%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:12 AM UTC 2026
% Result : Theorem 6.49s 1.41s
% Output : CNFRefutation 6.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 27
% Syntax : Number of formulae : 1323 ( 354 unt; 0 typ; 0 def)
% Number of atoms : 12715 (5096 equ; 0 cnn)
% Maximal formula atoms : 6 ( 9 avg)
% Number of connectives : 29504 (7752 ~;4926 |; 65 &;16660 @)
% ( 79 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 59 usr; 7 con; 0-5 aty)
% Number of variables : 4802 ( 0 ^;4786 !; 16 ?;4802 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_sK10_SY163,type,
sK10_SY163: $i > $i > $i > $i ).
thf(tp_sK11_SY165,type,
sK11_SY165: $i > $i > $i > $i ).
thf(tp_sK12_SY169,type,
sK12_SY169: $i > $i > $i > $i ).
thf(tp_sK13_SY171,type,
sK13_SY171: $i > $i > $i > $i ).
thf(tp_sK14_SY177,type,
sK14_SY177: $i > $i > $i > $i ).
thf(tp_sK15_SY131,type,
sK15_SY131: $i > $i > $i ).
thf(tp_sK16_SY182,type,
sK16_SY182: $i > $i > $i > $i ).
thf(tp_sK17_SY186,type,
sK17_SY186: $i > $i > $i > $i > $i ).
thf(tp_sK18_SY185,type,
sK18_SY185: $i > $i > $i ).
thf(tp_sK19_SY195,type,
sK19_SY195: $i > $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY192,type,
sK20_SY192: $i > $i > $i > $i ).
thf(tp_sK21_SY197,type,
sK21_SY197: $i > $i > $i > $i ).
thf(tp_sK22_SY185,type,
sK22_SY185: $i > $i > $i > $i ).
thf(tp_sK23_SY192,type,
sK23_SY192: $i > $i > $i > $i > $i > $i ).
thf(tp_sK24_SY198,type,
sK24_SY198: $i > $i > $i > $i > $i > $i ).
thf(tp_sK25_SY277,type,
sK25_SY277: $i > $i > $i ).
thf(tp_sK26_SY245,type,
sK26_SY245: $i > $i ).
thf(tp_sK27_SY260,type,
sK27_SY260: $i > $i > $i ).
thf(tp_sK28_SY286,type,
sK28_SY286: $i > $i > $i ).
thf(tp_sK29_SY290,type,
sK29_SY290: $i > $i > $i ).
thf(tp_sK2_SY59,type,
sK2_SY59: $i ).
thf(tp_sK30_SY297,type,
sK30_SY297: $i > $i > $i > $i ).
thf(tp_sK31_SY303,type,
sK31_SY303: $i > $i > $i > $i ).
thf(tp_sK32_SY309,type,
sK32_SY309: $i > $i > $i > $i ).
thf(tp_sK33_SY311,type,
sK33_SY311: $i > $i > $i > $i ).
thf(tp_sK34_SY315,type,
sK34_SY315: $i > $i > $i > $i ).
thf(tp_sK35_SY272,type,
sK35_SY272: $i > $i > $i ).
thf(tp_sK36_SY316,type,
sK36_SY316: $i > $i > $i > $i ).
thf(tp_sK37_SY320,type,
sK37_SY320: $i > $i > $i > $i > $i ).
thf(tp_sK38_SY319,type,
sK38_SY319: $i > $i > $i ).
thf(tp_sK39_SY329,type,
sK39_SY329: $i > $i > $i > $i > $i ).
thf(tp_sK3_SY62,type,
sK3_SY62: $i ).
thf(tp_sK40_SY326,type,
sK40_SY326: $i > $i > $i > $i ).
thf(tp_sK41_SY331,type,
sK41_SY331: $i > $i > $i > $i ).
thf(tp_sK42_SY319,type,
sK42_SY319: $i > $i > $i > $i ).
thf(tp_sK43_SY326,type,
sK43_SY326: $i > $i > $i > $i > $i > $i ).
thf(tp_sK44_SY332,type,
sK44_SY332: $i > $i > $i > $i > $i > $i ).
thf(tp_sK4_SY64,type,
sK4_SY64: $i ).
thf(tp_sK5_SY130,type,
sK5_SY130: $i > $i > $i ).
thf(tp_sK6_SY90,type,
sK6_SY90: $i > $i ).
thf(tp_sK7_SY136,type,
sK7_SY136: $i > $i > $i ).
thf(tp_sK8_SY146,type,
sK8_SY146: $i > $i > $i ).
thf(tp_sK9_SY161,type,
sK9_SY161: $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(41,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
thf(95,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(96,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[95]) ).
thf(97,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[96]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(100,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(101,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(102,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(103,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(104,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(105,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(106,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(107,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(108,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(109,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(110,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(111,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(113,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(115,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(116,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(117,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(118,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(120,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(121,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(122,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(123,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( in @ ( ordered_pair @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
<=> ( ( in @ A @ C )
& ( in @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(124,plain,
( ( ! [SY59: $i,SY60: $i,SY61: $i] :
( ( in @ ( ordered_pair @ sK1_A @ SY59 ) @ ( cartesian_product2 @ SY60 @ SY61 ) )
<=> ( ( in @ sK1_A @ SY60 )
& ( in @ SY59 @ SY61 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[97]) ).
thf(125,plain,
( ( ! [SY62: $i,SY63: $i] :
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ SY62 @ SY63 ) )
<=> ( ( in @ sK1_A @ SY62 )
& ( in @ sK2_SY59 @ SY63 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[124]) ).
thf(126,plain,
( ( ! [SY64: $i] :
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ SY64 ) )
<=> ( ( in @ sK1_A @ sK3_SY62 )
& ( in @ sK2_SY59 @ SY64 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[125]) ).
thf(127,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) )
<=> ( ( in @ sK1_A @ sK3_SY62 )
& ( in @ sK2_SY59 @ sK4_SY64 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[126]) ).
thf(128,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) )
=> ( ( in @ sK1_A @ sK3_SY62 )
& ( in @ sK2_SY59 @ sK4_SY64 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[127]) ).
thf(129,plain,
( ( ( ( in @ sK1_A @ sK3_SY62 )
& ( in @ sK2_SY59 @ sK4_SY64 ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[127]) ).
thf(130,plain,
( ( ~ ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) )
=> ( ( in @ sK1_A @ sK3_SY62 )
& ( in @ sK2_SY59 @ sK4_SY64 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[128]) ).
thf(131,plain,
( ( ~ ( ( ( in @ sK1_A @ sK3_SY62 )
& ( in @ sK2_SY59 @ sK4_SY64 ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[129]) ).
thf(132,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(copy,[status(thm)],[123]) ).
thf(133,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(134,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(135,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(137,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(138,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(139,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(140,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(copy,[status(thm)],[115]) ).
thf(141,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(142,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(143,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(144,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(145,plain,
$true = $true,
inference(copy,[status(thm)],[110]) ).
thf(146,plain,
$true = $true,
inference(copy,[status(thm)],[109]) ).
thf(147,plain,
$true = $true,
inference(copy,[status(thm)],[108]) ).
thf(148,plain,
$true = $true,
inference(copy,[status(thm)],[107]) ).
thf(149,plain,
$true = $true,
inference(copy,[status(thm)],[106]) ).
thf(150,plain,
$true = $true,
inference(copy,[status(thm)],[105]) ).
thf(151,plain,
$true = $true,
inference(copy,[status(thm)],[104]) ).
thf(152,plain,
$true = $true,
inference(copy,[status(thm)],[103]) ).
thf(153,plain,
$true = $true,
inference(copy,[status(thm)],[102]) ).
thf(154,plain,
$true = $true,
inference(copy,[status(thm)],[101]) ).
thf(155,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(156,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(157,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(158,plain,
( ( ~ ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) )
=> ( ( in @ sK1_A @ sK3_SY62 )
& ( in @ sK2_SY59 @ sK4_SY64 ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(159,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(160,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(161,plain,
( ( ~ ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) )
| ~ ( ~ ( in @ sK1_A @ sK3_SY62 )
| ~ ( in @ sK2_SY59 @ sK4_SY64 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(162,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(163,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(164,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(165,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(166,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(167,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(168,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(169,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(170,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(171,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( union @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(172,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(173,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(174,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(175,plain,
! [SV1: $i] :
( ( ! [SY65: $i] :
~ ( empty @ ( ordered_pair @ SV1 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(176,plain,
! [SV2: $i] :
( ( ! [SY66: $i,SY67: $i] :
~ ( ~ ( ( SY67
!= ( set_union2 @ SV2 @ SY66 ) )
| ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SY67 )
| ( in @ SY68 @ SV2 )
| ( in @ SY68 @ SY66 ) )
| ~ ( ~ ( ( in @ SY68 @ SV2 )
| ( in @ SY68 @ SY66 ) )
| ( in @ SY68 @ SY67 ) ) ) )
| ~ ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ SY67 )
| ( in @ SY69 @ SV2 )
| ( in @ SY69 @ SY66 ) )
| ~ ( ~ ( ( in @ SY69 @ SV2 )
| ( in @ SY69 @ SY66 ) )
| ( in @ SY69 @ SY67 ) ) )
| ( SY67
= ( set_union2 @ SV2 @ SY66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(177,plain,
! [SV3: $i] :
( ( ! [SY70: $i,SY71: $i] :
~ ( ~ ( ( SY71
!= ( unordered_pair @ SV3 @ SY70 ) )
| ! [SY72: $i] :
~ ( ~ ( ~ ( in @ SY72 @ SY71 )
| ( SY72 = SV3 )
| ( SY72 = SY70 ) )
| ~ ( ~ ( ( SY72 = SV3 )
| ( SY72 = SY70 ) )
| ( in @ SY72 @ SY71 ) ) ) )
| ~ ( ~ ! [SY73: $i] :
~ ( ~ ( ~ ( in @ SY73 @ SY71 )
| ( SY73 = SV3 )
| ( SY73 = SY70 ) )
| ~ ( ~ ( ( SY73 = SV3 )
| ( SY73 = SY70 ) )
| ( in @ SY73 @ SY71 ) ) )
| ( SY71
= ( unordered_pair @ SV3 @ SY70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(178,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) )
| ~ ( ~ ( in @ sK1_A @ sK3_SY62 )
| ~ ( in @ sK2_SY59 @ sK4_SY64 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(179,plain,
! [SV4: $i] :
( ( ! [SY74: $i,SY75: $i,SY76: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SY74 ) @ ( cartesian_product2 @ SY75 @ SY76 ) )
| ~ ( ~ ( in @ SV4 @ SY75 )
| ~ ( in @ SY74 @ SY76 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV4 @ SY75 )
| ~ ( in @ SY74 @ SY76 ) )
