] :
( ( ! [SY512: $i] :
( ( SV221
!= ( singleton @ SY512 ) )
| ( subset @ SV221 @ ( singleton @ SY512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(972,plain,
! [SV57: $i,SV174: $i] :
( ( ( ~ ( subset @ SV174 @ ( sK6_B @ SV57 ) ) )
= $true )
| ( ( are_equipotent @ SV174 @ ( sK6_B @ SV57 ) )
= $true )
| ( ( in @ SV174 @ ( sK6_B @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(973,plain,
! [SV57: $i] :
( ( ! [SY310: $i] :
( ~ ( ~ ! [SY311: $i] :
( ~ ( subset @ SY311 @ SY310 )
| ( in @ SY311 @ ( sK7_SY226 @ SY310 @ SV57 ) ) )
| ~ ( in @ ( sK7_SY226 @ SY310 @ SV57 ) @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SY310 @ ( sK6_B @ SV57 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(974,plain,
! [SV57: $i] :
( ( ~ ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ SY312 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SV57 @ ( sK6_B @ SV57 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(975,plain,
! [SV204: $i,SV106: $i,SV58: $i] :
( ( ( ! [SY493: $i] :
( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SV204 @ SY493 ) ) )
= $true )
| ( ( SV58 = SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(976,plain,
! [SV222: $i,SV205: $i,SV106: $i,SV58: $i] :
( ( ( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SV205 @ SV222 ) )
| ( SV106 = SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(977,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) ) )
| ~ ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 )
| ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) ) ) )
= $true )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(978,plain,
! [SV176: $i,SV59: $i,SV207: $i] :
( ( ( ( SV207
!= ( set_union2 @ SV59 @ SV176 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY495: $i] :
( ~ ( in @ SY495 @ SV207 )
| ( in @ SY495 @ SV59 )
| ( in @ SY495 @ SV176 ) )
| ~ ~ ( ~ ! [SY496: $i] :
( ~ ( in @ SY496 @ SV59 )
| ( in @ SY496 @ SV207 ) )
| ~ ! [SY497: $i] :
( ~ ( in @ SY497 @ SV176 )
| ( in @ SY497 @ SV207 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(979,plain,
! [SV223: $i,SV107: $i,SV208: $i,SV60: $i] :
( ( ~ ( in @ SV60 @ SV208 )
| ~ ( in @ SV107 @ SV223 )
| ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV208 @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(980,plain,
! [SV107: $i,SV60: $i] :
( ( ~ ! [SY391: $i] :
( ! [SY392: $i] :
~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY391 @ SY392 ) )
| ( in @ SV60 @ SY391 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(981,plain,
! [SV107: $i,SV60: $i] :
( ( ~ ! [SY393: $i,SY394: $i] :
( ~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY393 @ SY394 ) )
| ( in @ SV107 @ SY394 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[902]) ).
thf(982,plain,
! [SV61: $i,SV108: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 ) )
= $true )
| ( ( ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 ) )
= $true )
| ( ( SV61 = SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(983,plain,
! [SV61: $i,SV108: $i] :
( ( ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
= $true )
| ( ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 )
= $true )
| ( ( SV61 = SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(984,plain,
! [SV224: $i] :
( ( ( empty @ SV224 )
| ! [SY513: $i] :
( ~ ( element @ SY513 @ SV224 )
| ( in @ SY513 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(985,plain,
! [SV225: $i] :
( ( ( empty @ SV225 )
| ! [SY514: $i] :
( ~ ( in @ SY514 @ SV225 )
| ( element @ SY514 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(986,plain,
! [SV226: $i] :
( ( ~ ( empty @ SV226 )
| ! [SY515: $i] :
( ~ ( element @ SY515 @ SV226 )
| ( empty @ SY515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(987,plain,
! [SV227: $i] :
( ( ~ ( empty @ SV227 )
| ! [SY516: $i] :
( ~ ( empty @ SY516 )
| ( element @ SY516 @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(988,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
| ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) ) ) ) )
= $true )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(989,plain,
! [SV178: $i,SV63: $i,SV210: $i] :
( ( ( ( SV210
!= ( set_intersection2 @ SV63 @ SV178 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY499: $i] :
( ~ ( in @ SY499 @ SV63 )
| ~ ( in @ SY499 @ SV178 )
| ( in @ SY499 @ SV210 ) )
| ~ ~ ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SV210 )
| ( in @ SY500 @ SV63 ) )
| ~ ! [SY501: $i] :
( ~ ( in @ SY501 @ SV210 )
| ( in @ SY501 @ SV178 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(990,plain,
! [SV136: $i,SV179: $i] :
( ( ( ~ ( ( ( sK26_C @ SV179 @ SV136 )
!= SV136 )
| ~ ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 ) )
| ~ ( ( ( sK26_C @ SV179 @ SV136 )
= SV136 )
| ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 ) ) )
= $false )
| ( ( SV179
= ( singleton @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(991,plain,
! [SV137: $i,SV180: $i] :
( ( ( SV180
= ( singleton @ SV137 ) )
= $false )
| ( ( ~ ( ~ ! [SY465: $i] :
( ( SY465 != SV137 )
| ( in @ SY465 @ SV180 ) )
| ~ ! [SY466: $i] :
( ~ ( in @ SY466 @ SV180 )
| ( SY466 = SV137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(992,plain,
! [SV181: $i,SV138: $i] :
( ( ( ( set_intersection2 @ SV138 @ SV181 )
= empty_set )
= $false )
| ( ( disjoint @ SV138 @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(993,plain,
! [SV182: $i,SV139: $i] :
( ( ( disjoint @ SV139 @ SV182 )
= $false )
| ( ( ( set_intersection2 @ SV139 @ SV182 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(994,plain,
! [SV183: $i,SV140: $i] :
( ( ( ( set_difference @ SV140 @ SV183 )
= SV140 )
= $false )
| ( ( disjoint @ SV140 @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(995,plain,
! [SV184: $i,SV141: $i] :
( ( ( disjoint @ SV141 @ SV184 )
= $false )
| ( ( ( set_difference @ SV141 @ SV184 )
= SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(996,plain,
! [SV185: $i,SV211: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV211 )
| ~ ( in @ SV185 @ SV211 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV64 @ SV185 ) @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(997,plain,
! [SV64: $i] :
( ( ! [SY343: $i,SY344: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY343 ) @ SY344 )
| ( in @ SV64 @ SY344 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[919]) ).
thf(998,plain,
! [SV64: $i] :
( ( ! [SY345: $i,SY346: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SY345 ) @ SY346 )
| ( in @ SY345 @ SY346 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[920]) ).
thf(999,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
| ~ ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) ) ) ) )
= $true )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1000,plain,
! [SV187: $i,SV65: $i,SV213: $i] :
( ( ( ( SV213
!= ( set_difference @ SV65 @ SV187 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV65 )
| ( in @ SY502 @ SV187 )
| ( in @ SY502 @ SV213 ) )
| ~ ~ ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SV213 )
| ( in @ SY503 @ SV65 ) )
| ~ ! [SY504: $i] :
( ~ ( in @ SY504 @ SV213 )
| ~ ( in @ SY504 @ SV187 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(1001,plain,
! [SV143: $i,SV228: $i] :
( ( ( ~ ( in @ SV228 @ SV143 ) )
= $true )
| ( ( SV143 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1002,plain,
! [SV188: $i,SV66: $i] :
( ( ( subset @ SV66 @ SV188 )
= $false )
| ( ( ! [SY473: $i] : ( subset @ ( cartesian_product2 @ SV66 @ SY473 ) @ ( cartesian_product2 @ SV188 @ SY473 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[924]) ).
thf(1003,plain,
! [SV189: $i,SV66: $i] :
( ( ( subset @ SV66 @ SV189 )
= $false )
| ( ( ! [SY474: $i] : ( subset @ ( cartesian_product2 @ SY474 @ SV66 ) @ ( cartesian_product2 @ SY474 @ SV189 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(1004,plain,
! [SV229: $i,SV109: $i,SV214: $i,SV67: $i] :
( ( ~ ( in @ SV67 @ SV214 )
| ~ ( in @ SV109 @ SV229 )
| ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV214 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1005,plain,
! [SV109: $i,SV67: $i] :
( ( ~ ! [SY397: $i] :
( ! [SY398: $i] :
~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY397 @ SY398 ) )
| ( in @ SV67 @ SY397 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(1006,plain,
! [SV109: $i,SV67: $i] :
( ( ~ ! [SY399: $i,SY400: $i] :
( ~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY399 @ SY400 ) )
| ( in @ SV109 @ SY400 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(1007,plain,
! [SV144: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV190 @ SV144 ) @ SV144 )
| ~ ( in @ ( sK28_C @ SV190 @ SV144 ) @ SV190 ) )
= $false )
| ( ( disjoint @ SV144 @ SV190 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(1008,plain,
! [SV191: $i,SV145: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ SV145 )
| ~ ( in @ SV230 @ SV191 ) )
= $true )
| ( ( ~ ( disjoint @ SV145 @ SV191 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1009,plain,
! [SV192: $i,SV146: $i] :
( ( ( ( set_difference @ SV146 @ ( singleton @ SV192 ) )
= SV146 )
= $false )
| ( ( ~ ( in @ SV192 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(1010,plain,
! [SV148: $i,SV194: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
| ~ ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 ) )
| ~ ( ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
| ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 ) ) )
= $false )
| ( ( SV194
= ( powerset @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(1011,plain,
! [SV149: $i,SV195: $i] :
( ( ( SV195
= ( powerset @ SV149 ) )
= $false )
| ( ( ~ ( ~ ! [SY476: $i] :
( ~ ( in @ SY476 @ SV195 )
| ( subset @ SY476 @ SV149 ) )
| ~ ! [SY477: $i] :
( ~ ( subset @ SY477 @ SV149 )
| ( in @ SY477 @ SV195 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(1012,plain,
! [SV196: $i,SV150: $i] :
( ( ( subset @ SV150 @ ( singleton @ SV196 ) )
= $false )
| ( ( ( SV150 = empty_set )
| ( SV150
= ( singleton @ SV196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(1013,plain,
! [SV231: $i] :
( ( ( SV231 != empty_set )
| ! [SY517: $i] : ( subset @ SV231 @ ( singleton @ SY517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1014,plain,
! [SV232: $i] :
( ( ! [SY518: $i] :
( ( SV232
!= ( singleton @ SY518 ) )
| ( subset @ SV232 @ ( singleton @ SY518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1015,plain,
! [SV197: $i,SV151: $i] :
( ( ( SV151 = SV197 )
= $true )
| ( ( ~ ( subset @ SV151 @ SV197 ) )
= $true )
| ( ( proper_subset @ SV151 @ SV197 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1016,plain,
! [SV233: $i] :
( ( ! [SY519: $i] :
( ~ ( proper_subset @ SV233 @ SY519 )
| ( SV233 != SY519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1017,plain,
! [SV234: $i] :
( ( ! [SY520: $i] :
( ~ ( proper_subset @ SV234 @ SY520 )
| ( subset @ SV234 @ SY520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1018,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV68 ) )
| ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV198 ) ) )
| ~ ( ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV68 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV198 ) ) ) )
= $true )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1019,plain,
! [SV199: $i,SV68: $i,SV216: $i] :
( ( ( ( SV216
!= ( unordered_pair @ SV68 @ SV199 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY506: $i] :
( ~ ( in @ SY506 @ SV216 )
| ( SY506 = SV68 )
| ( SY506 = SV199 ) )
| ~ ~ ( ~ ! [SY507: $i] :
( ( SY507 != SV68 )
| ( in @ SY507 @ SV216 ) )
| ~ ! [SY508: $i] :
( ( SY508 != SV199 )
| ( in @ SY508 @ SV216 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1020,plain,
! [SV152: $i,SV200: $i] :
( ( ( ~ ( ! [SY483: $i] :
( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SY483 )
| ~ ( in @ SY483 @ SV152 ) )
| ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) )
| ~ ( ~ ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ ( sK14_SY232 @ SV200 @ SV152 ) )
| ~ ( in @ ( sK14_SY232 @ SV200 @ SV152 ) @ SV152 ) )
| ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) ) )
= $false )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(1021,plain,
! [SV153: $i,SV201: $i] :
( ( ( SV201
= ( union @ SV153 ) )
= $false )
| ( ( ~ ( ~ ! [SY484: $i] :
( ! [SY443: $i] :
( ~ ( in @ SY484 @ SY443 )
| ~ ( in @ SY443 @ SV153 ) )
| ( in @ SY484 @ SV201 ) )
| ~ ! [SY486: $i] :
( ~ ( in @ SY486 @ SV201 )
| ~ ( ~ ( in @ SY486 @ ( sK12_D @ SY486 @ SV201 @ SV153 ) )
| ~ ( in @ ( sK12_D @ SY486 @ SV201 @ SV153 ) @ SV153 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1022,plain,
! [SV79: $i,SV15: $i,SV120: $i,SV111: $i] :
( ( ( subset @ SV111 @ SV120 )
= $false )
| ( ( subset @ SV15 @ SV79 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV15 @ SV111 ) @ ( cartesian_product2 @ SV79 @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1023,plain,
! [SV55: $i,SV159: $i] :
( ( ( subset @ SV159 @ ( sK29_B @ SV55 ) )
= $false )
| ( ( are_equipotent @ SV159 @ ( sK29_B @ SV55 ) )
= $true )
| ( ( in @ SV159 @ ( sK29_B @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(1024,plain,
! [SV55: $i,SV235: $i] :
( ( ~ ( in @ SV235 @ ( sK29_B @ SV55 ) )
| ( in @ ( powerset @ SV235 ) @ ( sK29_B @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1025,plain,
! [SV55: $i] :
( ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( in @ SY297 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SY298 @ SY297 )
| ( in @ SY298 @ ( sK29_B @ SV55 ) ) )
| ~ ( in @ SV55 @ ( sK29_B @ SV55 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1026,plain,
! [SV128: $i,SV164: $i] :
( ( ( ~ ( in @ ( sK16_C @ SV164 @ SV128 ) @ SV128 ) )
= $false )
| ( ( subset @ SV128 @ SV164 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(1027,plain,
! [SV128: $i,SV164: $i] :
( ( ( ~ ~ ( in @ ( sK16_C @ SV164 @ SV128 ) @ SV164 ) )
= $false )
| ( ( subset @ SV128 @ SV164 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[959]) ).