| ( in @ ( ordered_pair @ SV4 @ SY74 ) @ ( cartesian_product2 @ SY75 @ SY76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(180,plain,
! [SV5: $i] :
( ( ! [SY77: $i] :
( ~ ! [SY78: $i] :
~ ( ~ ( ~ ( in @ SY78 @ SV5 )
| ( in @ SY78 @ SY77 ) )
| ~ ( ~ ( in @ SY78 @ SY77 )
| ( in @ SY78 @ SV5 ) ) )
| ( SV5 = SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(181,plain,
! [SV6: $i] :
( ( ! [SY79: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV6 @ SY79 )
| ~ ! [SY80: $i] :
~ ~ ( ~ ( in @ SY80 @ SV6 )
| ~ ( in @ SY80 @ SY79 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY81: $i] :
~ ~ ( ~ ( in @ SY81 @ SV6 )
| ~ ( in @ SY81 @ SY79 ) )
| ~ ( disjoint @ SV6 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(182,plain,
! [SV7: $i] :
( ( ! [SY82: $i,SY83: $i,SY84: $i] :
( ( ( ordered_pair @ SV7 @ SY82 )
!= ( ordered_pair @ SY83 @ SY84 ) )
| ~ ( ( SV7 != SY83 )
| ( SY82 != SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(183,plain,
! [SV8: $i] :
( ( ! [SY85: $i] :
~ ( ~ ( ( SY85
!= ( singleton @ SV8 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SY85 )
| ( SY86 = SV8 ) )
| ~ ( ( SY86 != SV8 )
| ( in @ SY86 @ SY85 ) ) ) )
| ~ ( ~ ! [SY87: $i] :
~ ( ~ ( ~ ( in @ SY87 @ SY85 )
| ( SY87 = SV8 ) )
| ~ ( ( SY87 != SV8 )
| ( in @ SY87 @ SY85 ) ) )
| ( SY85
= ( singleton @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(184,plain,
! [SV9: $i] :
( ( ! [SY88: $i] :
~ ~ ( ~ ( in @ SV9 @ SY88 )
| ~ ( empty @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(185,plain,
! [SV10: $i] :
( ( ~ ( ~ ( ( SV10 != empty_set )
| ! [SY89: $i] :
~ ( in @ SY89 @ SV10 ) )
| ~ ( ~ ! [SY90: $i] :
~ ( in @ SY90 @ SV10 )
| ( SV10 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(186,plain,
! [SV11: $i] :
( ( ! [SY91: $i,SY92: $i] :
~ ( ~ ( ( SY92
!= ( set_difference @ SV11 @ SY91 ) )
| ! [SY93: $i] :
~ ( ~ ( ~ ( in @ SY93 @ SY92 )
| ~ ( ~ ( in @ SY93 @ SV11 )
| ~ ~ ( in @ SY93 @ SY91 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY93 @ SV11 )
| ~ ~ ( in @ SY93 @ SY91 ) )
| ( in @ SY93 @ SY92 ) ) ) )
| ~ ( ~ ! [SY94: $i] :
~ ( ~ ( ~ ( in @ SY94 @ SY92 )
| ~ ( ~ ( in @ SY94 @ SV11 )
| ~ ~ ( in @ SY94 @ SY91 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY94 @ SV11 )
| ~ ~ ( in @ SY94 @ SY91 ) )
| ( in @ SY94 @ SY92 ) ) )
| ( SY92
= ( set_difference @ SV11 @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(187,plain,
! [SV12: $i] :
( ( ! [SY95: $i,SY96: $i] :
~ ( ~ ( ( SY96
!= ( set_intersection2 @ SV12 @ SY95 ) )
| ! [SY97: $i] :
~ ( ~ ( ~ ( in @ SY97 @ SY96 )
| ~ ( ~ ( in @ SY97 @ SV12 )
| ~ ( in @ SY97 @ SY95 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY97 @ SV12 )
| ~ ( in @ SY97 @ SY95 ) )
| ( in @ SY97 @ SY96 ) ) ) )
| ~ ( ~ ! [SY98: $i] :
~ ( ~ ( ~ ( in @ SY98 @ SY96 )
| ~ ( ~ ( in @ SY98 @ SV12 )
| ~ ( in @ SY98 @ SY95 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY98 @ SV12 )
| ~ ( in @ SY98 @ SY95 ) )
| ( in @ SY98 @ SY96 ) ) )
| ( SY96
= ( set_intersection2 @ SV12 @ SY95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(188,plain,
! [SV13: $i] :
( ( ! [SY99: $i] :
~ ( ~ ( ( SY99
!= ( union @ SV13 ) )
| ! [SY100: $i] :
~ ( ~ ( ~ ( in @ SY100 @ SY99 )
| ~ ! [SY101: $i] :
~ ~ ( ~ ( in @ SY100 @ SY101 )
| ~ ( in @ SY101 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY100 @ SY102 )
| ~ ( in @ SY102 @ SV13 ) )
| ( in @ SY100 @ SY99 ) ) ) )
| ~ ( ~ ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SY99 )
| ~ ! [SY104: $i] :
~ ~ ( ~ ( in @ SY103 @ SY104 )
| ~ ( in @ SY104 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY105: $i] :
~ ~ ( ~ ( in @ SY103 @ SY105 )
| ~ ( in @ SY105 @ SV13 ) )
| ( in @ SY103 @ SY99 ) ) )
| ( SY99
= ( union @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(189,plain,
! [SV14: $i] :
( ( ! [SY106: $i] :
( ~ ( in @ SV14 @ SY106 )
| ~ ( in @ SY106 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(190,plain,
! [SV15: $i] :
( ( ! [SY107: $i,SY108: $i] :
~ ( ~ ( ( SY108
!= ( cartesian_product2 @ SV15 @ SY107 ) )
| ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SY108 )
| ~ ! [SY110: $i] :
~ ~ ! [SY111: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY110 @ SV15 )
| ~ ( in @ SY111 @ SY107 ) )
| ( SY109
!= ( ordered_pair @ SY110 @ SY111 ) ) ) )
| ~ ( ~ ~ ! [SY112: $i] :
~ ~ ! [SY113: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY112 @ SV15 )
| ~ ( in @ SY113 @ SY107 ) )
| ( SY109
!= ( ordered_pair @ SY112 @ SY113 ) ) )
| ( in @ SY109 @ SY108 ) ) ) )
| ~ ( ~ ! [SY114: $i] :
~ ( ~ ( ~ ( in @ SY114 @ SY108 )
| ~ ! [SY115: $i] :
~ ~ ! [SY116: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY115 @ SV15 )
| ~ ( in @ SY116 @ SY107 ) )
| ( SY114
!= ( ordered_pair @ SY115 @ SY116 ) ) ) )
| ~ ( ~ ~ ! [SY117: $i] :
~ ~ ! [SY118: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY117 @ SV15 )
| ~ ( in @ SY118 @ SY107 ) )
| ( SY114
!= ( ordered_pair @ SY117 @ SY118 ) ) )
| ( in @ SY114 @ SY108 ) ) )
| ( SY108
= ( cartesian_product2 @ SV15 @ SY107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(191,plain,
! [SV16: $i] :
( ( ! [SY119: $i] :
~ ( ~ ( ~ ( subset @ SV16 @ SY119 )
| ! [SY120: $i] :
( ~ ( in @ SY120 @ SV16 )
| ( in @ SY120 @ SY119 ) ) )
| ~ ( ~ ! [SY121: $i] :
( ~ ( in @ SY121 @ SV16 )
| ( in @ SY121 @ SY119 ) )
| ( subset @ SV16 @ SY119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(192,plain,
! [SV17: $i,SV1: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV1 @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(193,plain,
! [SV18: $i,SV2: $i] :
( ( ! [SY122: $i] :
~ ( ~ ( ( SY122
!= ( set_union2 @ SV2 @ SV18 ) )
| ! [SY123: $i] :
~ ( ~ ( ~ ( in @ SY123 @ SY122 )
| ( in @ SY123 @ SV2 )
| ( in @ SY123 @ SV18 ) )
| ~ ( ~ ( ( in @ SY123 @ SV2 )
| ( in @ SY123 @ SV18 ) )
| ( in @ SY123 @ SY122 ) ) ) )
| ~ ( ~ ! [SY124: $i] :
~ ( ~ ( ~ ( in @ SY124 @ SY122 )
| ( in @ SY124 @ SV2 )
| ( in @ SY124 @ SV18 ) )
| ~ ( ~ ( ( in @ SY124 @ SV2 )
| ( in @ SY124 @ SV18 ) )
| ( in @ SY124 @ SY122 ) ) )
| ( SY122
= ( set_union2 @ SV2 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(194,plain,
! [SV19: $i,SV3: $i] :
( ( ! [SY125: $i] :
~ ( ~ ( ( SY125
!= ( unordered_pair @ SV3 @ SV19 ) )
| ! [SY126: $i] :
~ ( ~ ( ~ ( in @ SY126 @ SY125 )
| ( SY126 = SV3 )
| ( SY126 = SV19 ) )
| ~ ( ~ ( ( SY126 = SV3 )
| ( SY126 = SV19 ) )
| ( in @ SY126 @ SY125 ) ) ) )
| ~ ( ~ ! [SY127: $i] :
~ ( ~ ( ~ ( in @ SY127 @ SY125 )
| ( SY127 = SV3 )
| ( SY127 = SV19 ) )
| ~ ( ~ ( ( SY127 = SV3 )
| ( SY127 = SV19 ) )
| ( in @ SY127 @ SY125 ) ) )
| ( SY125
= ( unordered_pair @ SV3 @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(195,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(196,plain,
( ( ~ ( ~ ( in @ sK1_A @ sK3_SY62 )
| ~ ( in @ sK2_SY59 @ sK4_SY64 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(197,plain,
! [SV20: $i,SV4: $i] :
( ( ! [SY128: $i,SY129: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SY128 @ SY129 ) )
| ~ ( ~ ( in @ SV4 @ SY128 )
| ~ ( in @ SV20 @ SY129 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV4 @ SY128 )
| ~ ( in @ SV20 @ SY129 ) )
| ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SY128 @ SY129 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(198,plain,
! [SV21: $i,SV5: $i] :
( ( ~ ! [SY130: $i] :
~ ( ~ ( ~ ( in @ SY130 @ SV5 )
| ( in @ SY130 @ SV21 ) )
| ~ ( ~ ( in @ SY130 @ SV21 )
| ( in @ SY130 @ SV5 ) ) )
| ( SV5 = SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(199,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV6 @ SV22 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY131 @ SV6 )
| ~ ( in @ SY131 @ SV22 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV6 )
| ~ ( in @ SY132 @ SV22 ) )
| ~ ( disjoint @ SV6 @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(200,plain,
! [SV23: $i,SV7: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ( ( ordered_pair @ SV7 @ SV23 )
!= ( ordered_pair @ SY133 @ SY134 ) )
| ~ ( ( SV7 != SY133 )
| ( SV23 != SY134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(201,plain,
! [SV8: $i,SV24: $i] :
( ( ~ ( ~ ( ( SV24
!= ( singleton @ SV8 ) )
| ! [SY135: $i] :
~ ( ~ ( ~ ( in @ SY135 @ SV24 )
| ( SY135 = SV8 ) )
| ~ ( ( SY135 != SV8 )
| ( in @ SY135 @ SV24 ) ) ) )
| ~ ( ~ ! [SY136: $i] :
~ ( ~ ( ~ ( in @ SY136 @ SV24 )
| ( SY136 = SV8 ) )
| ~ ( ( SY136 != SV8 )
| ( in @ SY136 @ SV24 ) ) )
| ( SV24
= ( singleton @ SV8 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(202,plain,
! [SV25: $i,SV9: $i] :
( ( ~ ~ ( ~ ( in @ SV9 @ SV25 )
| ~ ( empty @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(203,plain,
! [SV10: $i] :
( ( ~ ( ( SV10 != empty_set )
| ! [SY89: $i] :
~ ( in @ SY89 @ SV10 ) )
| ~ ( ~ ! [SY90: $i] :
~ ( in @ SY90 @ SV10 )
| ( SV10 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(204,plain,
! [SV26: $i,SV11: $i] :
( ( ! [SY137: $i] :
~ ( ~ ( ( SY137
!= ( set_difference @ SV11 @ SV26 ) )
| ! [SY138: $i] :
~ ( ~ ( ~ ( in @ SY138 @ SY137 )
| ~ ( ~ ( in @ SY138 @ SV11 )
| ~ ~ ( in @ SY138 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY138 @ SV11 )
| ~ ~ ( in @ SY138 @ SV26 ) )
| ( in @ SY138 @ SY137 ) ) ) )
| ~ ( ~ ! [SY139: $i] :
~ ( ~ ( ~ ( in @ SY139 @ SY137 )
| ~ ( ~ ( in @ SY139 @ SV11 )
| ~ ~ ( in @ SY139 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY139 @ SV11 )
| ~ ~ ( in @ SY139 @ SV26 ) )
| ( in @ SY139 @ SY137 ) ) )
| ( SY137
= ( set_difference @ SV11 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(205,plain,
! [SV27: $i,SV12: $i] :
( ( ! [SY140: $i] :
~ ( ~ ( ( SY140
!= ( set_intersection2 @ SV12 @ SV27 ) )
| ! [SY141: $i] :
~ ( ~ ( ~ ( in @ SY141 @ SY140 )
| ~ ( ~ ( in @ SY141 @ SV12 )
| ~ ( in @ SY141 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY141 @ SV12 )
| ~ ( in @ SY141 @ SV27 ) )
| ( in @ SY141 @ SY140 ) ) ) )
| ~ ( ~ ! [SY142: $i] :
~ ( ~ ( ~ ( in @ SY142 @ SY140 )
| ~ ( ~ ( in @ SY142 @ SV12 )
| ~ ( in @ SY142 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY142 @ SV12 )
| ~ ( in @ SY142 @ SV27 ) )
| ( in @ SY142 @ SY140 ) ) )
| ( SY140
= ( set_intersection2 @ SV12 @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(206,plain,
! [SV13: $i,SV28: $i] :
( ( ~ ( ~ ( ( SV28
!= ( union @ SV13 ) )
| ! [SY143: $i] :
~ ( ~ ( ~ ( in @ SY143 @ SV28 )
| ~ ! [SY101: $i] :
~ ~ ( ~ ( in @ SY143 @ SY101 )
| ~ ( in @ SY101 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY143 @ SY102 )
| ~ ( in @ SY102 @ SV13 ) )
| ( in @ SY143 @ SV28 ) ) ) )
| ~ ( ~ ! [SY146: $i] :
~ ( ~ ( ~ ( in @ SY146 @ SV28 )
| ~ ! [SY104: $i] :
~ ~ ( ~ ( in @ SY146 @ SY104 )
| ~ ( in @ SY104 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY105: $i] :
~ ~ ( ~ ( in @ SY146 @ SY105 )
| ~ ( in @ SY105 @ SV13 ) )
| ( in @ SY146 @ SV28 ) ) )
| ( SV28
= ( union @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(207,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ( in @ SV14 @ SV29 )
| ~ ( in @ SV29 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(208,plain,
! [SV30: $i,SV15: $i] :
( ( ! [SY149: $i] :
~ ( ~ ( ( SY149
!= ( cartesian_product2 @ SV15 @ SV30 ) )