thf(1028,plain,
! [SV165: $i,SV129: $i,SV236: $i] :
( ( ( ~ ( in @ SV236 @ SV129 )
| ( in @ SV236 @ SV165 ) )
= $true )
| ( ( subset @ SV129 @ SV165 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1029,plain,
! [SV202: $i,SV166: $i,SV56: $i] :
( ( ( ~ ( ! [SY487: $i,SY488: $i] :
( ~ ( in @ SY487 @ SV56 )
| ~ ( in @ SY488 @ SV166 )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ SY487 @ SY488 ) ) )
| ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) @ SV166 ) )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) ) ) )
| ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) ) )
= $false )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(1030,plain,
! [SV167: $i,SV56: $i,SV203: $i] :
( ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false )
| ( ( ~ ( ~ ! [SY489: $i] :
( ! [SY451: $i,SY452: $i] :
( ~ ( in @ SY451 @ SV56 )
| ~ ( in @ SY452 @ SV167 )
| ( SY489
!= ( ordered_pair @ SY451 @ SY452 ) ) )
| ( in @ SY489 @ SV203 ) )
| ~ ! [SY492: $i] :
( ~ ( in @ SY492 @ SV203 )
| ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SY492 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SY492 @ SV203 @ SV167 @ SV56 ) @ SV167 ) )
| ( SY492
!= ( ordered_pair @ ( sK17_E @ SY492 @ SV203 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SY492 @ SV203 @ SV167 @ SV56 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(1031,plain,
! [SV169: $i,SV131: $i,SV217: $i] :
( ( ( in @ SV217 @ ( set_intersection2 @ SV131 @ SV169 ) )
= $false )
| ( ( ~ ( disjoint @ SV131 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1032,plain,
! [SV170: $i,SV132: $i] :
( ( ( subset @ SV132 @ SV170 )
= $false )
| ( ( ~ ( subset @ SV170 @ SV132 ) )
= $true )
| ( ( SV132 = SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1033,plain,
! [SV237: $i,SV218: $i] :
( ( ( SV218 != SV237 )
| ( subset @ SV218 @ SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1034,plain,
! [SV238: $i,SV219: $i] :
( ( ( SV219 != SV238 )
| ( subset @ SV238 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1035,plain,
! [SV173: $i,SV135: $i] :
( ( ( SV135 = empty_set )
= $true )
| ( ( SV135
= ( singleton @ SV173 ) )
= $true )
| ( ( subset @ SV135 @ ( singleton @ SV173 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1036,plain,
! [SV220: $i] :
( ( ( ( SV220 != empty_set ) )
= $true )
| ( ( ! [SY511: $i] : ( subset @ SV220 @ ( singleton @ SY511 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[970]) ).
thf(1037,plain,
! [SV239: $i,SV221: $i] :
( ( ( SV221
!= ( singleton @ SV239 ) )
| ( subset @ SV221 @ ( singleton @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1038,plain,
! [SV57: $i,SV174: $i] :
( ( ( subset @ SV174 @ ( sK6_B @ SV57 ) )
= $false )
| ( ( are_equipotent @ SV174 @ ( sK6_B @ SV57 ) )
= $true )
| ( ( in @ SV174 @ ( sK6_B @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1039,plain,
! [SV57: $i,SV240: $i] :
( ( ~ ( ~ ! [SY521: $i] :
( ~ ( subset @ SY521 @ SV240 )
| ( in @ SY521 @ ( sK7_SY226 @ SV240 @ SV57 ) ) )
| ~ ( in @ ( sK7_SY226 @ SV240 @ SV57 ) @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SV240 @ ( sK6_B @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1040,plain,
! [SV57: $i] :
( ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ SY312 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK6_B @ SV57 ) ) )
| ~ ( in @ SV57 @ ( sK6_B @ SV57 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1041,plain,
! [SV241: $i,SV204: $i,SV106: $i,SV58: $i] :
( ( ( ( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SV204 @ SV241 ) ) )
= $true )
| ( ( SV58 = SV204 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1042,plain,
! [SV222: $i,SV205: $i,SV106: $i,SV58: $i] :
( ( ( ( ( ordered_pair @ SV58 @ SV106 )
!= ( ordered_pair @ SV205 @ SV222 ) ) )
= $true )
| ( ( SV106 = SV222 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(1043,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) ) )
| ~ ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 )
| ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) ) )
= $false )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1044,plain,
! [SV176: $i,SV59: $i,SV207: $i] :
( ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false )
| ( ( ~ ( ~ ! [SY495: $i] :
( ~ ( in @ SY495 @ SV207 )
| ( in @ SY495 @ SV59 )
| ( in @ SY495 @ SV176 ) )
| ~ ~ ( ~ ! [SY496: $i] :
( ~ ( in @ SY496 @ SV59 )
| ( in @ SY496 @ SV207 ) )
| ~ ! [SY497: $i] :
( ~ ( in @ SY497 @ SV176 )
| ( in @ SY497 @ SV207 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(1045,plain,
! [SV223: $i,SV107: $i,SV208: $i,SV60: $i] :
( ( ( ~ ( in @ SV60 @ SV208 )
| ~ ( in @ SV107 @ SV223 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV208 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1046,plain,
! [SV107: $i,SV60: $i] :
( ( ! [SY391: $i] :
( ! [SY392: $i] :
~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY391 @ SY392 ) )
| ( in @ SV60 @ SY391 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[980]) ).
thf(1047,plain,
! [SV107: $i,SV60: $i] :
( ( ! [SY393: $i,SY394: $i] :
( ~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SY393 @ SY394 ) )
| ( in @ SV107 @ SY394 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[981]) ).
thf(1048,plain,
! [SV61: $i,SV108: $i] :
( ( ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
= $false )
| ( ( ~ ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 ) )
= $true )
| ( ( SV61 = SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1049,plain,
! [SV224: $i] :
( ( ( empty @ SV224 )
= $true )
| ( ( ! [SY513: $i] :
( ~ ( element @ SY513 @ SV224 )
| ( in @ SY513 @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1050,plain,
! [SV225: $i] :
( ( ( empty @ SV225 )
= $true )
| ( ( ! [SY514: $i] :
( ~ ( in @ SY514 @ SV225 )
| ( element @ SY514 @ SV225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[985]) ).
thf(1051,plain,
! [SV226: $i] :
( ( ( ~ ( empty @ SV226 ) )
= $true )
| ( ( ! [SY515: $i] :
( ~ ( element @ SY515 @ SV226 )
| ( empty @ SY515 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1052,plain,
! [SV227: $i] :
( ( ( ~ ( empty @ SV227 ) )
= $true )
| ( ( ! [SY516: $i] :
( ~ ( empty @ SY516 )
| ( element @ SY516 @ SV227 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1053,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
| ~ ~ ( ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
| ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) ) ) )
= $false )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1054,plain,
! [SV178: $i,SV63: $i,SV210: $i] :
( ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false )
| ( ( ~ ( ~ ! [SY499: $i] :
( ~ ( in @ SY499 @ SV63 )
| ~ ( in @ SY499 @ SV178 )
| ( in @ SY499 @ SV210 ) )
| ~ ~ ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SV210 )
| ( in @ SY500 @ SV63 ) )
| ~ ! [SY501: $i] :
( ~ ( in @ SY501 @ SV210 )
| ( in @ SY501 @ SV178 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1055,plain,
! [SV136: $i,SV179: $i] :
( ( ( ~ ( ( ( sK26_C @ SV179 @ SV136 )
!= SV136 )
| ~ ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 ) ) )
= $false )
| ( ( SV179
= ( singleton @ SV136 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1056,plain,
! [SV136: $i,SV179: $i] :
( ( ( ~ ( ( ( sK26_C @ SV179 @ SV136 )
= SV136 )
| ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 ) ) )
= $false )
| ( ( SV179
= ( singleton @ SV136 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1057,plain,
! [SV180: $i,SV137: $i] :
( ( ( ~ ! [SY465: $i] :
( ( SY465 != SV137 )
| ( in @ SY465 @ SV180 ) )
| ~ ! [SY466: $i] :
( ~ ( in @ SY466 @ SV180 )
| ( SY466 = SV137 ) ) )
= $false )
| ( ( SV180
= ( singleton @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1058,plain,
! [SV185: $i,SV211: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV211 ) )
= $true )
| ( ( ~ ( in @ SV185 @ SV211 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV64 @ SV185 ) @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1059,plain,
! [SV242: $i,SV64: $i] :
( ( ! [SY522: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SV242 ) @ SY522 )
| ( in @ SV64 @ SY522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1060,plain,
! [SV243: $i,SV64: $i] :
( ( ! [SY523: $i] :
( ~ ( subset @ ( unordered_pair @ SV64 @ SV243 ) @ SY523 )
| ( in @ SV243 @ SY523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1061,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
| ~ ~ ( ~ ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
| ~ ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) ) ) )
= $false )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1062,plain,
! [SV187: $i,SV65: $i,SV213: $i] :
( ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false )
| ( ( ~ ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV65 )
| ( in @ SY502 @ SV187 )
| ( in @ SY502 @ SV213 ) )
| ~ ~ ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SV213 )
| ( in @ SY503 @ SV65 ) )
| ~ ! [SY504: $i] :
( ~ ( in @ SY504 @ SV213 )
| ~ ( in @ SY504 @ SV187 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1063,plain,
! [SV143: $i,SV228: $i] :
( ( ( in @ SV228 @ SV143 )
= $false )
| ( ( SV143 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1064,plain,
! [SV188: $i,SV244: $i,SV66: $i] :
( ( ( subset @ ( cartesian_product2 @ SV66 @ SV244 ) @ ( cartesian_product2 @ SV188 @ SV244 ) )
= $true )
| ( ( subset @ SV66 @ SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1065,plain,
! [SV189: $i,SV66: $i,SV245: $i] :
( ( ( subset @ ( cartesian_product2 @ SV245 @ SV66 ) @ ( cartesian_product2 @ SV245 @ SV189 ) )
= $true )
| ( ( subset @ SV66 @ SV189 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1066,plain,
! [SV229: $i,SV109: $i,SV214: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV214 )
| ~ ( in @ SV109 @ SV229 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV214 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1067,plain,
! [SV109: $i,SV67: $i] :
( ( ! [SY397: $i] :
( ! [SY398: $i] :
~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY397 @ SY398 ) )
| ( in @ SV67 @ SY397 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1068,plain,
! [SV109: $i,SV67: $i] :
( ( ! [SY399: $i,SY400: $i] :
( ~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SY399 @ SY400 ) )
| ( in @ SV109 @ SY400 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1069,plain,
! [SV144: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV190 @ SV144 ) @ SV144 ) )
= $false )
| ( ( disjoint @ SV144 @ SV190 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1007]) ).
thf(1070,plain,
! [SV144: $i,SV190: $i] :
( ( ( ~ ( in @ ( sK28_C @ SV190 @ SV144 ) @ SV190 ) )
= $false )
| ( ( disjoint @ SV144 @ SV190 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1007]) ).
thf(1071,plain,
! [SV191: $i,SV145: $i,SV230: $i] :
( ( ( ~ ( in @ SV230 @ SV145 ) )
= $true )
| ( ( ~ ( in @ SV230 @ SV191 ) )
= $true )
| ( ( ~ ( disjoint @ SV145 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1072,plain,
! [SV146: $i,SV192: $i] :
( ( ( in @ SV192 @ SV146 )
= $false )
| ( ( ( set_difference @ SV146 @ ( singleton @ SV192 ) )
= SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1073,plain,
! [SV148: $i,SV194: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
| ~ ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 ) ) )
= $false )
| ( ( SV194
= ( powerset @ SV148 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1074,plain,
! [SV148: $i,SV194: $i] :
( ( ( ~ ( ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
| ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 ) ) )
= $false )
| ( ( SV194
= ( powerset @ SV148 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1010]) ).
thf(1075,plain,
! [SV149: $i,SV195: $i] :
( ( ( ~ ! [SY476: $i] :
( ~ ( in @ SY476 @ SV195 )
| ( subset @ SY476 @ SV149 ) )
| ~ ! [SY477: $i] :
( ~ ( subset @ SY477 @ SV149 )
| ( in @ SY477 @ SV195 ) ) )
= $false )
| ( ( SV195
= ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1076,plain,
! [SV196: $i,SV150: $i] :
( ( ( SV150 = empty_set )
= $true )
| ( ( SV150
= ( singleton @ SV196 ) )
= $true )
| ( ( subset @ SV150 @ ( singleton @ SV196 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1077,plain,
! [SV231: $i] :
( ( ( ( SV231 != empty_set ) )
= $true )
| ( ( ! [SY517: $i] : ( subset @ SV231 @ ( singleton @ SY517 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1078,plain,
! [SV246: $i,SV232: $i] :
( ( ( SV232
!= ( singleton @ SV246 ) )
| ( subset @ SV232 @ ( singleton @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1079,plain,
! [SV197: $i,SV151: $i] :
( ( ( subset @ SV151 @ SV197 )
= $false )
| ( ( SV151 = SV197 )
= $true )
| ( ( proper_subset @ SV151 @ SV197 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1080,plain,
! [SV247: $i,SV233: $i] :
( ( ~ ( proper_subset @ SV233 @ SV247 )
| ( SV233 != SV247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1081,plain,
! [SV248: $i,SV234: $i] :
( ( ~ ( proper_subset @ SV234 @ SV248 )
| ( subset @ SV234 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1082,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV68 ) )
| ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV198 ) ) )
| ~ ( ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV68 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV198 ) ) )
= $false )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1083,plain,
! [SV199: $i,SV68: $i,SV216: $i] :
( ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false )
| ( ( ~ ( ~ ! [SY506: $i] :
( ~ ( in @ SY506 @ SV216 )
| ( SY506 = SV68 )
| ( SY506 = SV199 ) )
| ~ ~ ( ~ ! [SY507: $i] :
( ( SY507 != SV68 )
| ( in @ SY507 @ SV216 ) )
| ~ ! [SY508: $i] :
( ( SY508 != SV199 )
| ( in @ SY508 @ SV216 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1084,plain,
! [SV152: $i,SV200: $i] :
( ( ( ~ ( ! [SY483: $i] :
( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SY483 )
| ~ ( in @ SY483 @ SV152 ) )
| ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) ) )
= $false )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1085,plain,
! [SV152: $i,SV200: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ ( sK14_SY232 @ SV200 @ SV152 ) )
| ~ ( in @ ( sK14_SY232 @ SV200 @ SV152 ) @ SV152 ) )
| ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) ) )
= $false )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1086,plain,
! [SV201: $i,SV153: $i] :
( ( ( ~ ! [SY484: $i] :
( ! [SY443: $i] :
( ~ ( in @ SY484 @ SY443 )
| ~ ( in @ SY443 @ SV153 ) )
| ( in @ SY484 @ SV201 ) )
| ~ ! [SY486: $i] :
( ~ ( in @ SY486 @ SV201 )
| ~ ( ~ ( in @ SY486 @ ( sK12_D @ SY486 @ SV201 @ SV153 ) )
| ~ ( in @ ( sK12_D @ SY486 @ SV201 @ SV153 ) @ SV153 ) ) ) )
= $false )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1087,plain,
! [SV55: $i,SV235: $i] :
( ( ( ~ ( in @ SV235 @ ( sK29_B @ SV55 ) ) )
= $true )
| ( ( in @ ( powerset @ SV235 ) @ ( sK29_B @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1088,plain,
! [SV55: $i] :
( ( ~ ! [SY297: $i,SY298: $i] :
( ~ ( in @ SY297 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SY298 @ SY297 )
| ( in @ SY298 @ ( sK29_B @ SV55 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1025]) ).