| ! [SY150: $i] :
~ ( ~ ( ~ ( in @ SY150 @ SY149 )
| ~ ! [SY151: $i] :
~ ~ ! [SY152: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY151 @ SV15 )
| ~ ( in @ SY152 @ SV30 ) )
| ( SY150
!= ( ordered_pair @ SY151 @ SY152 ) ) ) )
| ~ ( ~ ~ ! [SY153: $i] :
~ ~ ! [SY154: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY153 @ SV15 )
| ~ ( in @ SY154 @ SV30 ) )
| ( SY150
!= ( ordered_pair @ SY153 @ SY154 ) ) )
| ( in @ SY150 @ SY149 ) ) ) )
| ~ ( ~ ! [SY155: $i] :
~ ( ~ ( ~ ( in @ SY155 @ SY149 )
| ~ ! [SY156: $i] :
~ ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY156 @ SV15 )
| ~ ( in @ SY157 @ SV30 ) )
| ( SY155
!= ( ordered_pair @ SY156 @ SY157 ) ) ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ~ ! [SY159: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY158 @ SV15 )
| ~ ( in @ SY159 @ SV30 ) )
| ( SY155
!= ( ordered_pair @ SY158 @ SY159 ) ) )
| ( in @ SY155 @ SY149 ) ) )
| ( SY149
= ( cartesian_product2 @ SV15 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(209,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV16 @ SV31 )
| ! [SY160: $i] :
( ~ ( in @ SY160 @ SV16 )
| ( in @ SY160 @ SV31 ) ) )
| ~ ( ~ ! [SY161: $i] :
( ~ ( in @ SY161 @ SV16 )
| ( in @ SY161 @ SV31 ) )
| ( subset @ SV16 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(210,plain,
! [SV17: $i,SV1: $i] :
( ( empty @ ( ordered_pair @ SV1 @ SV17 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(211,plain,
! [SV18: $i,SV2: $i,SV32: $i] :
( ( ~ ( ~ ( ( SV32
!= ( set_union2 @ SV2 @ SV18 ) )
| ! [SY162: $i] :
~ ( ~ ( ~ ( in @ SY162 @ SV32 )
| ( in @ SY162 @ SV2 )
| ( in @ SY162 @ SV18 ) )
| ~ ( ~ ( ( in @ SY162 @ SV2 )
| ( in @ SY162 @ SV18 ) )
| ( in @ SY162 @ SV32 ) ) ) )
| ~ ( ~ ! [SY163: $i] :
~ ( ~ ( ~ ( in @ SY163 @ SV32 )
| ( in @ SY163 @ SV2 )
| ( in @ SY163 @ SV18 ) )
| ~ ( ~ ( ( in @ SY163 @ SV2 )
| ( in @ SY163 @ SV18 ) )
| ( in @ SY163 @ SV32 ) ) )
| ( SV32
= ( set_union2 @ SV2 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(212,plain,
! [SV19: $i,SV3: $i,SV33: $i] :
( ( ~ ( ~ ( ( SV33
!= ( unordered_pair @ SV3 @ SV19 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV33 )
| ( SY164 = SV3 )
| ( SY164 = SV19 ) )
| ~ ( ~ ( ( SY164 = SV3 )
| ( SY164 = SV19 ) )
| ( in @ SY164 @ SV33 ) ) ) )
| ~ ( ~ ! [SY165: $i] :
~ ( ~ ( ~ ( in @ SY165 @ SV33 )
| ( SY165 = SV3 )
| ( SY165 = SV19 ) )
| ~ ( ~ ( ( SY165 = SV3 )
| ( SY165 = SV19 ) )
| ( in @ SY165 @ SV33 ) ) )
| ( SV33
= ( unordered_pair @ SV3 @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(213,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(214,plain,
( ( ~ ( in @ sK1_A @ sK3_SY62 )
| ~ ( in @ sK2_SY59 @ sK4_SY64 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(215,plain,
! [SV34: $i,SV20: $i,SV4: $i] :
( ( ! [SY166: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SY166 ) )
| ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SY166 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SY166 ) )
| ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SY166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(216,plain,
! [SV21: $i,SV5: $i] :
( ( ( ~ ! [SY130: $i] :
~ ( ~ ( ~ ( in @ SY130 @ SV5 )
| ( in @ SY130 @ SV21 ) )
| ~ ( ~ ( in @ SY130 @ SV21 )
| ( in @ SY130 @ SV5 ) ) ) )
= $true )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(217,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV6 @ SV22 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY131 @ SV6 )
| ~ ( in @ SY131 @ SV22 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV6 )
| ~ ( in @ SY132 @ SV22 ) )
| ~ ( disjoint @ SV6 @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(218,plain,
! [SV35: $i,SV23: $i,SV7: $i] :
( ( ! [SY167: $i] :
( ( ( ordered_pair @ SV7 @ SV23 )
!= ( ordered_pair @ SV35 @ SY167 ) )
| ~ ( ( SV7 != SV35 )
| ( SV23 != SY167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(219,plain,
! [SV8: $i,SV24: $i] :
( ( ~ ( ( SV24
!= ( singleton @ SV8 ) )
| ! [SY135: $i] :
~ ( ~ ( ~ ( in @ SY135 @ SV24 )
| ( SY135 = SV8 ) )
| ~ ( ( SY135 != SV8 )
| ( in @ SY135 @ SV24 ) ) ) )
| ~ ( ~ ! [SY136: $i] :
~ ( ~ ( ~ ( in @ SY136 @ SV24 )
| ( SY136 = SV8 ) )
| ~ ( ( SY136 != SV8 )
| ( in @ SY136 @ SV24 ) ) )
| ( SV24
= ( singleton @ SV8 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(220,plain,
! [SV25: $i,SV9: $i] :
( ( ~ ( ~ ( in @ SV9 @ SV25 )
| ~ ( empty @ SV25 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(221,plain,
! [SV10: $i] :
( ( ~ ( ( SV10 != empty_set )
| ! [SY89: $i] :
~ ( in @ SY89 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(222,plain,
! [SV10: $i] :
( ( ~ ( ~ ! [SY90: $i] :
~ ( in @ SY90 @ SV10 )
| ( SV10 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(223,plain,
! [SV26: $i,SV11: $i,SV36: $i] :
( ( ~ ( ~ ( ( SV36
!= ( set_difference @ SV11 @ SV26 ) )
| ! [SY168: $i] :
~ ( ~ ( ~ ( in @ SY168 @ SV36 )
| ~ ( ~ ( in @ SY168 @ SV11 )
| ~ ~ ( in @ SY168 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY168 @ SV11 )
| ~ ~ ( in @ SY168 @ SV26 ) )
| ( in @ SY168 @ SV36 ) ) ) )
| ~ ( ~ ! [SY169: $i] :
~ ( ~ ( ~ ( in @ SY169 @ SV36 )
| ~ ( ~ ( in @ SY169 @ SV11 )
| ~ ~ ( in @ SY169 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY169 @ SV11 )
| ~ ~ ( in @ SY169 @ SV26 ) )
| ( in @ SY169 @ SV36 ) ) )
| ( SV36
= ( set_difference @ SV11 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(224,plain,
! [SV27: $i,SV12: $i,SV37: $i] :
( ( ~ ( ~ ( ( SV37
!= ( set_intersection2 @ SV12 @ SV27 ) )
| ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV37 )
| ~ ( ~ ( in @ SY170 @ SV12 )
| ~ ( in @ SY170 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY170 @ SV12 )
| ~ ( in @ SY170 @ SV27 ) )
| ( in @ SY170 @ SV37 ) ) ) )
| ~ ( ~ ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV37 )
| ~ ( ~ ( in @ SY171 @ SV12 )
| ~ ( in @ SY171 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY171 @ SV12 )
| ~ ( in @ SY171 @ SV27 ) )
| ( in @ SY171 @ SV37 ) ) )
| ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(225,plain,
! [SV13: $i,SV28: $i] :
( ( ~ ( ( SV28
!= ( union @ SV13 ) )
| ! [SY143: $i] :
~ ( ~ ( ~ ( in @ SY143 @ SV28 )
| ~ ! [SY101: $i] :
~ ~ ( ~ ( in @ SY143 @ SY101 )
| ~ ( in @ SY101 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY143 @ SY102 )
| ~ ( in @ SY102 @ SV13 ) )
| ( in @ SY143 @ SV28 ) ) ) )
| ~ ( ~ ! [SY146: $i] :
~ ( ~ ( ~ ( in @ SY146 @ SV28 )
| ~ ! [SY104: $i] :
~ ~ ( ~ ( in @ SY146 @ SY104 )
| ~ ( in @ SY104 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY105: $i] :
~ ~ ( ~ ( in @ SY146 @ SY105 )
| ~ ( in @ SY105 @ SV13 ) )
| ( in @ SY146 @ SV28 ) ) )
| ( SV28
= ( union @ SV13 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(226,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV29 ) )
= $true )
| ( ( ~ ( in @ SV29 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(227,plain,
! [SV30: $i,SV15: $i,SV38: $i] :
( ( ~ ( ~ ( ( SV38
!= ( cartesian_product2 @ SV15 @ SV30 ) )
| ! [SY172: $i] :
~ ( ~ ( ~ ( in @ SY172 @ SV38 )
| ~ ! [SY151: $i] :
~ ~ ! [SY152: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY151 @ SV15 )
| ~ ( in @ SY152 @ SV30 ) )
| ( SY172
!= ( ordered_pair @ SY151 @ SY152 ) ) ) )
| ~ ( ~ ~ ! [SY153: $i] :
~ ~ ! [SY154: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY153 @ SV15 )
| ~ ( in @ SY154 @ SV30 ) )
| ( SY172
!= ( ordered_pair @ SY153 @ SY154 ) ) )
| ( in @ SY172 @ SV38 ) ) ) )
| ~ ( ~ ! [SY177: $i] :
~ ( ~ ( ~ ( in @ SY177 @ SV38 )
| ~ ! [SY156: $i] :
~ ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY156 @ SV15 )
| ~ ( in @ SY157 @ SV30 ) )
| ( SY177
!= ( ordered_pair @ SY156 @ SY157 ) ) ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ~ ! [SY159: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY158 @ SV15 )
| ~ ( in @ SY159 @ SV30 ) )
| ( SY177
!= ( ordered_pair @ SY158 @ SY159 ) ) )
| ( in @ SY177 @ SV38 ) ) )
| ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(228,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( ~ ( subset @ SV16 @ SV31 )
| ! [SY160: $i] :
( ~ ( in @ SY160 @ SV16 )
| ( in @ SY160 @ SV31 ) ) )
| ~ ( ~ ! [SY161: $i] :
( ~ ( in @ SY161 @ SV16 )
| ( in @ SY161 @ SV31 ) )
| ( subset @ SV16 @ SV31 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(229,plain,
! [SV18: $i,SV2: $i,SV32: $i] :
( ( ~ ( ( SV32
!= ( set_union2 @ SV2 @ SV18 ) )
| ! [SY162: $i] :
~ ( ~ ( ~ ( in @ SY162 @ SV32 )
| ( in @ SY162 @ SV2 )
| ( in @ SY162 @ SV18 ) )
| ~ ( ~ ( ( in @ SY162 @ SV2 )
| ( in @ SY162 @ SV18 ) )
| ( in @ SY162 @ SV32 ) ) ) )
| ~ ( ~ ! [SY163: $i] :
~ ( ~ ( ~ ( in @ SY163 @ SV32 )
| ( in @ SY163 @ SV2 )
| ( in @ SY163 @ SV18 ) )
| ~ ( ~ ( ( in @ SY163 @ SV2 )
| ( in @ SY163 @ SV18 ) )
| ( in @ SY163 @ SV32 ) ) )
| ( SV32
= ( set_union2 @ SV2 @ SV18 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(230,plain,
! [SV19: $i,SV3: $i,SV33: $i] :
( ( ~ ( ( SV33
!= ( unordered_pair @ SV3 @ SV19 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV33 )
| ( SY164 = SV3 )
| ( SY164 = SV19 ) )
| ~ ( ~ ( ( SY164 = SV3 )
| ( SY164 = SV19 ) )
| ( in @ SY164 @ SV33 ) ) ) )
| ~ ( ~ ! [SY165: $i] :
~ ( ~ ( ~ ( in @ SY165 @ SV33 )
| ( SY165 = SV3 )
| ( SY165 = SV19 ) )
| ~ ( ~ ( ( SY165 = SV3 )
| ( SY165 = SV19 ) )
| ( in @ SY165 @ SV33 ) ) )
| ( SV33
= ( unordered_pair @ SV3 @ SV19 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(231,plain,
( ( ( ~ ( in @ sK1_A @ sK3_SY62 ) )
= $true )
| ( ( ~ ( in @ sK2_SY59 @ sK4_SY64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(232,plain,
! [SV39: $i,SV34: $i,SV20: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
| ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) )
| ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(233,plain,
! [SV21: $i,SV5: $i] :
( ( ( ! [SY130: $i] :
~ ( ~ ( ~ ( in @ SY130 @ SV5 )
| ( in @ SY130 @ SV21 ) )
| ~ ( ~ ( in @ SY130 @ SV21 )
| ( in @ SY130 @ SV5 ) ) ) )
= $false )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(234,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV6 @ SV22 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY131 @ SV6 )
| ~ ( in @ SY131 @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(235,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV6 )
| ~ ( in @ SY132 @ SV22 ) )
| ~ ( disjoint @ SV6 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(236,plain,
! [SV40: $i,SV35: $i,SV23: $i,SV7: $i] :
( ( ( ( ordered_pair @ SV7 @ SV23 )
!= ( ordered_pair @ SV35 @ SV40 ) )
| ~ ( ( SV7 != SV35 )
| ( SV23 != SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(237,plain,
! [SV8: $i,SV24: $i] :
( ( ~ ( ( SV24
!= ( singleton @ SV8 ) )
| ! [SY135: $i] :
~ ( ~ ( ~ ( in @ SY135 @ SV24 )
| ( SY135 = SV8 ) )
| ~ ( ( SY135 != SV8 )
| ( in @ SY135 @ SV24 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(238,plain,
! [SV8: $i,SV24: $i] :
( ( ~ ( ~ ! [SY136: $i] :
~ ( ~ ( ~ ( in @ SY136 @ SV24 )
| ( SY136 = SV8 ) )
| ~ ( ( SY136 != SV8 )
| ( in @ SY136 @ SV24 ) ) )
| ( SV24
= ( singleton @ SV8 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[219]) ).
thf(239,plain,
! [SV25: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ SV25 )
| ~ ( empty @ SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(240,plain,
! [SV10: $i] :
( ( ( SV10 != empty_set )
| ! [SY89: $i] :
~ ( in @ SY89 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(241,plain,
! [SV10: $i] :
( ( ~ ! [SY90: $i] :
~ ( in @ SY90 @ SV10 )
| ( SV10 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(242,plain,
! [SV26: $i,SV11: $i,SV36: $i] :
( ( ~ ( ( SV36
!= ( set_difference @ SV11 @ SV26 ) )
| ! [SY168: $i] :
~ ( ~ ( ~ ( in @ SY168 @ SV36 )
| ~ ( ~ ( in @ SY168 @ SV11 )
| ~ ~ ( in @ SY168 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY168 @ SV11 )
| ~ ~ ( in @ SY168 @ SV26 ) )
| ( in @ SY168 @ SV36 ) ) ) )
| ~ ( ~ ! [SY169: $i] :
~ ( ~ ( ~ ( in @ SY169 @ SV36 )
| ~ ( ~ ( in @ SY169 @ SV11 )
| ~ ~ ( in @ SY169 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY169 @ SV11 )
| ~ ~ ( in @ SY169 @ SV26 ) )
| ( in @ SY169 @ SV36 ) ) )
| ( SV36
= ( set_difference @ SV11 @ SV26 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(243,plain,
! [SV27: $i,SV12: $i,SV37: $i] :
( ( ~ ( ( SV37
!= ( set_intersection2 @ SV12 @ SV27 ) )
| ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV37 )
| ~ ( ~ ( in @ SY170 @ SV12 )
| ~ ( in @ SY170 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY170 @ SV12 )
| ~ ( in @ SY170 @ SV27 ) )
| ( in @ SY170 @ SV37 ) ) ) )
| ~ ( ~ ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV37 )
| ~ ( ~ ( in @ SY171 @ SV12 )
| ~ ( in @ SY171 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY171 @ SV12 )
| ~ ( in @ SY171 @ SV27 ) )
| ( in @ SY171 @ SV37 ) ) )
| ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(244,plain,
! [SV13: $i,SV28: $i] :
( ( ~ ( ( SV28
!= ( union @ SV13 ) )
| ! [SY143: $i] :
~ ( ~ ( ~ ( in @ SY143 @ SV28 )
| ~ ! [SY101: $i] :
~ ~ ( ~ ( in @ SY143 @ SY101 )
| ~ ( in @ SY101 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY143 @ SY102 )
| ~ ( in @ SY102 @ SV13 ) )
| ( in @ SY143 @ SV28 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(245,plain,
! [SV13: $i,SV28: $i] :
( ( ~ ( ~ ! [SY146: $i] :
~ ( ~ ( ~ ( in @ SY146 @ SV28 )
| ~ ! [SY104: $i] :
~ ~ ( ~ ( in @ SY146 @ SY104 )
| ~ ( in @ SY104 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY105: $i] :
~ ~ ( ~ ( in @ SY146 @ SY105 )
| ~ ( in @ SY105 @ SV13 ) )
| ( in @ SY146 @ SV28 ) ) )
| ( SV28
= ( union @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(246,plain,
! [SV29: $i,SV14: $i] :
( ( ( in @ SV14 @ SV29 )
= $false )
| ( ( ~ ( in @ SV29 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(247,plain,
! [SV30: $i,SV15: $i,SV38: $i] :
( ( ~ ( ( SV38
!= ( cartesian_product2 @ SV15 @ SV30 ) )
| ! [SY172: $i] :
~ ( ~ ( ~ ( in @ SY172 @ SV38 )
| ~ ! [SY151: $i] :
~ ~ ! [SY152: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY151 @ SV15 )
| ~ ( in @ SY152 @ SV30 ) )
| ( SY172
!= ( ordered_pair @ SY151 @ SY152 ) ) ) )
| ~ ( ~ ~ ! [SY153: $i] :
~ ~ ! [SY154: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY153 @ SV15 )
| ~ ( in @ SY154 @ SV30 ) )
| ( SY172
!= ( ordered_pair @ SY153 @ SY154 ) ) )
| ( in @ SY172 @ SV38 ) ) ) )
| ~ ( ~ ! [SY177: $i] :
~ ( ~ ( ~ ( in @ SY177 @ SV38 )
| ~ ! [SY156: $i] :
~ ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY156 @ SV15 )
| ~ ( in @ SY157 @ SV30 ) )
| ( SY177
!= ( ordered_pair @ SY156 @ SY157 ) ) ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ~ ! [SY159: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY158 @ SV15 )
| ~ ( in @ SY159 @ SV30 ) )
| ( SY177
!= ( ordered_pair @ SY158 @ SY159 ) ) )
| ( in @ SY177 @ SV38 ) ) )
| ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(248,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( ~ ( subset @ SV16 @ SV31 )
| ! [SY160: $i] :
( ~ ( in @ SY160 @ SV16 )
| ( in @ SY160 @ SV31 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(249,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( ~ ! [SY161: $i] :
( ~ ( in @ SY161 @ SV16 )
| ( in @ SY161 @ SV31 ) )
| ( subset @ SV16 @ SV31 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(250,plain,
! [SV18: $i,SV2: $i,SV32: $i] :
( ( ~ ( ( SV32
!= ( set_union2 @ SV2 @ SV18 ) )
| ! [SY162: $i] :
~ ( ~ ( ~ ( in @ SY162 @ SV32 )
| ( in @ SY162 @ SV2 )
| ( in @ SY162 @ SV18 ) )
| ~ ( ~ ( ( in @ SY162 @ SV2 )
| ( in @ SY162 @ SV18 ) )
| ( in @ SY162 @ SV32 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(251,plain,
! [SV18: $i,SV2: $i,SV32: $i] :
( ( ~ ( ~ ! [SY163: $i] :
~ ( ~ ( ~ ( in @ SY163 @ SV32 )
| ( in @ SY163 @ SV2 )
| ( in @ SY163 @ SV18 ) )
| ~ ( ~ ( ( in @ SY163 @ SV2 )
| ( in @ SY163 @ SV18 ) )
| ( in @ SY163 @ SV32 ) ) )
| ( SV32
= ( set_union2 @ SV2 @ SV18 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(252,plain,
! [SV19: $i,SV3: $i,SV33: $i] :
( ( ~ ( ( SV33
!= ( unordered_pair @ SV3 @ SV19 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV33 )
| ( SY164 = SV3 )
| ( SY164 = SV19 ) )
| ~ ( ~ ( ( SY164 = SV3 )
| ( SY164 = SV19 ) )
| ( in @ SY164 @ SV33 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(253,plain,
! [SV19: $i,SV3: $i,SV33: $i] :
( ( ~ ( ~ ! [SY165: $i] :
~ ( ~ ( ~ ( in @ SY165 @ SV33 )
| ( SY165 = SV3 )
| ( SY165 = SV19 ) )
| ~ ( ~ ( ( SY165 = SV3 )
| ( SY165 = SV19 ) )
| ( in @ SY165 @ SV33 ) ) )
| ( SV33
= ( unordered_pair @ SV3 @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(254,plain,
( ( ( in @ sK1_A @ sK3_SY62 )
= $false )
| ( ( ~ ( in @ sK2_SY59 @ sK4_SY64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(255,plain,
! [SV39: $i,SV34: $i,SV20: $i,SV4: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
| ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) )
| ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(256,plain,
! [SV5: $i,SV21: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 ) )
| ~ ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 ) ) ) )
= $false )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[233]) ).