thf(1089,plain,
! [SV55: $i] :
( ( ~ ( in @ SV55 @ ( sK29_B @ SV55 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1025]) ).
thf(1090,plain,
! [SV128: $i,SV164: $i] :
( ( ( in @ ( sK16_C @ SV164 @ SV128 ) @ SV128 )
= $true )
| ( ( subset @ SV128 @ SV164 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1091,plain,
! [SV128: $i,SV164: $i] :
( ( ( ~ ( in @ ( sK16_C @ SV164 @ SV128 ) @ SV164 ) )
= $true )
| ( ( subset @ SV128 @ SV164 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1092,plain,
! [SV165: $i,SV129: $i,SV236: $i] :
( ( ( ~ ( in @ SV236 @ SV129 ) )
= $true )
| ( ( in @ SV236 @ SV165 )
= $true )
| ( ( subset @ SV129 @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1093,plain,
! [SV202: $i,SV166: $i,SV56: $i] :
( ( ( ~ ( ! [SY487: $i,SY488: $i] :
( ~ ( in @ SY487 @ SV56 )
| ~ ( in @ SY488 @ SV166 )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ SY487 @ SY488 ) ) )
| ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) ) )
= $false )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1094,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) @ SV166 ) )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) ) ) )
| ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) ) )
= $false )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1095,plain,
! [SV203: $i,SV167: $i,SV56: $i] :
( ( ( ~ ! [SY489: $i] :
( ! [SY451: $i,SY452: $i] :
( ~ ( in @ SY451 @ SV56 )
| ~ ( in @ SY452 @ SV167 )
| ( SY489
!= ( ordered_pair @ SY451 @ SY452 ) ) )
| ( in @ SY489 @ SV203 ) )
| ~ ! [SY492: $i] :
( ~ ( in @ SY492 @ SV203 )
| ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SY492 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SY492 @ SV203 @ SV167 @ SV56 ) @ SV167 ) )
| ( SY492
!= ( ordered_pair @ ( sK17_E @ SY492 @ SV203 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SY492 @ SV203 @ SV167 @ SV56 ) ) ) ) ) )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1096,plain,
! [SV217: $i,SV169: $i,SV131: $i] :
( ( ( disjoint @ SV131 @ SV169 )
= $false )
| ( ( in @ SV217 @ ( set_intersection2 @ SV131 @ SV169 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1097,plain,
! [SV132: $i,SV170: $i] :
( ( ( subset @ SV170 @ SV132 )
= $false )
| ( ( subset @ SV132 @ SV170 )
= $false )
| ( ( SV132 = SV170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1098,plain,
! [SV237: $i,SV218: $i] :
( ( ( ( SV218 != SV237 ) )
= $true )
| ( ( subset @ SV218 @ SV237 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1099,plain,
! [SV238: $i,SV219: $i] :
( ( ( ( SV219 != SV238 ) )
= $true )
| ( ( subset @ SV238 @ SV219 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1100,plain,
! [SV220: $i] :
( ( ( SV220 = empty_set )
= $false )
| ( ( ! [SY511: $i] : ( subset @ SV220 @ ( singleton @ SY511 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1101,plain,
! [SV239: $i,SV221: $i] :
( ( ( ( SV221
!= ( singleton @ SV239 ) ) )
= $true )
| ( ( subset @ SV221 @ ( singleton @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1037]) ).
thf(1102,plain,
! [SV57: $i,SV240: $i] :
( ( ( ~ ( ~ ! [SY521: $i] :
( ~ ( subset @ SY521 @ SV240 )
| ( in @ SY521 @ ( sK7_SY226 @ SV240 @ SV57 ) ) )
| ~ ( in @ ( sK7_SY226 @ SV240 @ SV57 ) @ ( sK6_B @ SV57 ) ) ) )
= $true )
| ( ( ~ ( in @ SV240 @ ( sK6_B @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1103,plain,
! [SV57: $i] :
( ( ~ ! [SY312: $i,SY313: $i] :
( ~ ( in @ SY312 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK6_B @ SV57 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1104,plain,
! [SV57: $i] :
( ( ~ ( in @ SV57 @ ( sK6_B @ SV57 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1040]) ).
thf(1105,plain,
! [SV241: $i,SV204: $i,SV106: $i,SV58: $i] :
( ( ( ( ordered_pair @ SV58 @ SV106 )
= ( ordered_pair @ SV204 @ SV241 ) )
= $false )
| ( ( SV58 = SV204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1106,plain,
! [SV222: $i,SV205: $i,SV106: $i,SV58: $i] :
( ( ( ( ordered_pair @ SV58 @ SV106 )
= ( ordered_pair @ SV205 @ SV222 ) )
= $false )
| ( ( SV106 = SV222 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1107,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) ) ) )
= $false )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1108,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ~ ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 )
| ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) ) )
= $false )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1109,plain,
! [SV176: $i,SV59: $i,SV207: $i] :
( ( ( ~ ! [SY495: $i] :
( ~ ( in @ SY495 @ SV207 )
| ( in @ SY495 @ SV59 )
| ( in @ SY495 @ SV176 ) )
| ~ ~ ( ~ ! [SY496: $i] :
( ~ ( in @ SY496 @ SV59 )
| ( in @ SY496 @ SV207 ) )
| ~ ! [SY497: $i] :
( ~ ( in @ SY497 @ SV176 )
| ( in @ SY497 @ SV207 ) ) ) )
= $false )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1110,plain,
! [SV223: $i,SV107: $i,SV208: $i,SV60: $i] :
( ( ( ~ ( in @ SV60 @ SV208 ) )
= $true )
| ( ( ~ ( in @ SV107 @ SV223 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV208 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1045]) ).
thf(1111,plain,
! [SV249: $i,SV107: $i,SV60: $i] :
( ( ! [SY524: $i] :
~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV249 @ SY524 ) )
| ( in @ SV60 @ SV249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1112,plain,
! [SV250: $i,SV107: $i,SV60: $i] :
( ( ! [SY525: $i] :
( ~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV250 @ SY525 ) )
| ( in @ SV107 @ SY525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1113,plain,
! [SV61: $i,SV108: $i] :
( ( ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV108 )
= $false )
| ( ( in @ ( sK8_C @ SV108 @ SV61 ) @ SV61 )
= $false )
| ( ( SV61 = SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1114,plain,
! [SV224: $i,SV251: $i] :
( ( ( ~ ( element @ SV251 @ SV224 )
| ( in @ SV251 @ SV224 ) )
= $true )
| ( ( empty @ SV224 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1115,plain,
! [SV225: $i,SV252: $i] :
( ( ( ~ ( in @ SV252 @ SV225 )
| ( element @ SV252 @ SV225 ) )
= $true )
| ( ( empty @ SV225 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1116,plain,
! [SV226: $i] :
( ( ( empty @ SV226 )
= $false )
| ( ( ! [SY515: $i] :
( ~ ( element @ SY515 @ SV226 )
| ( empty @ SY515 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1117,plain,
! [SV227: $i] :
( ( ( empty @ SV227 )
= $false )
| ( ( ! [SY516: $i] :
( ~ ( empty @ SY516 )
| ( element @ SY516 @ SV227 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1118,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) ) )
= $false )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1119,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
| ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) ) ) )
= $false )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1120,plain,
! [SV210: $i,SV178: $i,SV63: $i] :
( ( ( ~ ! [SY499: $i] :
( ~ ( in @ SY499 @ SV63 )
| ~ ( in @ SY499 @ SV178 )
| ( in @ SY499 @ SV210 ) )
| ~ ~ ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SV210 )
| ( in @ SY500 @ SV63 ) )
| ~ ! [SY501: $i] :
( ~ ( in @ SY501 @ SV210 )
| ( in @ SY501 @ SV178 ) ) ) )
= $false )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1054]) ).
thf(1121,plain,
! [SV136: $i,SV179: $i] :
( ( ( ( ( sK26_C @ SV179 @ SV136 )
!= SV136 )
| ~ ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 ) )
= $true )
| ( ( SV179
= ( singleton @ SV136 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1055]) ).
thf(1122,plain,
! [SV136: $i,SV179: $i] :
( ( ( ( ( sK26_C @ SV179 @ SV136 )
= SV136 )
| ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 ) )
= $true )
| ( ( SV179
= ( singleton @ SV136 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1123,plain,
! [SV180: $i,SV137: $i] :
( ( ( ~ ! [SY465: $i] :
( ( SY465 != SV137 )
| ( in @ SY465 @ SV180 ) ) )
= $false )
| ( ( SV180
= ( singleton @ SV137 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1124,plain,
! [SV137: $i,SV180: $i] :
( ( ( ~ ! [SY466: $i] :
( ~ ( in @ SY466 @ SV180 )
| ( SY466 = SV137 ) ) )
= $false )
| ( ( SV180
= ( singleton @ SV137 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1057]) ).
thf(1125,plain,
! [SV185: $i,SV211: $i,SV64: $i] :
( ( ( in @ SV64 @ SV211 )
= $false )
| ( ( ~ ( in @ SV185 @ SV211 ) )
= $true )
| ( ( subset @ ( unordered_pair @ SV64 @ SV185 ) @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1126,plain,
! [SV253: $i,SV242: $i,SV64: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV64 @ SV242 ) @ SV253 )
| ( in @ SV64 @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1127,plain,
! [SV254: $i,SV243: $i,SV64: $i] :
( ( ~ ( subset @ ( unordered_pair @ SV64 @ SV243 ) @ SV254 )
| ( in @ SV243 @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1128,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) ) )
= $false )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1129,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
| ~ ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) ) ) )
= $false )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1061]) ).
thf(1130,plain,
! [SV213: $i,SV187: $i,SV65: $i] :
( ( ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV65 )
| ( in @ SY502 @ SV187 )
| ( in @ SY502 @ SV213 ) )
| ~ ~ ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SV213 )
| ( in @ SY503 @ SV65 ) )
| ~ ! [SY504: $i] :
( ~ ( in @ SY504 @ SV213 )
| ~ ( in @ SY504 @ SV187 ) ) ) )
= $false )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1131,plain,
! [SV229: $i,SV109: $i,SV214: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV214 ) )
= $true )
| ( ( ~ ( in @ SV109 @ SV229 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV214 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1132,plain,
! [SV255: $i,SV109: $i,SV67: $i] :
( ( ! [SY526: $i] :
~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV255 @ SY526 ) )
| ( in @ SV67 @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1133,plain,
! [SV256: $i,SV109: $i,SV67: $i] :
( ( ! [SY527: $i] :
( ~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV256 @ SY527 ) )
| ( in @ SV109 @ SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1134,plain,
! [SV144: $i,SV190: $i] :
( ( ( in @ ( sK28_C @ SV190 @ SV144 ) @ SV144 )
= $true )
| ( ( disjoint @ SV144 @ SV190 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1069]) ).
thf(1135,plain,
! [SV144: $i,SV190: $i] :
( ( ( in @ ( sK28_C @ SV190 @ SV144 ) @ SV190 )
= $true )
| ( ( disjoint @ SV144 @ SV190 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1136,plain,
! [SV191: $i,SV145: $i,SV230: $i] :
( ( ( in @ SV230 @ SV145 )
= $false )
| ( ( ~ ( in @ SV230 @ SV191 ) )
= $true )
| ( ( ~ ( disjoint @ SV145 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1137,plain,
! [SV148: $i,SV194: $i] :
( ( ( ~ ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
| ~ ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 ) )
= $true )
| ( ( SV194
= ( powerset @ SV148 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1138,plain,
! [SV148: $i,SV194: $i] :
( ( ( ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
| ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 ) )
= $true )
| ( ( SV194
= ( powerset @ SV148 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1074]) ).
thf(1139,plain,
! [SV149: $i,SV195: $i] :
( ( ( ~ ! [SY476: $i] :
( ~ ( in @ SY476 @ SV195 )
| ( subset @ SY476 @ SV149 ) ) )
= $false )
| ( ( SV195
= ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1140,plain,
! [SV195: $i,SV149: $i] :
( ( ( ~ ! [SY477: $i] :
( ~ ( subset @ SY477 @ SV149 )
| ( in @ SY477 @ SV195 ) ) )
= $false )
| ( ( SV195
= ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1075]) ).
thf(1141,plain,
! [SV231: $i] :
( ( ( SV231 = empty_set )
= $false )
| ( ( ! [SY517: $i] : ( subset @ SV231 @ ( singleton @ SY517 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1142,plain,
! [SV246: $i,SV232: $i] :
( ( ( ( SV232
!= ( singleton @ SV246 ) ) )
= $true )
| ( ( subset @ SV232 @ ( singleton @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1143,plain,
! [SV247: $i,SV233: $i] :
( ( ( ~ ( proper_subset @ SV233 @ SV247 ) )
= $true )
| ( ( ( SV233 != SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1144,plain,
! [SV248: $i,SV234: $i] :
( ( ( ~ ( proper_subset @ SV234 @ SV248 ) )
= $true )
| ( ( subset @ SV234 @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1145,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV68 ) )
| ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV198 ) ) ) )
= $false )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1146,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ~ ( ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV68 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV198 ) ) )
= $false )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1082]) ).
thf(1147,plain,
! [SV199: $i,SV68: $i,SV216: $i] :
( ( ( ~ ! [SY506: $i] :
( ~ ( in @ SY506 @ SV216 )
| ( SY506 = SV68 )
| ( SY506 = SV199 ) )
| ~ ~ ( ~ ! [SY507: $i] :
( ( SY507 != SV68 )
| ( in @ SY507 @ SV216 ) )
| ~ ! [SY508: $i] :
( ( SY508 != SV199 )
| ( in @ SY508 @ SV216 ) ) ) )
= $false )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1148,plain,
! [SV152: $i,SV200: $i] :
( ( ( ! [SY483: $i] :
( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SY483 )
| ~ ( in @ SY483 @ SV152 ) )
| ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1149,plain,
! [SV152: $i,SV200: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ ( sK14_SY232 @ SV200 @ SV152 ) )
| ~ ( in @ ( sK14_SY232 @ SV200 @ SV152 ) @ SV152 ) )
| ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1085]) ).
thf(1150,plain,
! [SV201: $i,SV153: $i] :
( ( ( ~ ! [SY484: $i] :
( ! [SY443: $i] :
( ~ ( in @ SY484 @ SY443 )
| ~ ( in @ SY443 @ SV153 ) )
| ( in @ SY484 @ SV201 ) ) )
= $false )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1086]) ).
thf(1151,plain,
! [SV153: $i,SV201: $i] :
( ( ( ~ ! [SY486: $i] :
( ~ ( in @ SY486 @ SV201 )
| ~ ( ~ ( in @ SY486 @ ( sK12_D @ SY486 @ SV201 @ SV153 ) )
| ~ ( in @ ( sK12_D @ SY486 @ SV201 @ SV153 ) @ SV153 ) ) ) )
= $false )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1086]) ).
thf(1152,plain,
! [SV55: $i,SV235: $i] :
( ( ( in @ SV235 @ ( sK29_B @ SV55 ) )
= $false )
| ( ( in @ ( powerset @ SV235 ) @ ( sK29_B @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1153,plain,
! [SV55: $i] :
( ( ! [SY297: $i,SY298: $i] :
( ~ ( in @ SY297 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SY298 @ SY297 )
| ( in @ SY298 @ ( sK29_B @ SV55 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1088]) ).
thf(1154,plain,
! [SV55: $i] :
( ( in @ SV55 @ ( sK29_B @ SV55 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1089]) ).
thf(1155,plain,
! [SV128: $i,SV164: $i] :
( ( ( in @ ( sK16_C @ SV164 @ SV128 ) @ SV164 )
= $false )
| ( ( subset @ SV128 @ SV164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1156,plain,
! [SV165: $i,SV129: $i,SV236: $i] :
( ( ( in @ SV236 @ SV129 )
= $false )
| ( ( in @ SV236 @ SV165 )
= $true )
| ( ( subset @ SV129 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1157,plain,
! [SV202: $i,SV166: $i,SV56: $i] :
( ( ( ! [SY487: $i,SY488: $i] :
( ~ ( in @ SY487 @ SV56 )
| ~ ( in @ SY488 @ SV166 )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ SY487 @ SY488 ) ) )
| ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1158,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) @ SV166 ) )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) ) ) )
| ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1159,plain,
! [SV203: $i,SV167: $i,SV56: $i] :
( ( ( ~ ! [SY489: $i] :
( ! [SY451: $i,SY452: $i] :
( ~ ( in @ SY451 @ SV56 )
| ~ ( in @ SY452 @ SV167 )
| ( SY489
!= ( ordered_pair @ SY451 @ SY452 ) ) )
| ( in @ SY489 @ SV203 ) ) )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1160,plain,
! [SV56: $i,SV167: $i,SV203: $i] :
( ( ( ~ ! [SY492: $i] :
( ~ ( in @ SY492 @ SV203 )
| ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SY492 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SY492 @ SV203 @ SV167 @ SV56 ) @ SV167 ) )
| ( SY492
!= ( ordered_pair @ ( sK17_E @ SY492 @ SV203 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SY492 @ SV203 @ SV167 @ SV56 ) ) ) ) ) )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1095]) ).
thf(1161,plain,
! [SV237: $i,SV218: $i] :
( ( ( SV218 = SV237 )
= $false )
| ( ( subset @ SV218 @ SV237 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1098]) ).
thf(1162,plain,
! [SV238: $i,SV219: $i] :
( ( ( SV219 = SV238 )
= $false )
| ( ( subset @ SV238 @ SV219 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1163,plain,
! [SV257: $i,SV220: $i] :
( ( ( subset @ SV220 @ ( singleton @ SV257 ) )
= $true )
| ( ( SV220 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1164,plain,
! [SV239: $i,SV221: $i] :
( ( ( SV221
= ( singleton @ SV239 ) )
= $false )
| ( ( subset @ SV221 @ ( singleton @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1165,plain,
! [SV57: $i,SV240: $i] :
( ( ( ~ ! [SY521: $i] :
( ~ ( subset @ SY521 @ SV240 )
| ( in @ SY521 @ ( sK7_SY226 @ SV240 @ SV57 ) ) )
| ~ ( in @ ( sK7_SY226 @ SV240 @ SV57 ) @ ( sK6_B @ SV57 ) ) )
= $false )
| ( ( ~ ( in @ SV240 @ ( sK6_B @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1166,plain,
! [SV57: $i] :
( ( ! [SY312: $i,SY313: $i] :
( ~ ( in @ SY312 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SY313 @ SY312 )
| ( in @ SY313 @ ( sK6_B @ SV57 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1167,plain,
! [SV57: $i] :
( ( in @ SV57 @ ( sK6_B @ SV57 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1104]) ).
thf(1168,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) ) ) )
= $true )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1169,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 )
| ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) )
= $true )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1108]) ).
thf(1170,plain,
! [SV176: $i,SV59: $i,SV207: $i] :
( ( ( ~ ! [SY495: $i] :
( ~ ( in @ SY495 @ SV207 )
| ( in @ SY495 @ SV59 )
| ( in @ SY495 @ SV176 ) ) )
= $false )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1171,plain,
! [SV176: $i,SV207: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ! [SY496: $i] :
( ~ ( in @ SY496 @ SV59 )
| ( in @ SY496 @ SV207 ) )
| ~ ! [SY497: $i] :
( ~ ( in @ SY497 @ SV176 )
| ( in @ SY497 @ SV207 ) ) ) )
= $false )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1109]) ).
thf(1172,plain,
! [SV223: $i,SV107: $i,SV208: $i,SV60: $i] :
( ( ( in @ SV60 @ SV208 )
= $false )
| ( ( ~ ( in @ SV107 @ SV223 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV208 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1173,plain,
! [SV249: $i,SV107: $i,SV60: $i] :
( ( ( ! [SY524: $i] :
~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV249 @ SY524 ) ) )
= $true )
| ( ( in @ SV60 @ SV249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1111]) ).
thf(1174,plain,
! [SV258: $i,SV250: $i,SV107: $i,SV60: $i] :
( ( ~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV250 @ SV258 ) )
| ( in @ SV107 @ SV258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1175,plain,
! [SV224: $i,SV251: $i] :
( ( ( ~ ( element @ SV251 @ SV224 ) )
= $true )
| ( ( in @ SV251 @ SV224 )
= $true )
| ( ( empty @ SV224 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1176,plain,
! [SV225: $i,SV252: $i] :
( ( ( ~ ( in @ SV252 @ SV225 ) )
= $true )
| ( ( element @ SV252 @ SV225 )
= $true )
| ( ( empty @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1177,plain,
! [SV226: $i,SV259: $i] :
( ( ( ~ ( element @ SV259 @ SV226 )
| ( empty @ SV259 ) )
= $true )
| ( ( empty @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1178,plain,
! [SV227: $i,SV260: $i] :
( ( ( ~ ( empty @ SV260 )
| ( element @ SV260 @ SV227 ) )
= $true )
| ( ( empty @ SV227 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1179,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1118]) ).
thf(1180,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
| ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) ) ) )
= $true )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1119]) ).
thf(1181,plain,
! [SV210: $i,SV178: $i,SV63: $i] :
( ( ( ~ ! [SY499: $i] :
( ~ ( in @ SY499 @ SV63 )
| ~ ( in @ SY499 @ SV178 )
| ( in @ SY499 @ SV210 ) ) )
= $false )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1120]) ).
thf(1182,plain,
! [SV178: $i,SV63: $i,SV210: $i] :
( ( ( ~ ~ ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SV210 )
| ( in @ SY500 @ SV63 ) )
| ~ ! [SY501: $i] :
( ~ ( in @ SY501 @ SV210 )
| ( in @ SY501 @ SV178 ) ) ) )
= $false )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1120]) ).
thf(1183,plain,
! [SV136: $i,SV179: $i] :
( ( ( ( ( sK26_C @ SV179 @ SV136 )
!= SV136 ) )
= $true )
| ( ( ~ ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 ) )
= $true )
| ( ( SV179
= ( singleton @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1184,plain,
! [SV136: $i,SV179: $i] :
( ( ( ( sK26_C @ SV179 @ SV136 )
= SV136 )
= $true )
| ( ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 )
= $true )
| ( ( SV179
= ( singleton @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1122]) ).
thf(1185,plain,
! [SV180: $i,SV137: $i] :
( ( ( ! [SY465: $i] :
( ( SY465 != SV137 )
| ( in @ SY465 @ SV180 ) ) )
= $true )
| ( ( SV180
= ( singleton @ SV137 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1123]) ).
thf(1186,plain,
! [SV137: $i,SV180: $i] :
( ( ( ! [SY466: $i] :
( ~ ( in @ SY466 @ SV180 )
| ( SY466 = SV137 ) ) )
= $true )
| ( ( SV180
= ( singleton @ SV137 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1187,plain,
! [SV64: $i,SV211: $i,SV185: $i] :
( ( ( in @ SV185 @ SV211 )
= $false )
| ( ( in @ SV64 @ SV211 )
= $false )
| ( ( subset @ ( unordered_pair @ SV64 @ SV185 ) @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1188,plain,
! [SV253: $i,SV242: $i,SV64: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV64 @ SV242 ) @ SV253 ) )
= $true )
| ( ( in @ SV64 @ SV253 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1189,plain,
! [SV254: $i,SV243: $i,SV64: $i] :
( ( ( ~ ( subset @ ( unordered_pair @ SV64 @ SV243 ) @ SV254 ) )
= $true )
| ( ( in @ SV243 @ SV254 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1190,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
= $true )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1191,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
| ~ ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) ) ) )
= $true )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1192,plain,
! [SV213: $i,SV187: $i,SV65: $i] :
( ( ( ~ ! [SY502: $i] :
( ~ ( in @ SY502 @ SV65 )
| ( in @ SY502 @ SV187 )
| ( in @ SY502 @ SV213 ) ) )
= $false )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1193,plain,
! [SV187: $i,SV65: $i,SV213: $i] :
( ( ( ~ ~ ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SV213 )
| ( in @ SY503 @ SV65 ) )
| ~ ! [SY504: $i] :
( ~ ( in @ SY504 @ SV213 )
| ~ ( in @ SY504 @ SV187 ) ) ) )
= $false )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1130]) ).
thf(1194,plain,
! [SV229: $i,SV109: $i,SV214: $i,SV67: $i] :
( ( ( in @ SV67 @ SV214 )
= $false )
| ( ( ~ ( in @ SV109 @ SV229 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV214 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1195,plain,
! [SV255: $i,SV109: $i,SV67: $i] :
( ( ( ! [SY526: $i] :
~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV255 @ SY526 ) ) )
= $true )
| ( ( in @ SV67 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1196,plain,
! [SV261: $i,SV256: $i,SV109: $i,SV67: $i] :
( ( ~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV256 @ SV261 ) )
| ( in @ SV109 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1197,plain,
! [SV145: $i,SV191: $i,SV230: $i] :
( ( ( in @ SV230 @ SV191 )
= $false )
| ( ( in @ SV230 @ SV145 )
= $false )
| ( ( ~ ( disjoint @ SV145 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1198,plain,
! [SV148: $i,SV194: $i] :
( ( ( ~ ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 ) )
= $true )
| ( ( ~ ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 ) )
= $true )
| ( ( SV194
= ( powerset @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1199,plain,
! [SV148: $i,SV194: $i] :
( ( ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
= $true )
| ( ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 )
= $true )
| ( ( SV194
= ( powerset @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1200,plain,
! [SV149: $i,SV195: $i] :
( ( ( ! [SY476: $i] :
( ~ ( in @ SY476 @ SV195 )
| ( subset @ SY476 @ SV149 ) ) )
= $true )
| ( ( SV195
= ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1201,plain,
! [SV195: $i,SV149: $i] :
( ( ( ! [SY477: $i] :
( ~ ( subset @ SY477 @ SV149 )
| ( in @ SY477 @ SV195 ) ) )
= $true )
| ( ( SV195
= ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1140]) ).
thf(1202,plain,
! [SV262: $i,SV231: $i] :
( ( ( subset @ SV231 @ ( singleton @ SV262 ) )
= $true )
| ( ( SV231 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1203,plain,
! [SV246: $i,SV232: $i] :
( ( ( SV232
= ( singleton @ SV246 ) )
= $false )
| ( ( subset @ SV232 @ ( singleton @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1204,plain,
! [SV247: $i,SV233: $i] :
( ( ( proper_subset @ SV233 @ SV247 )
= $false )
| ( ( ( SV233 != SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1143]) ).
thf(1205,plain,
! [SV248: $i,SV234: $i] :
( ( ( proper_subset @ SV234 @ SV248 )
= $false )
| ( ( subset @ SV234 @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1206,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV68 ) )
| ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV198 ) ) ) )
= $true )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1145]) ).
thf(1207,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV68 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV198 ) )
= $true )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1146]) ).
thf(1208,plain,
! [SV199: $i,SV68: $i,SV216: $i] :
( ( ( ~ ! [SY506: $i] :
( ~ ( in @ SY506 @ SV216 )
| ( SY506 = SV68 )
| ( SY506 = SV199 ) ) )
= $false )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1209,plain,
! [SV199: $i,SV216: $i,SV68: $i] :
( ( ( ~ ~ ( ~ ! [SY507: $i] :
( ( SY507 != SV68 )
| ( in @ SY507 @ SV216 ) )
| ~ ! [SY508: $i] :
( ( SY508 != SV199 )
| ( in @ SY508 @ SV216 ) ) ) )
= $false )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1147]) ).