thf(257,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV6 @ SV22 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY131 @ SV6 )
| ~ ( in @ SY131 @ SV22 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(258,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV6 )
| ~ ( in @ SY132 @ SV22 ) )
| ~ ( disjoint @ SV6 @ SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(259,plain,
! [SV40: $i,SV35: $i,SV23: $i,SV7: $i] :
( ( ( ( ordered_pair @ SV7 @ SV23 )
!= ( ordered_pair @ SV35 @ SV40 ) )
= $true )
| ( ( ~ ( ( SV7 != SV35 )
| ( SV23 != SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(260,plain,
! [SV8: $i,SV24: $i] :
( ( ( SV24
!= ( singleton @ SV8 ) )
| ! [SY135: $i] :
~ ( ~ ( ~ ( in @ SY135 @ SV24 )
| ( SY135 = SV8 ) )
| ~ ( ( SY135 != SV8 )
| ( in @ SY135 @ SV24 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(261,plain,
! [SV8: $i,SV24: $i] :
( ( ~ ! [SY136: $i] :
~ ( ~ ( ~ ( in @ SY136 @ SV24 )
| ( SY136 = SV8 ) )
| ~ ( ( SY136 != SV8 )
| ( in @ SY136 @ SV24 ) ) )
| ( SV24
= ( singleton @ SV8 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(262,plain,
! [SV25: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV25 ) )
= $true )
| ( ( ~ ( empty @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(263,plain,
! [SV10: $i] :
( ( ( SV10 != empty_set )
= $true )
| ( ( ! [SY89: $i] :
~ ( in @ SY89 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(264,plain,
! [SV10: $i] :
( ( ( ~ ! [SY90: $i] :
~ ( in @ SY90 @ SV10 ) )
= $true )
| ( ( SV10 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(265,plain,
! [SV26: $i,SV11: $i,SV36: $i] :
( ( ~ ( ( SV36
!= ( set_difference @ SV11 @ SV26 ) )
| ! [SY168: $i] :
~ ( ~ ( ~ ( in @ SY168 @ SV36 )
| ~ ( ~ ( in @ SY168 @ SV11 )
| ~ ~ ( in @ SY168 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY168 @ SV11 )
| ~ ~ ( in @ SY168 @ SV26 ) )
| ( in @ SY168 @ SV36 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(266,plain,
! [SV26: $i,SV11: $i,SV36: $i] :
( ( ~ ( ~ ! [SY169: $i] :
~ ( ~ ( ~ ( in @ SY169 @ SV36 )
| ~ ( ~ ( in @ SY169 @ SV11 )
| ~ ~ ( in @ SY169 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY169 @ SV11 )
| ~ ~ ( in @ SY169 @ SV26 ) )
| ( in @ SY169 @ SV36 ) ) )
| ( SV36
= ( set_difference @ SV11 @ SV26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(267,plain,
! [SV27: $i,SV12: $i,SV37: $i] :
( ( ~ ( ( SV37
!= ( set_intersection2 @ SV12 @ SV27 ) )
| ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV37 )
| ~ ( ~ ( in @ SY170 @ SV12 )
| ~ ( in @ SY170 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY170 @ SV12 )
| ~ ( in @ SY170 @ SV27 ) )
| ( in @ SY170 @ SV37 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(268,plain,
! [SV27: $i,SV12: $i,SV37: $i] :
( ( ~ ( ~ ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV37 )
| ~ ( ~ ( in @ SY171 @ SV12 )
| ~ ( in @ SY171 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY171 @ SV12 )
| ~ ( in @ SY171 @ SV27 ) )
| ( in @ SY171 @ SV37 ) ) )
| ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(269,plain,
! [SV13: $i,SV28: $i] :
( ( ( SV28
!= ( union @ SV13 ) )
| ! [SY143: $i] :
~ ( ~ ( ~ ( in @ SY143 @ SV28 )
| ~ ! [SY101: $i] :
~ ~ ( ~ ( in @ SY143 @ SY101 )
| ~ ( in @ SY101 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY143 @ SY102 )
| ~ ( in @ SY102 @ SV13 ) )
| ( in @ SY143 @ SV28 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(270,plain,
! [SV13: $i,SV28: $i] :
( ( ~ ! [SY146: $i] :
~ ( ~ ( ~ ( in @ SY146 @ SV28 )
| ~ ! [SY104: $i] :
~ ~ ( ~ ( in @ SY146 @ SY104 )
| ~ ( in @ SY104 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY105: $i] :
~ ~ ( ~ ( in @ SY146 @ SY105 )
| ~ ( in @ SY105 @ SV13 ) )
| ( in @ SY146 @ SV28 ) ) )
| ( SV28
= ( union @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(271,plain,
! [SV14: $i,SV29: $i] :
( ( ( in @ SV29 @ SV14 )
= $false )
| ( ( in @ SV14 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(272,plain,
! [SV30: $i,SV15: $i,SV38: $i] :
( ( ~ ( ( SV38
!= ( cartesian_product2 @ SV15 @ SV30 ) )
| ! [SY172: $i] :
~ ( ~ ( ~ ( in @ SY172 @ SV38 )
| ~ ! [SY151: $i] :
~ ~ ! [SY152: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY151 @ SV15 )
| ~ ( in @ SY152 @ SV30 ) )
| ( SY172
!= ( ordered_pair @ SY151 @ SY152 ) ) ) )
| ~ ( ~ ~ ! [SY153: $i] :
~ ~ ! [SY154: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY153 @ SV15 )
| ~ ( in @ SY154 @ SV30 ) )
| ( SY172
!= ( ordered_pair @ SY153 @ SY154 ) ) )
| ( in @ SY172 @ SV38 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(273,plain,
! [SV30: $i,SV15: $i,SV38: $i] :
( ( ~ ( ~ ! [SY177: $i] :
~ ( ~ ( ~ ( in @ SY177 @ SV38 )
| ~ ! [SY156: $i] :
~ ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY156 @ SV15 )
| ~ ( in @ SY157 @ SV30 ) )
| ( SY177
!= ( ordered_pair @ SY156 @ SY157 ) ) ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ~ ! [SY159: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY158 @ SV15 )
| ~ ( in @ SY159 @ SV30 ) )
| ( SY177
!= ( ordered_pair @ SY158 @ SY159 ) ) )
| ( in @ SY177 @ SV38 ) ) )
| ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(274,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV31 )
| ! [SY160: $i] :
( ~ ( in @ SY160 @ SV16 )
| ( in @ SY160 @ SV31 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(275,plain,
! [SV31: $i,SV16: $i] :
( ( ~ ! [SY161: $i] :
( ~ ( in @ SY161 @ SV16 )
| ( in @ SY161 @ SV31 ) )
| ( subset @ SV16 @ SV31 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(276,plain,
! [SV18: $i,SV2: $i,SV32: $i] :
( ( ( SV32
!= ( set_union2 @ SV2 @ SV18 ) )
| ! [SY162: $i] :
~ ( ~ ( ~ ( in @ SY162 @ SV32 )
| ( in @ SY162 @ SV2 )
| ( in @ SY162 @ SV18 ) )
| ~ ( ~ ( ( in @ SY162 @ SV2 )
| ( in @ SY162 @ SV18 ) )
| ( in @ SY162 @ SV32 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(277,plain,
! [SV18: $i,SV2: $i,SV32: $i] :
( ( ~ ! [SY163: $i] :
~ ( ~ ( ~ ( in @ SY163 @ SV32 )
| ( in @ SY163 @ SV2 )
| ( in @ SY163 @ SV18 ) )
| ~ ( ~ ( ( in @ SY163 @ SV2 )
| ( in @ SY163 @ SV18 ) )
| ( in @ SY163 @ SV32 ) ) )
| ( SV32
= ( set_union2 @ SV2 @ SV18 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(278,plain,
! [SV19: $i,SV3: $i,SV33: $i] :
( ( ( SV33
!= ( unordered_pair @ SV3 @ SV19 ) )
| ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV33 )
| ( SY164 = SV3 )
| ( SY164 = SV19 ) )
| ~ ( ~ ( ( SY164 = SV3 )
| ( SY164 = SV19 ) )
| ( in @ SY164 @ SV33 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(279,plain,
! [SV19: $i,SV3: $i,SV33: $i] :
( ( ~ ! [SY165: $i] :
~ ( ~ ( ~ ( in @ SY165 @ SV33 )
| ( SY165 = SV3 )
| ( SY165 = SV19 ) )
| ~ ( ~ ( ( SY165 = SV3 )
| ( SY165 = SV19 ) )
| ( in @ SY165 @ SV33 ) ) )
| ( SV33
= ( unordered_pair @ SV3 @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(280,plain,
( ( ( in @ sK2_SY59 @ sK4_SY64 )
= $false )
| ( ( in @ sK1_A @ sK3_SY62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(281,plain,
! [SV39: $i,SV34: $i,SV20: $i,SV4: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
| ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(282,plain,
! [SV39: $i,SV20: $i,SV34: $i,SV4: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) )
| ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(283,plain,
! [SV5: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 ) )
| ~ ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(284,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV6 @ SV22 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY131 @ SV6 )
| ~ ( in @ SY131 @ SV22 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(285,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ( ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV6 )
| ~ ( in @ SY132 @ SV22 ) )
| ~ ( disjoint @ SV6 @ SV22 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(286,plain,
! [SV40: $i,SV35: $i,SV23: $i,SV7: $i] :
( ( ( ( ordered_pair @ SV7 @ SV23 )
= ( ordered_pair @ SV35 @ SV40 ) )
= $false )
| ( ( ~ ( ( SV7 != SV35 )
| ( SV23 != SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(287,plain,
! [SV8: $i,SV24: $i] :
( ( ( SV24
!= ( singleton @ SV8 ) )
= $true )
| ( ( ! [SY135: $i] :
~ ( ~ ( ~ ( in @ SY135 @ SV24 )
| ( SY135 = SV8 ) )
| ~ ( ( SY135 != SV8 )
| ( in @ SY135 @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(288,plain,
! [SV8: $i,SV24: $i] :
( ( ( ~ ! [SY136: $i] :
~ ( ~ ( ~ ( in @ SY136 @ SV24 )
| ( SY136 = SV8 ) )
| ~ ( ( SY136 != SV8 )
| ( in @ SY136 @ SV24 ) ) ) )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(289,plain,
! [SV25: $i,SV9: $i] :
( ( ( in @ SV9 @ SV25 )
= $false )
| ( ( ~ ( empty @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(290,plain,
! [SV10: $i] :
( ( ( SV10 = empty_set )
= $false )
| ( ( ! [SY89: $i] :
~ ( in @ SY89 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(291,plain,
! [SV10: $i] :
( ( ( ! [SY90: $i] :
~ ( in @ SY90 @ SV10 ) )
= $false )
| ( ( SV10 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(292,plain,
! [SV26: $i,SV11: $i,SV36: $i] :
( ( ( SV36
!= ( set_difference @ SV11 @ SV26 ) )
| ! [SY168: $i] :
~ ( ~ ( ~ ( in @ SY168 @ SV36 )
| ~ ( ~ ( in @ SY168 @ SV11 )
| ~ ~ ( in @ SY168 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY168 @ SV11 )
| ~ ~ ( in @ SY168 @ SV26 ) )
| ( in @ SY168 @ SV36 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(293,plain,
! [SV26: $i,SV11: $i,SV36: $i] :
( ( ~ ! [SY169: $i] :
~ ( ~ ( ~ ( in @ SY169 @ SV36 )
| ~ ( ~ ( in @ SY169 @ SV11 )
| ~ ~ ( in @ SY169 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY169 @ SV11 )
| ~ ~ ( in @ SY169 @ SV26 ) )
| ( in @ SY169 @ SV36 ) ) )
| ( SV36
= ( set_difference @ SV11 @ SV26 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(294,plain,
! [SV27: $i,SV12: $i,SV37: $i] :
( ( ( SV37
!= ( set_intersection2 @ SV12 @ SV27 ) )
| ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV37 )
| ~ ( ~ ( in @ SY170 @ SV12 )
| ~ ( in @ SY170 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY170 @ SV12 )
| ~ ( in @ SY170 @ SV27 ) )
| ( in @ SY170 @ SV37 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(295,plain,
! [SV27: $i,SV12: $i,SV37: $i] :
( ( ~ ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV37 )
| ~ ( ~ ( in @ SY171 @ SV12 )
| ~ ( in @ SY171 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY171 @ SV12 )
| ~ ( in @ SY171 @ SV27 ) )
| ( in @ SY171 @ SV37 ) ) )
| ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(296,plain,
! [SV13: $i,SV28: $i] :
( ( ( SV28
!= ( union @ SV13 ) )
= $true )
| ( ( ! [SY143: $i] :
~ ( ~ ( ~ ( in @ SY143 @ SV28 )
| ~ ! [SY101: $i] :
~ ~ ( ~ ( in @ SY143 @ SY101 )
| ~ ( in @ SY101 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY143 @ SY102 )
| ~ ( in @ SY102 @ SV13 ) )
| ( in @ SY143 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(297,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ! [SY146: $i] :
~ ( ~ ( ~ ( in @ SY146 @ SV28 )
| ~ ! [SY104: $i] :
~ ~ ( ~ ( in @ SY146 @ SY104 )
| ~ ( in @ SY104 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY105: $i] :
~ ~ ( ~ ( in @ SY146 @ SY105 )
| ~ ( in @ SY105 @ SV13 ) )
| ( in @ SY146 @ SV28 ) ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(298,plain,
! [SV30: $i,SV15: $i,SV38: $i] :
( ( ( SV38
!= ( cartesian_product2 @ SV15 @ SV30 ) )
| ! [SY172: $i] :