thf(1210,plain,
! [SV152: $i,SV200: $i] :
( ( ( ! [SY483: $i] :
( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SY483 )
| ~ ( in @ SY483 @ SV152 ) ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1211,plain,
! [SV152: $i,SV200: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ ( sK14_SY232 @ SV200 @ SV152 ) )
| ~ ( in @ ( sK14_SY232 @ SV200 @ SV152 ) @ SV152 ) ) )
= $true )
| ( ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1212,plain,
! [SV201: $i,SV153: $i] :
( ( ( ! [SY484: $i] :
( ! [SY443: $i] :
( ~ ( in @ SY484 @ SY443 )
| ~ ( in @ SY443 @ SV153 ) )
| ( in @ SY484 @ SV201 ) ) )
= $true )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1213,plain,
! [SV153: $i,SV201: $i] :
( ( ( ! [SY486: $i] :
( ~ ( in @ SY486 @ SV201 )
| ~ ( ~ ( in @ SY486 @ ( sK12_D @ SY486 @ SV201 @ SV153 ) )
| ~ ( in @ ( sK12_D @ SY486 @ SV201 @ SV153 ) @ SV153 ) ) ) )
= $true )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1151]) ).
thf(1214,plain,
! [SV55: $i,SV263: $i] :
( ( ! [SY528: $i] :
( ~ ( in @ SV263 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SY528 @ SV263 )
| ( in @ SY528 @ ( sK29_B @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1215,plain,
! [SV202: $i,SV166: $i,SV56: $i] :
( ( ( ! [SY487: $i,SY488: $i] :
( ~ ( in @ SY487 @ SV56 )
| ~ ( in @ SY488 @ SV166 )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ SY487 @ SY488 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1216,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) @ SV166 ) )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) ) ) ) )
= $true )
| ( ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1217,plain,
! [SV203: $i,SV167: $i,SV56: $i] :
( ( ( ! [SY489: $i] :
( ! [SY451: $i,SY452: $i] :
( ~ ( in @ SY451 @ SV56 )
| ~ ( in @ SY452 @ SV167 )
| ( SY489
!= ( ordered_pair @ SY451 @ SY452 ) ) )
| ( in @ SY489 @ SV203 ) ) )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1159]) ).
thf(1218,plain,
! [SV56: $i,SV167: $i,SV203: $i] :
( ( ( ! [SY492: $i] :
( ~ ( in @ SY492 @ SV203 )
| ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SY492 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SY492 @ SV203 @ SV167 @ SV56 ) @ SV167 ) )
| ( SY492
!= ( ordered_pair @ ( sK17_E @ SY492 @ SV203 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SY492 @ SV203 @ SV167 @ SV56 ) ) ) ) ) )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1160]) ).
thf(1219,plain,
! [SV57: $i,SV240: $i] :
( ( ( ~ ! [SY521: $i] :
( ~ ( subset @ SY521 @ SV240 )
| ( in @ SY521 @ ( sK7_SY226 @ SV240 @ SV57 ) ) ) )
= $false )
| ( ( ~ ( in @ SV240 @ ( sK6_B @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1165]) ).
thf(1220,plain,
! [SV57: $i,SV240: $i] :
( ( ( ~ ( in @ ( sK7_SY226 @ SV240 @ SV57 ) @ ( sK6_B @ SV57 ) ) )
= $false )
| ( ( ~ ( in @ SV240 @ ( sK6_B @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1165]) ).
thf(1221,plain,
! [SV57: $i,SV264: $i] :
( ( ! [SY529: $i] :
( ~ ( in @ SV264 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SY529 @ SV264 )
| ( in @ SY529 @ ( sK6_B @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1222,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 ) )
| ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) ) )
= $false )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1223,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
= $true )
| ( ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 )
| ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) )
= $true )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1224,plain,
! [SV176: $i,SV59: $i,SV207: $i] :
( ( ( ! [SY495: $i] :
( ~ ( in @ SY495 @ SV207 )
| ( in @ SY495 @ SV59 )
| ( in @ SY495 @ SV176 ) ) )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1170]) ).
thf(1225,plain,
! [SV176: $i,SV207: $i,SV59: $i] :
( ( ( ~ ( ~ ! [SY496: $i] :
( ~ ( in @ SY496 @ SV59 )
| ( in @ SY496 @ SV207 ) )
| ~ ! [SY497: $i] :
( ~ ( in @ SY497 @ SV176 )
| ( in @ SY497 @ SV207 ) ) ) )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1171]) ).
thf(1226,plain,
! [SV208: $i,SV60: $i,SV223: $i,SV107: $i] :
( ( ( in @ SV107 @ SV223 )
= $false )
| ( ( in @ SV60 @ SV208 )
= $false )
| ( ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV208 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1227,plain,
! [SV265: $i,SV249: $i,SV107: $i,SV60: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV249 @ SV265 ) ) )
= $true )
| ( ( in @ SV60 @ SV249 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1228,plain,
! [SV258: $i,SV250: $i,SV107: $i,SV60: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV250 @ SV258 ) ) )
= $true )
| ( ( in @ SV107 @ SV258 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1229,plain,
! [SV224: $i,SV251: $i] :
( ( ( element @ SV251 @ SV224 )
= $false )
| ( ( in @ SV251 @ SV224 )
= $true )
| ( ( empty @ SV224 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1230,plain,
! [SV225: $i,SV252: $i] :
( ( ( in @ SV252 @ SV225 )
= $false )
| ( ( element @ SV252 @ SV225 )
= $true )
| ( ( empty @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1231,plain,
! [SV226: $i,SV259: $i] :
( ( ( ~ ( element @ SV259 @ SV226 ) )
= $true )
| ( ( empty @ SV259 )
= $true )
| ( ( empty @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1232,plain,
! [SV227: $i,SV260: $i] :
( ( ( ~ ( empty @ SV260 ) )
= $true )
| ( ( element @ SV260 @ SV227 )
= $true )
| ( ( empty @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1233,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1234,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
| ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) ) )
= $false )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1235,plain,
! [SV210: $i,SV178: $i,SV63: $i] :
( ( ( ! [SY499: $i] :
( ~ ( in @ SY499 @ SV63 )
| ~ ( in @ SY499 @ SV178 )
| ( in @ SY499 @ SV210 ) ) )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1181]) ).
thf(1236,plain,
! [SV178: $i,SV63: $i,SV210: $i] :
( ( ( ~ ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SV210 )
| ( in @ SY500 @ SV63 ) )
| ~ ! [SY501: $i] :
( ~ ( in @ SY501 @ SV210 )
| ( in @ SY501 @ SV178 ) ) ) )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1237,plain,
! [SV136: $i,SV179: $i] :
( ( ( ( sK26_C @ SV179 @ SV136 )
= SV136 )
= $false )
| ( ( ~ ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 ) )
= $true )
| ( ( SV179
= ( singleton @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1183]) ).
thf(1238,plain,
! [SV180: $i,SV137: $i,SV266: $i] :
( ( ( ( SV266 != SV137 )
| ( in @ SV266 @ SV180 ) )
= $true )
| ( ( SV180
= ( singleton @ SV137 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1239,plain,
! [SV137: $i,SV180: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ SV180 )
| ( SV267 = SV137 ) )
= $true )
| ( ( SV180
= ( singleton @ SV137 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1240,plain,
! [SV253: $i,SV242: $i,SV64: $i] :
( ( ( subset @ ( unordered_pair @ SV64 @ SV242 ) @ SV253 )
= $false )
| ( ( in @ SV64 @ SV253 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1188]) ).
thf(1241,plain,
! [SV254: $i,SV243: $i,SV64: $i] :
( ( ( subset @ ( unordered_pair @ SV64 @ SV243 ) @ SV254 )
= $false )
| ( ( in @ SV243 @ SV254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1242,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 ) )
= $true )
| ( ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
= $true )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1243,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
| ~ ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) ) )
= $false )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1244,plain,
! [SV213: $i,SV187: $i,SV65: $i] :
( ( ( ! [SY502: $i] :
( ~ ( in @ SY502 @ SV65 )
| ( in @ SY502 @ SV187 )
| ( in @ SY502 @ SV213 ) ) )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1192]) ).
thf(1245,plain,
! [SV187: $i,SV65: $i,SV213: $i] :
( ( ( ~ ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SV213 )
| ( in @ SY503 @ SV65 ) )
| ~ ! [SY504: $i] :
( ~ ( in @ SY504 @ SV213 )
| ~ ( in @ SY504 @ SV187 ) ) ) )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1193]) ).
thf(1246,plain,
! [SV214: $i,SV67: $i,SV229: $i,SV109: $i] :
( ( ( in @ SV109 @ SV229 )
= $false )
| ( ( in @ SV67 @ SV214 )
= $false )
| ( ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV214 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1247,plain,
! [SV268: $i,SV255: $i,SV109: $i,SV67: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV255 @ SV268 ) ) )
= $true )
| ( ( in @ SV67 @ SV255 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1248,plain,
! [SV261: $i,SV256: $i,SV109: $i,SV67: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV256 @ SV261 ) ) )
= $true )
| ( ( in @ SV109 @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1249,plain,
! [SV230: $i,SV191: $i,SV145: $i] :
( ( ( disjoint @ SV145 @ SV191 )
= $false )
| ( ( in @ SV230 @ SV145 )
= $false )
| ( ( in @ SV230 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1197]) ).
thf(1250,plain,
! [SV148: $i,SV194: $i] :
( ( ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
= $false )
| ( ( ~ ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 ) )
= $true )
| ( ( SV194
= ( powerset @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1198]) ).
thf(1251,plain,
! [SV149: $i,SV195: $i,SV269: $i] :
( ( ( ~ ( in @ SV269 @ SV195 )
| ( subset @ SV269 @ SV149 ) )
= $true )
| ( ( SV195
= ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1252,plain,
! [SV195: $i,SV149: $i,SV270: $i] :
( ( ( ~ ( subset @ SV270 @ SV149 )
| ( in @ SV270 @ SV195 ) )
= $true )
| ( ( SV195
= ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1253,plain,
! [SV247: $i,SV233: $i] :
( ( ( SV233 = SV247 )
= $false )
| ( ( proper_subset @ SV233 @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1254,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV68 ) )
| ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV198 ) ) )
= $false )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1206]) ).
thf(1255,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
= $true )
| ( ( ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV68 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV198 ) )
= $true )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1256,plain,
! [SV199: $i,SV68: $i,SV216: $i] :
( ( ( ! [SY506: $i] :
( ~ ( in @ SY506 @ SV216 )
| ( SY506 = SV68 )
| ( SY506 = SV199 ) ) )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1208]) ).
thf(1257,plain,
! [SV199: $i,SV216: $i,SV68: $i] :
( ( ( ~ ( ~ ! [SY507: $i] :
( ( SY507 != SV68 )
| ( in @ SY507 @ SV216 ) )
| ~ ! [SY508: $i] :
( ( SY508 != SV199 )
| ( in @ SY508 @ SV216 ) ) ) )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1258,plain,
! [SV271: $i,SV152: $i,SV200: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV271 )
| ~ ( in @ SV271 @ SV152 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1259,plain,
! [SV152: $i,SV200: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ ( sK14_SY232 @ SV200 @ SV152 ) )
| ~ ( in @ ( sK14_SY232 @ SV200 @ SV152 ) @ SV152 ) )
= $false )
| ( ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1260,plain,
! [SV201: $i,SV153: $i,SV272: $i] :
( ( ( ! [SY530: $i] :
( ~ ( in @ SV272 @ SY530 )
| ~ ( in @ SY530 @ SV153 ) )
| ( in @ SV272 @ SV201 ) )
= $true )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1261,plain,
! [SV153: $i,SV201: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ SV201 )
| ~ ( ~ ( in @ SV273 @ ( sK12_D @ SV273 @ SV201 @ SV153 ) )
| ~ ( in @ ( sK12_D @ SV273 @ SV201 @ SV153 ) @ SV153 ) ) )
= $true )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1262,plain,
! [SV274: $i,SV55: $i,SV263: $i] :
( ( ~ ( in @ SV263 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SV274 @ SV263 )
| ( in @ SV274 @ ( sK29_B @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1263,plain,
! [SV202: $i,SV166: $i,SV56: $i,SV275: $i] :
( ( ( ! [SY531: $i] :
( ~ ( in @ SV275 @ SV56 )
| ~ ( in @ SY531 @ SV166 )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ SV275 @ SY531 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1264,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) @ SV166 ) )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) ) ) )
= $false )
| ( ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1265,plain,
! [SV203: $i,SV276: $i,SV167: $i,SV56: $i] :
( ( ( ! [SY532: $i,SY533: $i] :
( ~ ( in @ SY532 @ SV56 )
| ~ ( in @ SY533 @ SV167 )
| ( SV276
!= ( ordered_pair @ SY532 @ SY533 ) ) )
| ( in @ SV276 @ SV203 ) )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1266,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( ~ ( in @ SV277 @ SV203 )
| ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV167 ) )
| ( SV277
!= ( ordered_pair @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) ) ) ) )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1267,plain,
! [SV57: $i,SV240: $i] :
( ( ( ! [SY521: $i] :
( ~ ( subset @ SY521 @ SV240 )
| ( in @ SY521 @ ( sK7_SY226 @ SV240 @ SV57 ) ) ) )
= $true )
| ( ( ~ ( in @ SV240 @ ( sK6_B @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1268,plain,
! [SV57: $i,SV240: $i] :
( ( ( in @ ( sK7_SY226 @ SV240 @ SV57 ) @ ( sK6_B @ SV57 ) )
= $true )
| ( ( ~ ( in @ SV240 @ ( sK6_B @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1269,plain,
! [SV278: $i,SV57: $i,SV264: $i] :
( ( ~ ( in @ SV264 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SV278 @ SV264 )
| ( in @ SV278 @ ( sK6_B @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1270,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 ) ) )
= $false )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1222]) ).
thf(1271,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) ) )
= $false )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1222]) ).
thf(1272,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 )
= $true )
| ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 )
= $true )
| ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
= $true )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1223]) ).