~ ( ~ ( ~ ( in @ SY172 @ SV38 )
| ~ ! [SY151: $i] :
~ ~ ! [SY152: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY151 @ SV15 )
| ~ ( in @ SY152 @ SV30 ) )
| ( SY172
!= ( ordered_pair @ SY151 @ SY152 ) ) ) )
| ~ ( ~ ~ ! [SY153: $i] :
~ ~ ! [SY154: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY153 @ SV15 )
| ~ ( in @ SY154 @ SV30 ) )
| ( SY172
!= ( ordered_pair @ SY153 @ SY154 ) ) )
| ( in @ SY172 @ SV38 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(299,plain,
! [SV30: $i,SV15: $i,SV38: $i] :
( ( ~ ! [SY177: $i] :
~ ( ~ ( ~ ( in @ SY177 @ SV38 )
| ~ ! [SY156: $i] :
~ ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY156 @ SV15 )
| ~ ( in @ SY157 @ SV30 ) )
| ( SY177
!= ( ordered_pair @ SY156 @ SY157 ) ) ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ~ ! [SY159: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY158 @ SV15 )
| ~ ( in @ SY159 @ SV30 ) )
| ( SY177
!= ( ordered_pair @ SY158 @ SY159 ) ) )
| ( in @ SY177 @ SV38 ) ) )
| ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(300,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV31 ) )
= $true )
| ( ( ! [SY160: $i] :
( ~ ( in @ SY160 @ SV16 )
| ( in @ SY160 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(301,plain,
! [SV31: $i,SV16: $i] :
( ( ( ~ ! [SY161: $i] :
( ~ ( in @ SY161 @ SV16 )
| ( in @ SY161 @ SV31 ) ) )
= $true )
| ( ( subset @ SV16 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(302,plain,
! [SV18: $i,SV2: $i,SV32: $i] :
( ( ( SV32
!= ( set_union2 @ SV2 @ SV18 ) )
= $true )
| ( ( ! [SY162: $i] :
~ ( ~ ( ~ ( in @ SY162 @ SV32 )
| ( in @ SY162 @ SV2 )
| ( in @ SY162 @ SV18 ) )
| ~ ( ~ ( ( in @ SY162 @ SV2 )
| ( in @ SY162 @ SV18 ) )
| ( in @ SY162 @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(303,plain,
! [SV18: $i,SV2: $i,SV32: $i] :
( ( ( ~ ! [SY163: $i] :
~ ( ~ ( ~ ( in @ SY163 @ SV32 )
| ( in @ SY163 @ SV2 )
| ( in @ SY163 @ SV18 ) )
| ~ ( ~ ( ( in @ SY163 @ SV2 )
| ( in @ SY163 @ SV18 ) )
| ( in @ SY163 @ SV32 ) ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(304,plain,
! [SV19: $i,SV3: $i,SV33: $i] :
( ( ( SV33
!= ( unordered_pair @ SV3 @ SV19 ) )
= $true )
| ( ( ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV33 )
| ( SY164 = SV3 )
| ( SY164 = SV19 ) )
| ~ ( ~ ( ( SY164 = SV3 )
| ( SY164 = SV19 ) )
| ( in @ SY164 @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(305,plain,
! [SV19: $i,SV3: $i,SV33: $i] :
( ( ( ~ ! [SY165: $i] :
~ ( ~ ( ~ ( in @ SY165 @ SV33 )
| ( SY165 = SV3 )
| ( SY165 = SV19 ) )
| ~ ( ~ ( ( SY165 = SV3 )
| ( SY165 = SV19 ) )
| ( in @ SY165 @ SV33 ) ) ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(306,plain,
! [SV39: $i,SV34: $i,SV20: $i,SV4: $i] :
( ( ~ ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
| ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(307,plain,
! [SV39: $i,SV20: $i,SV34: $i,SV4: $i] :
( ( ~ ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) )
| ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(308,plain,
! [SV5: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(309,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ~ ( disjoint @ SV6 @ SV22 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY131 @ SV6 )
| ~ ( in @ SY131 @ SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(310,plain,
! [SV22: $i,SV6: $i] :
( ( ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV6 )
| ~ ( in @ SY132 @ SV22 ) )
| ~ ( disjoint @ SV6 @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(311,plain,
! [SV40: $i,SV23: $i,SV35: $i,SV7: $i] :
( ( ( ( SV7 != SV35 )
| ( SV23 != SV40 ) )
= $false )
| ( ( ( ordered_pair @ SV7 @ SV23 )
= ( ordered_pair @ SV35 @ SV40 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(312,plain,
! [SV8: $i,SV24: $i] :
( ( ( SV24
= ( singleton @ SV8 ) )
= $false )
| ( ( ! [SY135: $i] :
~ ( ~ ( ~ ( in @ SY135 @ SV24 )
| ( SY135 = SV8 ) )
| ~ ( ( SY135 != SV8 )
| ( in @ SY135 @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(313,plain,
! [SV8: $i,SV24: $i] :
( ( ( ! [SY136: $i] :
~ ( ~ ( ~ ( in @ SY136 @ SV24 )
| ( SY136 = SV8 ) )
| ~ ( ( SY136 != SV8 )
| ( in @ SY136 @ SV24 ) ) ) )
= $false )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(314,plain,
! [SV9: $i,SV25: $i] :
( ( ( empty @ SV25 )
= $false )
| ( ( in @ SV9 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(315,plain,
! [SV10: $i,SV41: $i] :
( ( ( ~ ( in @ SV41 @ SV10 ) )
= $true )
| ( ( SV10 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(316,plain,
! [SV10: $i] :
( ( ( ~ ( in @ ( sK6_SY90 @ SV10 ) @ SV10 ) )
= $false )
| ( ( SV10 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[291]) ).
thf(317,plain,
! [SV26: $i,SV11: $i,SV36: $i] :
( ( ( SV36
!= ( set_difference @ SV11 @ SV26 ) )
= $true )
| ( ( ! [SY168: $i] :
~ ( ~ ( ~ ( in @ SY168 @ SV36 )
| ~ ( ~ ( in @ SY168 @ SV11 )
| ~ ~ ( in @ SY168 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY168 @ SV11 )
| ~ ~ ( in @ SY168 @ SV26 ) )
| ( in @ SY168 @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(318,plain,
! [SV26: $i,SV11: $i,SV36: $i] :
( ( ( ~ ! [SY169: $i] :
~ ( ~ ( ~ ( in @ SY169 @ SV36 )
| ~ ( ~ ( in @ SY169 @ SV11 )
| ~ ~ ( in @ SY169 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY169 @ SV11 )
| ~ ~ ( in @ SY169 @ SV26 ) )
| ( in @ SY169 @ SV36 ) ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(319,plain,
! [SV27: $i,SV12: $i,SV37: $i] :
( ( ( SV37
!= ( set_intersection2 @ SV12 @ SV27 ) )
= $true )
| ( ( ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV37 )
| ~ ( ~ ( in @ SY170 @ SV12 )
| ~ ( in @ SY170 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY170 @ SV12 )
| ~ ( in @ SY170 @ SV27 ) )
| ( in @ SY170 @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(320,plain,
! [SV27: $i,SV12: $i,SV37: $i] :
( ( ( ~ ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV37 )
| ~ ( ~ ( in @ SY171 @ SV12 )
| ~ ( in @ SY171 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY171 @ SV12 )
| ~ ( in @ SY171 @ SV27 ) )
| ( in @ SY171 @ SV37 ) ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(321,plain,
! [SV13: $i,SV28: $i] :
( ( ( SV28
= ( union @ SV13 ) )
= $false )
| ( ( ! [SY143: $i] :
~ ( ~ ( ~ ( in @ SY143 @ SV28 )
| ~ ! [SY101: $i] :
~ ~ ( ~ ( in @ SY143 @ SY101 )
| ~ ( in @ SY101 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY102: $i] :
~ ~ ( ~ ( in @ SY143 @ SY102 )
| ~ ( in @ SY102 @ SV13 ) )
| ( in @ SY143 @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(322,plain,
! [SV13: $i,SV28: $i] :
( ( ( ! [SY146: $i] :
~ ( ~ ( ~ ( in @ SY146 @ SV28 )
| ~ ! [SY104: $i] :
~ ~ ( ~ ( in @ SY146 @ SY104 )
| ~ ( in @ SY104 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY105: $i] :
~ ~ ( ~ ( in @ SY146 @ SY105 )
| ~ ( in @ SY105 @ SV13 ) )
| ( in @ SY146 @ SV28 ) ) ) )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(323,plain,
! [SV30: $i,SV15: $i,SV38: $i] :
( ( ( SV38
!= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true )
| ( ( ! [SY172: $i] :
~ ( ~ ( ~ ( in @ SY172 @ SV38 )
| ~ ! [SY151: $i] :
~ ~ ! [SY152: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY151 @ SV15 )
| ~ ( in @ SY152 @ SV30 ) )
| ( SY172
!= ( ordered_pair @ SY151 @ SY152 ) ) ) )
| ~ ( ~ ~ ! [SY153: $i] :
~ ~ ! [SY154: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY153 @ SV15 )
| ~ ( in @ SY154 @ SV30 ) )
| ( SY172
!= ( ordered_pair @ SY153 @ SY154 ) ) )
| ( in @ SY172 @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(324,plain,
! [SV30: $i,SV15: $i,SV38: $i] :
( ( ( ~ ! [SY177: $i] :
~ ( ~ ( ~ ( in @ SY177 @ SV38 )
| ~ ! [SY156: $i] :
~ ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY156 @ SV15 )
| ~ ( in @ SY157 @ SV30 ) )
| ( SY177
!= ( ordered_pair @ SY156 @ SY157 ) ) ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ~ ! [SY159: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY158 @ SV15 )
| ~ ( in @ SY159 @ SV30 ) )
| ( SY177
!= ( ordered_pair @ SY158 @ SY159 ) ) )
| ( in @ SY177 @ SV38 ) ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(325,plain,
! [SV31: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV31 )
= $false )
| ( ( ! [SY160: $i] :
( ~ ( in @ SY160 @ SV16 )
| ( in @ SY160 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(326,plain,
! [SV31: $i,SV16: $i] :
( ( ( ! [SY161: $i] :
( ~ ( in @ SY161 @ SV16 )
| ( in @ SY161 @ SV31 ) ) )
= $false )
| ( ( subset @ SV16 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(327,plain,
! [SV18: $i,SV2: $i,SV32: $i] :
( ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false )
| ( ( ! [SY162: $i] :
~ ( ~ ( ~ ( in @ SY162 @ SV32 )
| ( in @ SY162 @ SV2 )
| ( in @ SY162 @ SV18 ) )
| ~ ( ~ ( ( in @ SY162 @ SV2 )
| ( in @ SY162 @ SV18 ) )
| ( in @ SY162 @ SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(328,plain,
! [SV18: $i,SV2: $i,SV32: $i] :
( ( ( ! [SY163: $i] :
~ ( ~ ( ~ ( in @ SY163 @ SV32 )
| ( in @ SY163 @ SV2 )
| ( in @ SY163 @ SV18 ) )
| ~ ( ~ ( ( in @ SY163 @ SV2 )
| ( in @ SY163 @ SV18 ) )
| ( in @ SY163 @ SV32 ) ) ) )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(329,plain,
! [SV19: $i,SV3: $i,SV33: $i] :
( ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false )
| ( ( ! [SY164: $i] :
~ ( ~ ( ~ ( in @ SY164 @ SV33 )
| ( SY164 = SV3 )
| ( SY164 = SV19 ) )
| ~ ( ~ ( ( SY164 = SV3 )
| ( SY164 = SV19 ) )
| ( in @ SY164 @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(330,plain,
! [SV19: $i,SV3: $i,SV33: $i] :
( ( ( ! [SY165: $i] :
~ ( ~ ( ~ ( in @ SY165 @ SV33 )
| ( SY165 = SV3 )
| ( SY165 = SV19 ) )
| ~ ( ~ ( ( SY165 = SV3 )
| ( SY165 = SV19 ) )
| ( in @ SY165 @ SV33 ) ) ) )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(331,plain,
! [SV39: $i,SV34: $i,SV20: $i,SV4: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(332,plain,
! [SV39: $i,SV20: $i,SV34: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(333,plain,
! [SV5: $i,SV21: $i] :
( ( ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(334,plain,
! [SV22: $i,SV6: $i] :
( ( ( ~ ~ ( disjoint @ SV6 @ SV22 ) )
= $true )
| ( ( ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY131 @ SV6 )
| ~ ( in @ SY131 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(335,plain,
! [SV22: $i,SV6: $i] :
( ( ( ~ ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV6 )
| ~ ( in @ SY132 @ SV22 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(336,plain,
! [SV40: $i,SV23: $i,SV35: $i,SV7: $i] :
( ( ( SV7 != SV35 )
= $false )
| ( ( ( ordered_pair @ SV7 @ SV23 )
= ( ordered_pair @ SV35 @ SV40 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(337,plain,
! [SV35: $i,SV7: $i,SV40: $i,SV23: $i] :
( ( ( SV23 != SV40 )
= $false )
| ( ( ( ordered_pair @ SV7 @ SV23 )
= ( ordered_pair @ SV35 @ SV40 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(338,plain,
! [SV8: $i,SV24: $i,SV42: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV42 @ SV24 )
| ( SV42 = SV8 ) )
| ~ ( ( SV42 != SV8 )
| ( in @ SV42 @ SV24 ) ) ) )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(339,plain,
! [SV24: $i,SV8: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 )
| ( ( sK7_SY136 @ SV8 @ SV24 )
= SV8 ) )
| ~ ( ( ( sK7_SY136 @ SV8 @ SV24 )
!= SV8 )
| ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 ) ) ) )
= $false )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[313]) ).
thf(340,plain,
! [SV10: $i,SV41: $i] :
( ( ( in @ SV41 @ SV10 )
= $false )
| ( ( SV10 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(341,plain,
! [SV10: $i] :
( ( ( in @ ( sK6_SY90 @ SV10 ) @ SV10 )
= $true )
| ( ( SV10 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(342,plain,
! [SV26: $i,SV11: $i,SV36: $i] :
( ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false )
| ( ( ! [SY168: $i] :
~ ( ~ ( ~ ( in @ SY168 @ SV36 )
| ~ ( ~ ( in @ SY168 @ SV11 )
| ~ ~ ( in @ SY168 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY168 @ SV11 )
| ~ ~ ( in @ SY168 @ SV26 ) )
| ( in @ SY168 @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(343,plain,
! [SV26: $i,SV11: $i,SV36: $i] :
( ( ( ! [SY169: $i] :
~ ( ~ ( ~ ( in @ SY169 @ SV36 )
| ~ ( ~ ( in @ SY169 @ SV11 )
| ~ ~ ( in @ SY169 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY169 @ SV11 )
| ~ ~ ( in @ SY169 @ SV26 ) )
| ( in @ SY169 @ SV36 ) ) ) )
= $false )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(344,plain,
! [SV27: $i,SV12: $i,SV37: $i] :
( ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false )
| ( ( ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV37 )
| ~ ( ~ ( in @ SY170 @ SV12 )
| ~ ( in @ SY170 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY170 @ SV12 )
| ~ ( in @ SY170 @ SV27 ) )
| ( in @ SY170 @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(345,plain,
! [SV27: $i,SV12: $i,SV37: $i] :
( ( ( ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV37 )
| ~ ( ~ ( in @ SY171 @ SV12 )
| ~ ( in @ SY171 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY171 @ SV12 )
| ~ ( in @ SY171 @ SV27 ) )
| ( in @ SY171 @ SV37 ) ) ) )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(346,plain,
! [SV13: $i,SV28: $i,SV43: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV43 @ SV28 )
| ~ ! [SY182: $i] :
~ ~ ( ~ ( in @ SV43 @ SY182 )
| ~ ( in @ SY182 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY183: $i] :
~ ~ ( ~ ( in @ SV43 @ SY183 )
| ~ ( in @ SY183 @ SV13 ) )
| ( in @ SV43 @ SV28 ) ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(347,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
| ~ ! [SY184: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY184 )
| ~ ( in @ SY184 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) ) )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[322]) ).
thf(348,plain,
! [SV30: $i,SV15: $i,SV38: $i] :
( ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false )
| ( ( ! [SY172: $i] :
~ ( ~ ( ~ ( in @ SY172 @ SV38 )
| ~ ! [SY151: $i] :
~ ~ ! [SY152: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY151 @ SV15 )
| ~ ( in @ SY152 @ SV30 ) )
| ( SY172
!= ( ordered_pair @ SY151 @ SY152 ) ) ) )
| ~ ( ~ ~ ! [SY153: $i] :
~ ~ ! [SY154: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY153 @ SV15 )
| ~ ( in @ SY154 @ SV30 ) )
| ( SY172
!= ( ordered_pair @ SY153 @ SY154 ) ) )
| ( in @ SY172 @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(349,plain,
! [SV30: $i,SV15: $i,SV38: $i] :
( ( ( ! [SY177: $i] :
~ ( ~ ( ~ ( in @ SY177 @ SV38 )
| ~ ! [SY156: $i] :
~ ~ ! [SY157: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY156 @ SV15 )
| ~ ( in @ SY157 @ SV30 ) )
| ( SY177
!= ( ordered_pair @ SY156 @ SY157 ) ) ) )
| ~ ( ~ ~ ! [SY158: $i] :
~ ~ ! [SY159: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY158 @ SV15 )
| ~ ( in @ SY159 @ SV30 ) )
| ( SY177
!= ( ordered_pair @ SY158 @ SY159 ) ) )
| ( in @ SY177 @ SV38 ) ) ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(350,plain,
! [SV31: $i,SV16: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ SV16 )
| ( in @ SV44 @ SV31 ) )
= $true )
| ( ( subset @ SV16 @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(351,plain,
! [SV16: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK9_SY161 @ SV31 @ SV16 ) @ SV16 )
| ( in @ ( sK9_SY161 @ SV31 @ SV16 ) @ SV31 ) )
= $false )
| ( ( subset @ SV16 @ SV31 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[326]) ).
thf(352,plain,
! [SV18: $i,SV2: $i,SV32: $i,SV45: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV45 @ SV32 )
| ( in @ SV45 @ SV2 )
| ( in @ SV45 @ SV18 ) )
| ~ ( ~ ( ( in @ SV45 @ SV2 )
| ( in @ SV45 @ SV18 ) )
| ( in @ SV45 @ SV32 ) ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(353,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ~ ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) ) ) )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[328]) ).
thf(354,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV46 @ SV33 )
| ( SV46 = SV3 )
| ( SV46 = SV19 ) )
| ~ ( ~ ( ( SV46 = SV3 )
| ( SV46 = SV19 ) )
| ( in @ SV46 @ SV33 ) ) ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(355,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ~ ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) ) ) )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[330]) ).
thf(356,plain,
! [SV39: $i,SV34: $i,SV20: $i,SV4: $i] :
( ( ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(357,plain,
! [SV39: $i,SV20: $i,SV34: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(358,plain,
! [SV5: $i,SV21: $i] :
( ( ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(359,plain,
! [SV5: $i,SV21: $i] :
( ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(360,plain,
! [SV22: $i,SV6: $i] :
( ( ( ~ ( disjoint @ SV6 @ SV22 ) )
= $false )
| ( ( ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY131 @ SV6 )
| ~ ( in @ SY131 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(361,plain,
! [SV22: $i,SV6: $i] :
( ( ( ~ ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV6 )
| ~ ( in @ SY132 @ SV22 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(362,plain,
! [SV40: $i,SV23: $i,SV35: $i,SV7: $i] :
( ( ( SV7 = SV35 )
= $true )
| ( ( ( ordered_pair @ SV7 @ SV23 )
= ( ordered_pair @ SV35 @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(363,plain,
! [SV35: $i,SV7: $i,SV40: $i,SV23: $i] :
( ( ( SV23 = SV40 )
= $true )
| ( ( ( ordered_pair @ SV7 @ SV23 )
= ( ordered_pair @ SV35 @ SV40 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(364,plain,
! [SV8: $i,SV24: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ SV42 @ SV24 )
| ( SV42 = SV8 ) )
| ~ ( ( SV42 != SV8 )
| ( in @ SV42 @ SV24 ) ) )
= $false )
| ( ( SV24
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(365,plain,
! [SV24: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 )
| ( ( sK7_SY136 @ SV8 @ SV24 )
= SV8 ) )
| ~ ( ( ( sK7_SY136 @ SV8 @ SV24 )
!= SV8 )
| ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(366,plain,
! [SV26: $i,SV11: $i,SV36: $i,SV47: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV47 @ SV36 )
| ~ ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) )
| ( in @ SV47 @ SV36 ) ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(367,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
| ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) ) ) )
= $false )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[343]) ).
thf(368,plain,
! [SV27: $i,SV12: $i,SV37: $i,SV48: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV48 @ SV37 )
| ~ ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) )
| ( in @ SV48 @ SV37 ) ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(369,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
| ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) ) ) )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[345]) ).
thf(370,plain,
! [SV13: $i,SV28: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ SV43 @ SV28 )
| ~ ! [SY182: $i] :
~ ~ ( ~ ( in @ SV43 @ SY182 )
| ~ ( in @ SY182 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY183: $i] :
~ ~ ( ~ ( in @ SV43 @ SY183 )
| ~ ( in @ SY183 @ SV13 ) )
| ( in @ SV43 @ SV28 ) ) )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(371,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
| ~ ! [SY184: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY184 )
| ~ ( in @ SY184 @ SV13 ) ) )
| ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(372,plain,
! [SV30: $i,SV15: $i,SV38: $i,SV49: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV49 @ SV38 )
| ~ ! [SY186: $i] :
~ ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY186 @ SV15 )
| ~ ( in @ SY187 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY186 @ SY187 ) ) ) )
| ~ ( ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY188 @ SV15 )
| ~ ( in @ SY189 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY188 @ SY189 ) ) )
| ( in @ SV49 @ SV38 ) ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(373,plain,
! [SV38: $i,SV15: $i,SV30: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
| ~ ! [SY190: $i] :
~ ~ ! [SY191: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ SV15 )
| ~ ( in @ SY191 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY190 @ SY191 ) ) ) )
| ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[349]) ).
thf(374,plain,
! [SV31: $i,SV16: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ SV16 ) )
= $true )
| ( ( in @ SV44 @ SV31 )
= $true )
| ( ( subset @ SV16 @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(375,plain,
! [SV16: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK9_SY161 @ SV31 @ SV16 ) @ SV16 ) )
= $false )
| ( ( subset @ SV16 @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(376,plain,
! [SV16: $i,SV31: $i] :
( ( ( in @ ( sK9_SY161 @ SV31 @ SV16 ) @ SV31 )
= $false )
| ( ( subset @ SV16 @ SV31 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[351]) ).
thf(377,plain,
! [SV18: $i,SV2: $i,SV32: $i,SV45: $i] :
( ( ( ~ ( ~ ( in @ SV45 @ SV32 )
| ( in @ SV45 @ SV2 )
| ( in @ SV45 @ SV18 ) )
| ~ ( ~ ( ( in @ SV45 @ SV2 )
| ( in @ SV45 @ SV18 ) )
| ( in @ SV45 @ SV32 ) ) )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(378,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ~ ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(379,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( ~ ( in @ SV46 @ SV33 )
| ( SV46 = SV3 )
| ( SV46 = SV19 ) )
| ~ ( ~ ( ( SV46 = SV3 )
| ( SV46 = SV19 ) )
| ( in @ SV46 @ SV33 ) ) )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(380,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ~ ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(381,plain,
! [SV39: $i,SV20: $i,SV34: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(382,plain,
! [SV39: $i,SV20: $i,SV34: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV34 )
| ~ ( in @ SV20 @ SV39 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(383,plain,
! [SV5: $i,SV21: $i] :
( ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(384,plain,
! [SV5: $i,SV21: $i] :
( ( ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
= $false )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(385,plain,
! [SV22: $i,SV6: $i] :
( ( ( disjoint @ SV6 @ SV22 )
= $true )
| ( ( ~ ! [SY131: $i] :
~ ~ ( ~ ( in @ SY131 @ SV6 )
| ~ ( in @ SY131 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(386,plain,
! [SV22: $i,SV6: $i] :
( ( ( ! [SY132: $i] :
~ ~ ( ~ ( in @ SY132 @ SV6 )
| ~ ( in @ SY132 @ SV22 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(387,plain,
! [SV8: $i,SV24: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ SV42 @ SV24 )
| ( SV42 = SV8 ) ) )
= $false )
| ( ( SV24
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(388,plain,
! [SV24: $i,SV8: $i,SV42: $i] :
( ( ( ~ ( ( SV42 != SV8 )
| ( in @ SV42 @ SV24 ) ) )
= $false )
| ( ( SV24
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(389,plain,
! [SV24: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 )
| ( ( sK7_SY136 @ SV8 @ SV24 )
= SV8 ) ) )
= $true )
| ( ( ~ ( ( ( sK7_SY136 @ SV8 @ SV24 )
!= SV8 )
| ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(390,plain,
! [SV26: $i,SV11: $i,SV36: $i,SV47: $i] :
( ( ( ~ ( ~ ( in @ SV47 @ SV36 )
| ~ ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) )
| ( in @ SV47 @ SV36 ) ) )
= $false )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(391,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
| ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(392,plain,
! [SV27: $i,SV12: $i,SV37: $i,SV48: $i] :
( ( ( ~ ( ~ ( in @ SV48 @ SV37 )
| ~ ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) )
| ( in @ SV48 @ SV37 ) ) )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(393,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
| ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(394,plain,
! [SV13: $i,SV28: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ SV43 @ SV28 )
| ~ ! [SY182: $i] :
~ ~ ( ~ ( in @ SV43 @ SY182 )
| ~ ( in @ SY182 @ SV13 ) ) ) )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(395,plain,
! [SV28: $i,SV13: $i,SV43: $i] :
( ( ( ~ ( ~ ~ ! [SY183: $i] :
~ ~ ( ~ ( in @ SV43 @ SY183 )
| ~ ( in @ SY183 @ SV13 ) )
| ( in @ SV43 @ SV28 ) ) )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(396,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
| ~ ! [SY184: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY184 )
| ~ ( in @ SY184 @ SV13 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(397,plain,
! [SV30: $i,SV15: $i,SV38: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ SV49 @ SV38 )
| ~ ! [SY186: $i] :
~ ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY186 @ SV15 )
| ~ ( in @ SY187 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY186 @ SY187 ) ) ) )
| ~ ( ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY188 @ SV15 )
| ~ ( in @ SY189 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY188 @ SY189 ) ) )
| ( in @ SV49 @ SV38 ) ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(398,plain,
! [SV38: $i,SV15: $i,SV30: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
| ~ ! [SY190: $i] :
~ ~ ! [SY191: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ SV15 )
| ~ ( in @ SY191 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY190 @ SY191 ) ) ) )
| ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(399,plain,
! [SV31: $i,SV16: $i,SV44: $i] :
( ( ( in @ SV44 @ SV16 )
= $false )
| ( ( in @ SV44 @ SV31 )
= $true )
| ( ( subset @ SV16 @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(400,plain,
! [SV16: $i,SV31: $i] :
( ( ( in @ ( sK9_SY161 @ SV31 @ SV16 ) @ SV16 )
= $true )
| ( ( subset @ SV16 @ SV31 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(401,plain,
! [SV18: $i,SV2: $i,SV32: $i,SV45: $i] :
( ( ( ~ ( ~ ( in @ SV45 @ SV32 )
| ( in @ SV45 @ SV2 )
| ( in @ SV45 @ SV18 ) ) )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[377]) ).