thf(1273,plain,
! [SV176: $i,SV59: $i,SV207: $i,SV279: $i] :
( ( ( ~ ( in @ SV279 @ SV207 )
| ( in @ SV279 @ SV59 )
| ( in @ SV279 @ SV176 ) )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1274,plain,
! [SV176: $i,SV207: $i,SV59: $i] :
( ( ( ~ ! [SY496: $i] :
( ~ ( in @ SY496 @ SV59 )
| ( in @ SY496 @ SV207 ) )
| ~ ! [SY497: $i] :
( ~ ( in @ SY497 @ SV176 )
| ( in @ SY497 @ SV207 ) ) )
= $false )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1275,plain,
! [SV265: $i,SV249: $i,SV107: $i,SV60: $i] :
( ( ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV249 @ SV265 ) )
= $false )
| ( ( in @ SV60 @ SV249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1276,plain,
! [SV258: $i,SV250: $i,SV107: $i,SV60: $i] :
( ( ( in @ ( ordered_pair @ SV60 @ SV107 ) @ ( cartesian_product2 @ SV250 @ SV258 ) )
= $false )
| ( ( in @ SV107 @ SV258 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1277,plain,
! [SV226: $i,SV259: $i] :
( ( ( element @ SV259 @ SV226 )
= $false )
| ( ( empty @ SV259 )
= $true )
| ( ( empty @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1278,plain,
! [SV227: $i,SV260: $i] :
( ( ( empty @ SV260 )
= $false )
| ( ( element @ SV260 @ SV227 )
= $true )
| ( ( empty @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1279,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1280,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) ) )
= $false )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1234]) ).
thf(1281,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ~ ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) ) )
= $false )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1234]) ).
thf(1282,plain,
! [SV210: $i,SV178: $i,SV63: $i,SV280: $i] :
( ( ( ~ ( in @ SV280 @ SV63 )
| ~ ( in @ SV280 @ SV178 )
| ( in @ SV280 @ SV210 ) )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1283,plain,
! [SV178: $i,SV63: $i,SV210: $i] :
( ( ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SV210 )
| ( in @ SY500 @ SV63 ) )
| ~ ! [SY501: $i] :
( ~ ( in @ SY501 @ SV210 )
| ( in @ SY501 @ SV178 ) ) )
= $false )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1284,plain,
! [SV136: $i,SV179: $i] :
( ( ( in @ ( sK26_C @ SV179 @ SV136 ) @ SV179 )
= $false )
| ( ( ( sK26_C @ SV179 @ SV136 )
= SV136 )
= $false )
| ( ( SV179
= ( singleton @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1285,plain,
! [SV180: $i,SV137: $i,SV266: $i] :
( ( ( ( SV266 != SV137 ) )
= $true )
| ( ( in @ SV266 @ SV180 )
= $true )
| ( ( SV180
= ( singleton @ SV137 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1286,plain,
! [SV137: $i,SV180: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ SV180 ) )
= $true )
| ( ( SV267 = SV137 )
= $true )
| ( ( SV180
= ( singleton @ SV137 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1287,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 ) )
= $true )
| ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
= $true )
| ( ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
= $true )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1288,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) ) )
= $false )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1289,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) ) )
= $false )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1243]) ).
thf(1290,plain,
! [SV213: $i,SV187: $i,SV65: $i,SV281: $i] :
( ( ( ~ ( in @ SV281 @ SV65 )
| ( in @ SV281 @ SV187 )
| ( in @ SV281 @ SV213 ) )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1291,plain,
! [SV187: $i,SV65: $i,SV213: $i] :
( ( ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SV213 )
| ( in @ SY503 @ SV65 ) )
| ~ ! [SY504: $i] :
( ~ ( in @ SY504 @ SV213 )
| ~ ( in @ SY504 @ SV187 ) ) )
= $false )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1292,plain,
! [SV268: $i,SV255: $i,SV109: $i,SV67: $i] :
( ( ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV255 @ SV268 ) )
= $false )
| ( ( in @ SV67 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1293,plain,
! [SV261: $i,SV256: $i,SV109: $i,SV67: $i] :
( ( ( in @ ( ordered_pair @ SV67 @ SV109 ) @ ( cartesian_product2 @ SV256 @ SV261 ) )
= $false )
| ( ( in @ SV109 @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1294,plain,
! [SV148: $i,SV194: $i] :
( ( ( subset @ ( sK24_C @ SV194 @ SV148 ) @ SV148 )
= $false )
| ( ( in @ ( sK24_C @ SV194 @ SV148 ) @ SV194 )
= $false )
| ( ( SV194
= ( powerset @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1295,plain,
! [SV149: $i,SV195: $i,SV269: $i] :
( ( ( ~ ( in @ SV269 @ SV195 ) )
= $true )
| ( ( subset @ SV269 @ SV149 )
= $true )
| ( ( SV195
= ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1296,plain,
! [SV195: $i,SV149: $i,SV270: $i] :
( ( ( ~ ( subset @ SV270 @ SV149 ) )
= $true )
| ( ( in @ SV270 @ SV195 )
= $true )
| ( ( SV195
= ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1297,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV68 ) ) )
= $false )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1254]) ).
thf(1298,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV198 ) ) )
= $false )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1254]) ).
thf(1299,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV68 )
= $true )
| ( ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV198 )
= $true )
| ( ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
= $true )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1300,plain,
! [SV199: $i,SV68: $i,SV216: $i,SV282: $i] :
( ( ( ~ ( in @ SV282 @ SV216 )
| ( SV282 = SV68 )
| ( SV282 = SV199 ) )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1301,plain,
! [SV199: $i,SV216: $i,SV68: $i] :
( ( ( ~ ! [SY507: $i] :
( ( SY507 != SV68 )
| ( in @ SY507 @ SV216 ) )
| ~ ! [SY508: $i] :
( ( SY508 != SV199 )
| ( in @ SY508 @ SV216 ) ) )
= $false )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1302,plain,
! [SV271: $i,SV152: $i,SV200: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV271 ) )
= $true )
| ( ( ~ ( in @ SV271 @ SV152 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1303,plain,
! [SV152: $i,SV200: $i] :
( ( ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ ( sK14_SY232 @ SV200 @ SV152 ) ) )
= $false )
| ( ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1304,plain,
! [SV152: $i,SV200: $i] :
( ( ( ~ ( in @ ( sK14_SY232 @ SV200 @ SV152 ) @ SV152 ) )
= $false )
| ( ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1259]) ).
thf(1305,plain,
! [SV201: $i,SV153: $i,SV272: $i] :
( ( ( ! [SY530: $i] :
( ~ ( in @ SV272 @ SY530 )
| ~ ( in @ SY530 @ SV153 ) ) )
= $true )
| ( ( in @ SV272 @ SV201 )
= $true )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1260]) ).
thf(1306,plain,
! [SV153: $i,SV201: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ SV201 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV273 @ ( sK12_D @ SV273 @ SV201 @ SV153 ) )
| ~ ( in @ ( sK12_D @ SV273 @ SV201 @ SV153 ) @ SV153 ) ) )
= $true )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1307,plain,
! [SV274: $i,SV55: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ ( sK29_B @ SV55 ) )
| ~ ( subset @ SV274 @ SV263 ) )
= $true )
| ( ( in @ SV274 @ ( sK29_B @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1308,plain,
! [SV202: $i,SV166: $i,SV283: $i,SV56: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV56 )
| ~ ( in @ SV283 @ SV166 )
| ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ SV275 @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1309,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) @ SV166 ) ) )
= $false )
| ( ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1264]) ).
thf(1310,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) ) ) )
= $false )
| ( ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1264]) ).
thf(1311,plain,
! [SV203: $i,SV276: $i,SV167: $i,SV56: $i] :
( ( ( ! [SY532: $i,SY533: $i] :
( ~ ( in @ SY532 @ SV56 )
| ~ ( in @ SY533 @ SV167 )
| ( SV276
!= ( ordered_pair @ SY532 @ SY533 ) ) ) )
= $true )
| ( ( in @ SV276 @ SV203 )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1265]) ).
thf(1312,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( ~ ( in @ SV277 @ SV203 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV167 ) )
| ( SV277
!= ( ordered_pair @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) ) ) ) )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1266]) ).
thf(1313,plain,
! [SV57: $i,SV240: $i,SV284: $i] :
( ( ( ~ ( subset @ SV284 @ SV240 )
| ( in @ SV284 @ ( sK7_SY226 @ SV240 @ SV57 ) ) )
= $true )
| ( ( ~ ( in @ SV240 @ ( sK6_B @ SV57 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1314,plain,
! [SV57: $i,SV240: $i] :
( ( ( in @ SV240 @ ( sK6_B @ SV57 ) )
= $false )
| ( ( in @ ( sK7_SY226 @ SV240 @ SV57 ) @ ( sK6_B @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1315,plain,
! [SV278: $i,SV57: $i,SV264: $i] :
( ( ( ~ ( in @ SV264 @ ( sK6_B @ SV57 ) )
| ~ ( subset @ SV278 @ SV264 ) )
= $true )
| ( ( in @ SV278 @ ( sK6_B @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1269]) ).
thf(1316,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 ) )
= $true )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1270]) ).
thf(1317,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
| ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) )
= $true )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1271]) ).
thf(1318,plain,
! [SV176: $i,SV59: $i,SV207: $i,SV279: $i] :
( ( ( ~ ( in @ SV279 @ SV207 ) )
= $true )
| ( ( ( in @ SV279 @ SV59 )
| ( in @ SV279 @ SV176 ) )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1273]) ).
thf(1319,plain,
! [SV176: $i,SV207: $i,SV59: $i] :
( ( ( ~ ! [SY496: $i] :
( ~ ( in @ SY496 @ SV59 )
| ( in @ SY496 @ SV207 ) ) )
= $false )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1274]) ).
thf(1320,plain,
! [SV59: $i,SV207: $i,SV176: $i] :
( ( ( ~ ! [SY497: $i] :
( ~ ( in @ SY497 @ SV176 )
| ( in @ SY497 @ SV207 ) ) )
= $false )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1274]) ).
thf(1321,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
= $false )
| ( ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 ) )
= $true )
| ( ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1322,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1280]) ).
thf(1323,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
| ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1281]) ).
thf(1324,plain,
! [SV210: $i,SV178: $i,SV63: $i,SV280: $i] :
( ( ( ~ ( in @ SV280 @ SV63 )
| ~ ( in @ SV280 @ SV178 ) )
= $true )
| ( ( in @ SV280 @ SV210 )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1325,plain,
! [SV178: $i,SV63: $i,SV210: $i] :
( ( ( ~ ! [SY500: $i] :
( ~ ( in @ SY500 @ SV210 )
| ( in @ SY500 @ SV63 ) ) )
= $false )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1326,plain,
! [SV63: $i,SV178: $i,SV210: $i] :
( ( ( ~ ! [SY501: $i] :
( ~ ( in @ SY501 @ SV210 )
| ( in @ SY501 @ SV178 ) ) )
= $false )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1283]) ).
thf(1327,plain,
! [SV180: $i,SV137: $i,SV266: $i] :
( ( ( SV266 = SV137 )
= $false )
| ( ( in @ SV266 @ SV180 )
= $true )
| ( ( SV180
= ( singleton @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1328,plain,
! [SV137: $i,SV180: $i,SV267: $i] :
( ( ( in @ SV267 @ SV180 )
= $false )
| ( ( SV267 = SV137 )
= $true )
| ( ( SV180
= ( singleton @ SV137 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1329,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
= $false )
| ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
= $true )
| ( ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
= $true )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1330,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
= $true )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1288]) ).
thf(1331,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
| ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 ) )
= $true )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1289]) ).
thf(1332,plain,
! [SV213: $i,SV187: $i,SV65: $i,SV281: $i] :
( ( ( ~ ( in @ SV281 @ SV65 )
| ( in @ SV281 @ SV187 ) )
= $true )
| ( ( in @ SV281 @ SV213 )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1333,plain,
! [SV187: $i,SV65: $i,SV213: $i] :
( ( ( ~ ! [SY503: $i] :
( ~ ( in @ SY503 @ SV213 )
| ( in @ SY503 @ SV65 ) ) )
= $false )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1334,plain,
! [SV65: $i,SV187: $i,SV213: $i] :
( ( ( ~ ! [SY504: $i] :
( ~ ( in @ SY504 @ SV213 )
| ~ ( in @ SY504 @ SV187 ) ) )
= $false )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1291]) ).
thf(1335,plain,
! [SV149: $i,SV195: $i,SV269: $i] :
( ( ( in @ SV269 @ SV195 )
= $false )
| ( ( subset @ SV269 @ SV149 )
= $true )
| ( ( SV195
= ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1336,plain,
! [SV195: $i,SV149: $i,SV270: $i] :
( ( ( subset @ SV270 @ SV149 )
= $false )
| ( ( in @ SV270 @ SV195 )
= $true )
| ( ( SV195
= ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1337,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV68 ) )
= $true )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1297]) ).
thf(1338,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
| ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV198 ) )
= $true )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1298]) ).
thf(1339,plain,
! [SV199: $i,SV68: $i,SV216: $i,SV282: $i] :
( ( ( ~ ( in @ SV282 @ SV216 ) )
= $true )
| ( ( ( SV282 = SV68 )
| ( SV282 = SV199 ) )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1340,plain,
! [SV199: $i,SV216: $i,SV68: $i] :
( ( ( ~ ! [SY507: $i] :
( ( SY507 != SV68 )
| ( in @ SY507 @ SV216 ) ) )
= $false )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1301]) ).
thf(1341,plain,
! [SV68: $i,SV216: $i,SV199: $i] :
( ( ( ~ ! [SY508: $i] :
( ( SY508 != SV199 )
| ( in @ SY508 @ SV216 ) ) )
= $false )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1301]) ).
thf(1342,plain,
! [SV271: $i,SV152: $i,SV200: $i] :
( ( ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV271 )
= $false )
| ( ( ~ ( in @ SV271 @ SV152 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1343,plain,
! [SV152: $i,SV200: $i] :
( ( ( in @ ( sK13_C @ SV200 @ SV152 ) @ ( sK14_SY232 @ SV200 @ SV152 ) )
= $true )
| ( ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1303]) ).
thf(1344,plain,
! [SV152: $i,SV200: $i] :
( ( ( in @ ( sK14_SY232 @ SV200 @ SV152 ) @ SV152 )
= $true )
| ( ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1304]) ).
thf(1345,plain,
! [SV201: $i,SV153: $i,SV285: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV285 )
| ~ ( in @ SV285 @ SV153 ) )
= $true )
| ( ( in @ SV272 @ SV201 )
= $true )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1346,plain,
! [SV153: $i,SV201: $i,SV273: $i] :
( ( ( in @ SV273 @ SV201 )
= $false )
| ( ( ~ ( ~ ( in @ SV273 @ ( sK12_D @ SV273 @ SV201 @ SV153 ) )
| ~ ( in @ ( sK12_D @ SV273 @ SV201 @ SV153 ) @ SV153 ) ) )
= $true )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1347,plain,
! [SV274: $i,SV55: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ ( sK29_B @ SV55 ) ) )
= $true )
| ( ( ~ ( subset @ SV274 @ SV263 ) )
= $true )
| ( ( in @ SV274 @ ( sK29_B @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1307]) ).
thf(1348,plain,
! [SV202: $i,SV166: $i,SV283: $i,SV56: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV56 )
| ~ ( in @ SV283 @ SV166 ) )
= $true )
| ( ( ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ SV275 @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1349,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) @ SV166 ) ) )
= $true )
| ( ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1309]) ).
thf(1350,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( ( sK19_D @ SV202 @ SV166 @ SV56 )
= ( ordered_pair @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) ) )
= $true )
| ( ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1310]) ).
thf(1351,plain,
! [SV203: $i,SV276: $i,SV167: $i,SV56: $i,SV286: $i] :
( ( ( ! [SY534: $i] :
( ~ ( in @ SV286 @ SV56 )
| ~ ( in @ SY534 @ SV167 )
| ( SV276
!= ( ordered_pair @ SV286 @ SY534 ) ) ) )
= $true )
| ( ( in @ SV276 @ SV203 )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1352,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( in @ SV277 @ SV203 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV167 ) )
| ( SV277
!= ( ordered_pair @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) ) ) ) )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1353,plain,
! [SV57: $i,SV240: $i,SV284: $i] :
( ( ( ~ ( subset @ SV284 @ SV240 ) )
= $true )
| ( ( in @ SV284 @ ( sK7_SY226 @ SV240 @ SV57 ) )
= $true )
| ( ( ~ ( in @ SV240 @ ( sK6_B @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1313]) ).
thf(1354,plain,
! [SV278: $i,SV57: $i,SV264: $i] :
( ( ( ~ ( in @ SV264 @ ( sK6_B @ SV57 ) ) )
= $true )
| ( ( ~ ( subset @ SV278 @ SV264 ) )
= $true )
| ( ( in @ SV278 @ ( sK6_B @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1355,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 ) )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 ) )
= $true )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1356,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 ) )
= $true )
| ( ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) )
= $true )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1357,plain,
! [SV176: $i,SV59: $i,SV207: $i,SV279: $i] :
( ( ( in @ SV279 @ SV207 )
= $false )
| ( ( ( in @ SV279 @ SV59 )
| ( in @ SV279 @ SV176 ) )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1358,plain,
! [SV176: $i,SV207: $i,SV59: $i] :
( ( ( ! [SY496: $i] :
( ~ ( in @ SY496 @ SV59 )
| ( in @ SY496 @ SV207 ) ) )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1319]) ).
thf(1359,plain,
! [SV59: $i,SV207: $i,SV176: $i] :
( ( ( ! [SY497: $i] :
( ~ ( in @ SY497 @ SV176 )
| ( in @ SY497 @ SV207 ) ) )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1320]) ).
thf(1360,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
= $false )
| ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
= $false )
| ( ( ~ ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 ) )
= $true )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1361,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
= $true )
| ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1322]) ).
thf(1362,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
= $true )
| ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 )
= $true )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1363,plain,
! [SV210: $i,SV178: $i,SV63: $i,SV280: $i] :
( ( ( ~ ( in @ SV280 @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV280 @ SV178 ) )
= $true )
| ( ( in @ SV280 @ SV210 )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1364,plain,
! [SV178: $i,SV63: $i,SV210: $i] :
( ( ( ! [SY500: $i] :
( ~ ( in @ SY500 @ SV210 )
| ( in @ SY500 @ SV63 ) ) )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1325]) ).
thf(1365,plain,
! [SV63: $i,SV178: $i,SV210: $i] :
( ( ( ! [SY501: $i] :
( ~ ( in @ SY501 @ SV210 )
| ( in @ SY501 @ SV178 ) ) )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1326]) ).
thf(1366,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 )
= $false )
| ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
= $true )
| ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
= $false )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1367,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV65 )
= $true )
| ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 )
= $true )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1368,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 ) )
= $true )
| ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 )
= $true )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1369,plain,
! [SV213: $i,SV187: $i,SV65: $i,SV281: $i] :
( ( ( ~ ( in @ SV281 @ SV65 ) )
= $true )
| ( ( in @ SV281 @ SV187 )
= $true )
| ( ( in @ SV281 @ SV213 )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1370,plain,
! [SV187: $i,SV65: $i,SV213: $i] :
( ( ( ! [SY503: $i] :
( ~ ( in @ SY503 @ SV213 )
| ( in @ SY503 @ SV65 ) ) )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1371,plain,
! [SV65: $i,SV187: $i,SV213: $i] :
( ( ( ! [SY504: $i] :
( ~ ( in @ SY504 @ SV213 )
| ~ ( in @ SY504 @ SV187 ) ) )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1372,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 ) )
= $true )
| ( ( ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV68 ) )
= $true )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1373,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ~ ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 ) )
= $true )
| ( ( ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV198 ) )
= $true )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1374,plain,
! [SV199: $i,SV68: $i,SV216: $i,SV282: $i] :
( ( ( in @ SV282 @ SV216 )
= $false )
| ( ( ( SV282 = SV68 )
| ( SV282 = SV199 ) )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1375,plain,
! [SV199: $i,SV216: $i,SV68: $i] :
( ( ( ! [SY507: $i] :
( ( SY507 != SV68 )
| ( in @ SY507 @ SV216 ) ) )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1340]) ).
thf(1376,plain,
! [SV68: $i,SV216: $i,SV199: $i] :
( ( ( ! [SY508: $i] :
( ( SY508 != SV199 )
| ( in @ SY508 @ SV216 ) ) )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1341]) ).
thf(1377,plain,
! [SV200: $i,SV152: $i,SV271: $i] :
( ( ( in @ SV271 @ SV152 )
= $false )
| ( ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV271 )
= $false )
| ( ( ~ ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 ) )
= $true )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1378,plain,
! [SV201: $i,SV153: $i,SV285: $i,SV272: $i] :
( ( ( ~ ( in @ SV272 @ SV285 ) )
= $true )
| ( ( ~ ( in @ SV285 @ SV153 ) )
= $true )
| ( ( in @ SV272 @ SV201 )
= $true )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1379,plain,
! [SV153: $i,SV201: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ ( sK12_D @ SV273 @ SV201 @ SV153 ) )
| ~ ( in @ ( sK12_D @ SV273 @ SV201 @ SV153 ) @ SV153 ) )
= $false )
| ( ( in @ SV273 @ SV201 )
= $false )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1380,plain,
! [SV274: $i,SV55: $i,SV263: $i] :
( ( ( in @ SV263 @ ( sK29_B @ SV55 ) )
= $false )
| ( ( ~ ( subset @ SV274 @ SV263 ) )
= $true )
| ( ( in @ SV274 @ ( sK29_B @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1347]) ).
thf(1381,plain,
! [SV202: $i,SV166: $i,SV283: $i,SV56: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV56 ) )
= $true )
| ( ( ~ ( in @ SV283 @ SV166 ) )
= $true )
| ( ( ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ SV275 @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1382,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( ~ ( in @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) @ SV166 ) )
= $false )
| ( ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1349]) ).
thf(1383,plain,
! [SV203: $i,SV276: $i,SV167: $i,SV287: $i,SV56: $i,SV286: $i] :
( ( ( ~ ( in @ SV286 @ SV56 )
| ~ ( in @ SV287 @ SV167 )
| ( SV276
!= ( ordered_pair @ SV286 @ SV287 ) ) )
= $true )
| ( ( in @ SV276 @ SV203 )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1384,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV167 ) )
| ( SV277
!= ( ordered_pair @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) ) ) )
= $false )
| ( ( in @ SV277 @ SV203 )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1385,plain,
! [SV57: $i,SV240: $i,SV284: $i] :
( ( ( subset @ SV284 @ SV240 )
= $false )
| ( ( in @ SV284 @ ( sK7_SY226 @ SV240 @ SV57 ) )
= $true )
| ( ( ~ ( in @ SV240 @ ( sK6_B @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1386,plain,
! [SV278: $i,SV57: $i,SV264: $i] :
( ( ( in @ SV264 @ ( sK6_B @ SV57 ) )
= $false )
| ( ( ~ ( subset @ SV278 @ SV264 ) )
= $true )
| ( ( in @ SV278 @ ( sK6_B @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1387,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
= $false )
| ( ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 ) )
= $true )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1388,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
= $false )
| ( ( ~ ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 ) )
= $true )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1356]) ).
thf(1389,plain,
! [SV207: $i,SV176: $i,SV59: $i,SV279: $i] :
( ( ( in @ SV279 @ SV59 )
= $true )
| ( ( in @ SV279 @ SV176 )
= $true )
| ( ( in @ SV279 @ SV207 )
= $false )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1390,plain,
! [SV176: $i,SV207: $i,SV59: $i,SV288: $i] :
( ( ( ~ ( in @ SV288 @ SV59 )
| ( in @ SV288 @ SV207 ) )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1391,plain,
! [SV59: $i,SV207: $i,SV176: $i,SV289: $i] :
( ( ( ~ ( in @ SV289 @ SV176 )
| ( in @ SV289 @ SV207 ) )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1392,plain,
! [SV63: $i,SV177: $i,SV209: $i] :
( ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV209 )
= $false )
| ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV63 )
= $false )
| ( ( in @ ( sK15_D @ SV209 @ SV177 @ SV63 ) @ SV177 )
= $false )
| ( ( SV209
= ( set_intersection2 @ SV63 @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1393,plain,
! [SV210: $i,SV178: $i,SV63: $i,SV280: $i] :
( ( ( in @ SV280 @ SV63 )
= $false )
| ( ( ~ ( in @ SV280 @ SV178 ) )
= $true )
| ( ( in @ SV280 @ SV210 )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1394,plain,
! [SV178: $i,SV63: $i,SV210: $i,SV290: $i] :
( ( ( ~ ( in @ SV290 @ SV210 )
| ( in @ SV290 @ SV63 ) )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1395,plain,
! [SV63: $i,SV178: $i,SV210: $i,SV291: $i] :
( ( ( ~ ( in @ SV291 @ SV210 )
| ( in @ SV291 @ SV178 ) )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1396,plain,
! [SV65: $i,SV186: $i,SV212: $i] :
( ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV186 )
= $false )
| ( ( in @ ( sK11_D @ SV212 @ SV186 @ SV65 ) @ SV212 )
= $true )
| ( ( SV212
= ( set_difference @ SV65 @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1368]) ).
thf(1397,plain,
! [SV213: $i,SV187: $i,SV65: $i,SV281: $i] :
( ( ( in @ SV281 @ SV65 )
= $false )
| ( ( in @ SV281 @ SV187 )
= $true )
| ( ( in @ SV281 @ SV213 )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1398,plain,
! [SV187: $i,SV65: $i,SV213: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV213 )
| ( in @ SV292 @ SV65 ) )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1399,plain,
! [SV65: $i,SV187: $i,SV213: $i,SV293: $i] :
( ( ( ~ ( in @ SV293 @ SV213 )
| ~ ( in @ SV293 @ SV187 ) )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1400,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
= $false )
| ( ( ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV68 ) )
= $true )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1401,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
= $false )
| ( ( ( ( sK23_D @ SV215 @ SV198 @ SV68 )
!= SV198 ) )
= $true )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1402,plain,
! [SV216: $i,SV199: $i,SV68: $i,SV282: $i] :
( ( ( SV282 = SV68 )
= $true )
| ( ( SV282 = SV199 )
= $true )
| ( ( in @ SV282 @ SV216 )
= $false )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1403,plain,
! [SV199: $i,SV216: $i,SV68: $i,SV294: $i] :
( ( ( ( SV294 != SV68 )
| ( in @ SV294 @ SV216 ) )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1404,plain,
! [SV68: $i,SV216: $i,SV199: $i,SV295: $i] :
( ( ( ( SV295 != SV199 )
| ( in @ SV295 @ SV216 ) )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1405,plain,
! [SV271: $i,SV152: $i,SV200: $i] :
( ( ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV200 )
= $false )
| ( ( in @ ( sK13_C @ SV200 @ SV152 ) @ SV271 )
= $false )
| ( ( in @ SV271 @ SV152 )
= $false )
| ( ( SV200
= ( union @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1377]) ).
thf(1406,plain,
! [SV201: $i,SV153: $i,SV285: $i,SV272: $i] :
( ( ( in @ SV272 @ SV285 )
= $false )
| ( ( ~ ( in @ SV285 @ SV153 ) )
= $true )
| ( ( in @ SV272 @ SV201 )
= $true )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1407,plain,
! [SV153: $i,SV201: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ ( sK12_D @ SV273 @ SV201 @ SV153 ) ) )
= $false )
| ( ( in @ SV273 @ SV201 )
= $false )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1379]) ).
thf(1408,plain,
! [SV153: $i,SV201: $i,SV273: $i] :
( ( ( ~ ( in @ ( sK12_D @ SV273 @ SV201 @ SV153 ) @ SV153 ) )
= $false )
| ( ( in @ SV273 @ SV201 )
= $false )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1379]) ).
thf(1409,plain,
! [SV55: $i,SV263: $i,SV274: $i] :
( ( ( subset @ SV274 @ SV263 )
= $false )
| ( ( in @ SV263 @ ( sK29_B @ SV55 ) )
= $false )
| ( ( in @ SV274 @ ( sK29_B @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1410,plain,
! [SV202: $i,SV166: $i,SV283: $i,SV56: $i,SV275: $i] :
( ( ( in @ SV275 @ SV56 )
= $false )
| ( ( ~ ( in @ SV283 @ SV166 ) )
= $true )
| ( ( ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ SV275 @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1411,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( ~ ( in @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ SV56 ) )
= $false )
| ( ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1382]) ).
thf(1412,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( ~ ( in @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) @ SV166 ) )
= $false )
| ( ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1382]) ).
thf(1413,plain,
! [SV203: $i,SV276: $i,SV167: $i,SV287: $i,SV56: $i,SV286: $i] :
( ( ( ~ ( in @ SV286 @ SV56 )
| ~ ( in @ SV287 @ SV167 ) )
= $true )
| ( ( ( SV276
!= ( ordered_pair @ SV286 @ SV287 ) ) )
= $true )
| ( ( in @ SV276 @ SV203 )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1414,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV167 ) ) )
= $false )
| ( ( in @ SV277 @ SV203 )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1415,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( ( SV277
!= ( ordered_pair @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) ) ) )
= $false )
| ( ( in @ SV277 @ SV203 )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1416,plain,
! [SV284: $i,SV57: $i,SV240: $i] :
( ( ( in @ SV240 @ ( sK6_B @ SV57 ) )
= $false )
| ( ( in @ SV284 @ ( sK7_SY226 @ SV240 @ SV57 ) )
= $true )
| ( ( subset @ SV284 @ SV240 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1417,plain,
! [SV57: $i,SV264: $i,SV278: $i] :
( ( ( subset @ SV278 @ SV264 )
= $false )
| ( ( in @ SV264 @ ( sK6_B @ SV57 ) )
= $false )
| ( ( in @ SV278 @ ( sK6_B @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1386]) ).
thf(1418,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV59 )
= $false )
| ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
= $false )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1419,plain,
! [SV59: $i,SV175: $i,SV206: $i] :
( ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV175 )
= $false )
| ( ( in @ ( sK22_D @ SV206 @ SV175 @ SV59 ) @ SV206 )
= $false )
| ( ( SV206
= ( set_union2 @ SV59 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1420,plain,
! [SV176: $i,SV207: $i,SV59: $i,SV288: $i] :
( ( ( ~ ( in @ SV288 @ SV59 ) )
= $true )
| ( ( in @ SV288 @ SV207 )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1421,plain,
! [SV59: $i,SV207: $i,SV176: $i,SV289: $i] :
( ( ( ~ ( in @ SV289 @ SV176 ) )
= $true )
| ( ( in @ SV289 @ SV207 )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1422,plain,
! [SV210: $i,SV63: $i,SV178: $i,SV280: $i] :
( ( ( in @ SV280 @ SV178 )
= $false )
| ( ( in @ SV280 @ SV63 )
= $false )
| ( ( in @ SV280 @ SV210 )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1423,plain,
! [SV178: $i,SV63: $i,SV210: $i,SV290: $i] :
( ( ( ~ ( in @ SV290 @ SV210 ) )
= $true )
| ( ( in @ SV290 @ SV63 )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1394]) ).
thf(1424,plain,
! [SV63: $i,SV178: $i,SV210: $i,SV291: $i] :
( ( ( ~ ( in @ SV291 @ SV210 ) )
= $true )
| ( ( in @ SV291 @ SV178 )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1425,plain,
! [SV187: $i,SV65: $i,SV213: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV213 ) )
= $true )
| ( ( in @ SV292 @ SV65 )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1426,plain,
! [SV65: $i,SV187: $i,SV213: $i,SV293: $i] :
( ( ( ~ ( in @ SV293 @ SV213 ) )
= $true )
| ( ( ~ ( in @ SV293 @ SV187 ) )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1427,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV68 )
= $false )
| ( ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
= $false )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1428,plain,
! [SV68: $i,SV198: $i,SV215: $i] :
( ( ( ( sK23_D @ SV215 @ SV198 @ SV68 )
= SV198 )
= $false )
| ( ( in @ ( sK23_D @ SV215 @ SV198 @ SV68 ) @ SV215 )
= $false )
| ( ( SV215
= ( unordered_pair @ SV68 @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1429,plain,
! [SV199: $i,SV216: $i,SV68: $i,SV294: $i] :
( ( ( ( SV294 != SV68 ) )
= $true )
| ( ( in @ SV294 @ SV216 )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1430,plain,
! [SV68: $i,SV216: $i,SV199: $i,SV295: $i] :
( ( ( ( SV295 != SV199 ) )
= $true )
| ( ( in @ SV295 @ SV216 )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1404]) ).
thf(1431,plain,
! [SV201: $i,SV272: $i,SV153: $i,SV285: $i] :
( ( ( in @ SV285 @ SV153 )
= $false )
| ( ( in @ SV272 @ SV285 )
= $false )
| ( ( in @ SV272 @ SV201 )
= $true )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1406]) ).
thf(1432,plain,
! [SV153: $i,SV201: $i,SV273: $i] :
( ( ( in @ SV273 @ ( sK12_D @ SV273 @ SV201 @ SV153 ) )
= $true )
| ( ( in @ SV273 @ SV201 )
= $false )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1407]) ).
thf(1433,plain,
! [SV153: $i,SV201: $i,SV273: $i] :
( ( ( in @ ( sK12_D @ SV273 @ SV201 @ SV153 ) @ SV153 )
= $true )
| ( ( in @ SV273 @ SV201 )
= $false )
| ( ( SV201
= ( union @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1408]) ).
thf(1434,plain,
! [SV202: $i,SV56: $i,SV275: $i,SV166: $i,SV283: $i] :
( ( ( in @ SV283 @ SV166 )
= $false )
| ( ( in @ SV275 @ SV56 )
= $false )
| ( ( ( ( sK19_D @ SV202 @ SV166 @ SV56 )
!= ( ordered_pair @ SV275 @ SV283 ) ) )
= $true )
| ( ( ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1435,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( in @ ( sK20_SY236 @ SV202 @ SV166 @ SV56 ) @ SV56 )
= $true )
| ( ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1411]) ).
thf(1436,plain,
! [SV56: $i,SV166: $i,SV202: $i] :
( ( ( in @ ( sK21_SY238 @ SV202 @ SV166 @ SV56 ) @ SV166 )
= $true )
| ( ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1412]) ).
thf(1437,plain,
! [SV203: $i,SV276: $i,SV167: $i,SV287: $i,SV56: $i,SV286: $i] :
( ( ( ~ ( in @ SV286 @ SV56 ) )
= $true )
| ( ( ~ ( in @ SV287 @ SV167 ) )
= $true )
| ( ( ( SV276
!= ( ordered_pair @ SV286 @ SV287 ) ) )
= $true )
| ( ( in @ SV276 @ SV203 )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1438,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV167 ) ) )
= $true )
| ( ( in @ SV277 @ SV203 )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1414]) ).
thf(1439,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( SV277
= ( ordered_pair @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) ) )
= $true )
| ( ( in @ SV277 @ SV203 )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1415]) ).
thf(1440,plain,
! [SV176: $i,SV207: $i,SV59: $i,SV288: $i] :
( ( ( in @ SV288 @ SV59 )
= $false )
| ( ( in @ SV288 @ SV207 )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1420]) ).
thf(1441,plain,
! [SV59: $i,SV207: $i,SV176: $i,SV289: $i] :
( ( ( in @ SV289 @ SV176 )
= $false )
| ( ( in @ SV289 @ SV207 )
= $true )
| ( ( SV207
= ( set_union2 @ SV59 @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1442,plain,
! [SV178: $i,SV63: $i,SV210: $i,SV290: $i] :
( ( ( in @ SV290 @ SV210 )
= $false )
| ( ( in @ SV290 @ SV63 )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1423]) ).
thf(1443,plain,
! [SV63: $i,SV178: $i,SV210: $i,SV291: $i] :
( ( ( in @ SV291 @ SV210 )
= $false )
| ( ( in @ SV291 @ SV178 )
= $true )
| ( ( SV210
= ( set_intersection2 @ SV63 @ SV178 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1424]) ).
thf(1444,plain,
! [SV187: $i,SV65: $i,SV213: $i,SV292: $i] :
( ( ( in @ SV292 @ SV213 )
= $false )
| ( ( in @ SV292 @ SV65 )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1425]) ).
thf(1445,plain,
! [SV65: $i,SV187: $i,SV213: $i,SV293: $i] :
( ( ( in @ SV293 @ SV213 )
= $false )
| ( ( ~ ( in @ SV293 @ SV187 ) )
= $true )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1446,plain,
! [SV199: $i,SV216: $i,SV68: $i,SV294: $i] :
( ( ( SV294 = SV68 )
= $false )
| ( ( in @ SV294 @ SV216 )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1447,plain,
! [SV68: $i,SV216: $i,SV199: $i,SV295: $i] :
( ( ( SV295 = SV199 )
= $false )
| ( ( in @ SV295 @ SV216 )
= $true )
| ( ( SV216
= ( unordered_pair @ SV68 @ SV199 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1448,plain,
! [SV283: $i,SV275: $i,SV56: $i,SV166: $i,SV202: $i] :
( ( ( ( sK19_D @ SV202 @ SV166 @ SV56 )
= ( ordered_pair @ SV275 @ SV283 ) )
= $false )
| ( ( in @ SV275 @ SV56 )
= $false )
| ( ( in @ SV283 @ SV166 )
= $false )
| ( ( ~ ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 ) )
= $true )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1449,plain,
! [SV203: $i,SV276: $i,SV167: $i,SV287: $i,SV56: $i,SV286: $i] :
( ( ( in @ SV286 @ SV56 )
= $false )
| ( ( ~ ( in @ SV287 @ SV167 ) )
= $true )
| ( ( ( SV276
!= ( ordered_pair @ SV286 @ SV287 ) ) )
= $true )
| ( ( in @ SV276 @ SV203 )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1437]) ).
thf(1450,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( ~ ( in @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV56 )
| ~ ( in @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV167 ) )
= $false )
| ( ( in @ SV277 @ SV203 )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1451,plain,
! [SV65: $i,SV213: $i,SV187: $i,SV293: $i] :
( ( ( in @ SV293 @ SV187 )
= $false )
| ( ( in @ SV293 @ SV213 )
= $false )
| ( ( SV213
= ( set_difference @ SV65 @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1452,plain,
! [SV275: $i,SV283: $i,SV56: $i,SV166: $i,SV202: $i] :
( ( ( in @ ( sK19_D @ SV202 @ SV166 @ SV56 ) @ SV202 )
= $false )
| ( ( in @ SV283 @ SV166 )
= $false )
| ( ( in @ SV275 @ SV56 )
= $false )
| ( ( ( sK19_D @ SV202 @ SV166 @ SV56 )
= ( ordered_pair @ SV275 @ SV283 ) )
= $false )
| ( ( SV202
= ( cartesian_product2 @ SV56 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1448]) ).
thf(1453,plain,
! [SV203: $i,SV276: $i,SV56: $i,SV286: $i,SV167: $i,SV287: $i] :
( ( ( in @ SV287 @ SV167 )
= $false )
| ( ( in @ SV286 @ SV56 )
= $false )
| ( ( ( SV276
!= ( ordered_pair @ SV286 @ SV287 ) ) )
= $true )
| ( ( in @ SV276 @ SV203 )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1454,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( ~ ( in @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV56 ) )
= $false )
| ( ( in @ SV277 @ SV203 )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1455,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( ~ ( in @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV167 ) )
= $false )
| ( ( in @ SV277 @ SV203 )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1450]) ).
thf(1456,plain,
! [SV203: $i,SV167: $i,SV56: $i,SV287: $i,SV286: $i,SV276: $i] :
( ( ( SV276
= ( ordered_pair @ SV286 @ SV287 ) )
= $false )
| ( ( in @ SV286 @ SV56 )
= $false )
| ( ( in @ SV287 @ SV167 )
= $false )
| ( ( in @ SV276 @ SV203 )
= $true )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1457,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( in @ ( sK17_E @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV56 )
= $true )
| ( ( in @ SV277 @ SV203 )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1454]) ).
thf(1458,plain,
! [SV56: $i,SV167: $i,SV203: $i,SV277: $i] :
( ( ( in @ ( sK18_SY233 @ SV277 @ SV203 @ SV167 @ SV56 ) @ SV167 )
= $true )
| ( ( in @ SV277 @ SV203 )
= $false )
| ( ( SV203
= ( cartesian_product2 @ SV56 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1455]) ).
thf(1459,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[283,1458,1457,1456,1452,1451,1447,1446,1444,1443,1442,1441,1440,1439,1436,1435,1433,1432,1431,1428,1427,1422,1419,1418,1417,1416,1409,1405,1402,1397,1396,1392,1389,1367,1366,1362,1361,1350,1344,1343,1336,1335,1328,1327,1314,1299,1294,1293,1292,1284,1278,1277,1276,1275,1272,1253,1249,1246,1241,1240,1230,1229,1226,1205,1203,1202,1199,1187,1184,1167,1164,1163,1162,1161,1156,1155,1154,1152,1135,1134,1113,1106,1105,1097,1096,1090,1079,1076,1072,1065,1064,1063,1038,1035,1023,1022,995,994,993,992,983,968,967,958,957,956,955,951,950,949,948,947,946,944,931,909,884,870,863,841,827,789,788,785,784,783,777,776,775,729,707,706,705,701,698,696,692,686,685,684,682,639,617,613,605,590,527,526,525,524,520,516,514,512,511,505,500,498,454,453,452,451,449,448,447,446,433,423,410,408,366,356,350]) ).
thf(1460,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU169+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 04:36:38 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.19/0.37 ..
% 0.19/0.39
% 0.19/0.39 No.of.Axioms: 104
% 0.19/0.39
% 0.19/0.39 Length.of.Defs: 0
% 0.19/0.39
% 0.19/0.39 Contains.Choice.Funs: false
% 0.19/0.43 .......
% 0.19/0.46 (rf:2,axioms:91,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:106,loop_count:0,foatp_calls:0,translation:fof_full)..........................................................................................................
% 3.68/3.86
% 3.68/3.86 ********************************
% 3.68/3.86 * All subproblems solved! *
% 3.68/3.86 ********************************
% 3.68/3.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:92,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1459,loop_count:0,foatp_calls:1,translation:fof_full)
% 4.37/4.60
% 4.37/4.60 %**** Beginning of derivation protocol ****
% 4.37/4.60 % SZS output start CNFRefutation
% See solution above
% 4.43/4.61
% 4.43/4.61 %**** End of derivation protocol ****
% 4.43/4.61 %**** no. of clauses in derivation: 1447 ****
% 4.43/4.61 %**** clause counter: 1459 ****
% 4.43/4.61
% 4.43/4.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:92,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1459,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------