thf(402,plain,
! [SV32: $i,SV18: $i,SV2: $i,SV45: $i] :
( ( ( ~ ( ~ ( ( in @ SV45 @ SV2 )
| ( in @ SV45 @ SV18 ) )
| ( in @ SV45 @ SV32 ) ) )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[377]) ).
thf(403,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(404,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( ~ ( in @ SV46 @ SV33 )
| ( SV46 = SV3 )
| ( SV46 = SV19 ) ) )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(405,plain,
! [SV33: $i,SV19: $i,SV3: $i,SV46: $i] :
( ( ( ~ ( ~ ( ( SV46 = SV3 )
| ( SV46 = SV19 ) )
| ( in @ SV46 @ SV33 ) ) )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(406,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(407,plain,
! [SV39: $i,SV20: $i,SV34: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV34 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(408,plain,
! [SV34: $i,SV4: $i,SV39: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV39 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(409,plain,
! [SV39: $i,SV20: $i,SV34: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV34 ) )
= $true )
| ( ( ~ ( in @ SV20 @ SV39 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(410,plain,
! [SV5: $i,SV21: $i] :
( ( ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
| ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(411,plain,
! [SV5: $i,SV21: $i] :
( ( ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 ) )
= $false )
| ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
= $false )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(412,plain,
! [SV5: $i,SV21: $i] :
( ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 )
= $false )
| ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
= $false )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(413,plain,
! [SV22: $i,SV6: $i] :
( ( ( ! [SY131: $i] :
~ ~ ( ~ ( in @ SY131 @ SV6 )
| ~ ( in @ SY131 @ SV22 ) ) )
= $false )
| ( ( disjoint @ SV6 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(414,plain,
! [SV22: $i,SV6: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( in @ SV50 @ SV6 )
| ~ ( in @ SV50 @ SV22 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(415,plain,
! [SV8: $i,SV24: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ SV24 )
| ( SV42 = SV8 ) )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(416,plain,
! [SV24: $i,SV8: $i,SV42: $i] :
( ( ( ( SV42 != SV8 )
| ( in @ SV42 @ SV24 ) )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(417,plain,
! [SV24: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 )
| ( ( sK7_SY136 @ SV8 @ SV24 )
= SV8 ) )
= $false )
| ( ( ~ ( ( ( sK7_SY136 @ SV8 @ SV24 )
!= SV8 )
| ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(418,plain,
! [SV26: $i,SV11: $i,SV36: $i,SV47: $i] :
( ( ( ~ ( ~ ( in @ SV47 @ SV36 )
| ~ ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) ) ) )
= $false )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(419,plain,
! [SV36: $i,SV26: $i,SV11: $i,SV47: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) )
| ( in @ SV47 @ SV36 ) ) )
= $false )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(420,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
| ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(421,plain,
! [SV27: $i,SV12: $i,SV37: $i,SV48: $i] :
( ( ( ~ ( ~ ( in @ SV48 @ SV37 )
| ~ ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) ) ) )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[392]) ).
thf(422,plain,
! [SV37: $i,SV27: $i,SV12: $i,SV48: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) )
| ( in @ SV48 @ SV37 ) ) )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[392]) ).
thf(423,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
| ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(424,plain,
! [SV13: $i,SV28: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ SV28 )
| ~ ! [SY182: $i] :
~ ~ ( ~ ( in @ SV43 @ SY182 )
| ~ ( in @ SY182 @ SV13 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(425,plain,
! [SV28: $i,SV13: $i,SV43: $i] :
( ( ( ~ ~ ! [SY183: $i] :
~ ~ ( ~ ( in @ SV43 @ SY183 )
| ~ ( in @ SY183 @ SV13 ) )
| ( in @ SV43 @ SV28 ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(426,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
| ~ ! [SY184: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY184 )
| ~ ( in @ SY184 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(427,plain,
! [SV30: $i,SV15: $i,SV38: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ SV49 @ SV38 )
| ~ ! [SY186: $i] :
~ ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY186 @ SV15 )
| ~ ( in @ SY187 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY186 @ SY187 ) ) ) ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(428,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV15: $i] :
( ( ( ~ ( ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY188 @ SV15 )
| ~ ( in @ SY189 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY188 @ SY189 ) ) )
| ( in @ SV49 @ SV38 ) ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(429,plain,
! [SV38: $i,SV15: $i,SV30: $i] :
( ( ( ~ ( ~ ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
| ~ ! [SY190: $i] :
~ ~ ! [SY191: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ SV15 )
| ~ ( in @ SY191 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY190 @ SY191 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(430,plain,
! [SV18: $i,SV2: $i,SV32: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV32 )
| ( in @ SV45 @ SV2 )
| ( in @ SV45 @ SV18 ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(431,plain,
! [SV32: $i,SV18: $i,SV2: $i,SV45: $i] :
( ( ( ~ ( ( in @ SV45 @ SV2 )
| ( in @ SV45 @ SV18 ) )
| ( in @ SV45 @ SV32 ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(432,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(433,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ SV33 )
| ( SV46 = SV3 )
| ( SV46 = SV19 ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(434,plain,
! [SV33: $i,SV19: $i,SV3: $i,SV46: $i] :
( ( ( ~ ( ( SV46 = SV3 )
| ( SV46 = SV19 ) )
| ( in @ SV46 @ SV33 ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(435,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(436,plain,
! [SV39: $i,SV20: $i,SV34: $i,SV4: $i] :
( ( ( in @ SV4 @ SV34 )
= $true )
| ( ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(437,plain,
! [SV34: $i,SV4: $i,SV39: $i,SV20: $i] :
( ( ( in @ SV20 @ SV39 )
= $true )
| ( ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(438,plain,
! [SV39: $i,SV20: $i,SV34: $i,SV4: $i] :
( ( ( in @ SV4 @ SV34 )
= $false )
| ( ( ~ ( in @ SV20 @ SV39 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(439,plain,
! [SV5: $i,SV21: $i] :
( ( ( ~ ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 ) )
= $false )
| ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(440,plain,
! [SV5: $i,SV21: $i] :
( ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 )
= $false )
| ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(441,plain,
! [SV5: $i,SV21: $i] :
( ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
= $true )
| ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
= $false )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(442,plain,
! [SV6: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK15_SY131 @ SV22 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK15_SY131 @ SV22 @ SV6 ) @ SV22 ) ) )
= $false )
| ( ( disjoint @ SV6 @ SV22 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[413]) ).
thf(443,plain,
! [SV22: $i,SV6: $i,SV50: $i] :
( ( ( ~ ( ~ ( in @ SV50 @ SV6 )
| ~ ( in @ SV50 @ SV22 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(444,plain,
! [SV8: $i,SV24: $i,SV42: $i] :
( ( ( ~ ( in @ SV42 @ SV24 ) )
= $true )
| ( ( SV42 = SV8 )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(445,plain,
! [SV24: $i,SV8: $i,SV42: $i] :
( ( ( SV42 != SV8 )
= $true )
| ( ( in @ SV42 @ SV24 )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(446,plain,
! [SV24: $i,SV8: $i] :
( ( ( ~ ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 ) )
= $false )
| ( ( ~ ( ( ( sK7_SY136 @ SV8 @ SV24 )
!= SV8 )
| ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(447,plain,
! [SV24: $i,SV8: $i] :
( ( ( ( sK7_SY136 @ SV8 @ SV24 )
= SV8 )
= $false )
| ( ( ~ ( ( ( sK7_SY136 @ SV8 @ SV24 )
!= SV8 )
| ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(448,plain,
! [SV26: $i,SV11: $i,SV36: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV36 )
| ~ ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(449,plain,
! [SV36: $i,SV26: $i,SV11: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) )
| ( in @ SV47 @ SV36 ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(450,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
| ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(451,plain,
! [SV27: $i,SV12: $i,SV37: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV37 )
| ~ ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(452,plain,
! [SV37: $i,SV27: $i,SV12: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) )
| ( in @ SV48 @ SV37 ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(453,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
| ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(454,plain,
! [SV13: $i,SV28: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ SV28 ) )
= $true )
| ( ( ~ ! [SY182: $i] :
~ ~ ( ~ ( in @ SV43 @ SY182 )
| ~ ( in @ SY182 @ SV13 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(455,plain,
! [SV28: $i,SV13: $i,SV43: $i] :
( ( ( ~ ~ ! [SY183: $i] :
~ ~ ( ~ ( in @ SV43 @ SY183 )
| ~ ( in @ SY183 @ SV13 ) ) )
= $true )
| ( ( in @ SV43 @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(456,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(457,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ! [SY184: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY184 )
| ~ ( in @ SY184 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(458,plain,
! [SV30: $i,SV15: $i,SV38: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV38 )
| ~ ! [SY186: $i] :
~ ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY186 @ SV15 )
| ~ ( in @ SY187 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY186 @ SY187 ) ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(459,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV15: $i] :
( ( ( ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY188 @ SV15 )
| ~ ( in @ SY189 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY188 @ SY189 ) ) )
| ( in @ SV49 @ SV38 ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(460,plain,
! [SV38: $i,SV15: $i,SV30: $i] :
( ( ( ~ ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
| ~ ! [SY190: $i] :
~ ~ ! [SY191: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ SV15 )
| ~ ( in @ SY191 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY190 @ SY191 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(461,plain,
! [SV18: $i,SV2: $i,SV32: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV32 ) )
= $true )
| ( ( ( in @ SV45 @ SV2 )
| ( in @ SV45 @ SV18 ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(462,plain,
! [SV32: $i,SV18: $i,SV2: $i,SV45: $i] :
( ( ( ~ ( ( in @ SV45 @ SV2 )
| ( in @ SV45 @ SV18 ) ) )
= $true )
| ( ( in @ SV45 @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(463,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(464,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(465,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ SV33 ) )
= $true )
| ( ( ( SV46 = SV3 )
| ( SV46 = SV19 ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(466,plain,
! [SV33: $i,SV19: $i,SV3: $i,SV46: $i] :
( ( ( ~ ( ( SV46 = SV3 )
| ( SV46 = SV19 ) ) )
= $true )
| ( ( in @ SV46 @ SV33 )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(467,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(468,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(469,plain,
! [SV34: $i,SV4: $i,SV39: $i,SV20: $i] :
( ( ( in @ SV20 @ SV39 )
= $false )
| ( ( in @ SV4 @ SV34 )
= $false )
| ( ( in @ ( ordered_pair @ SV4 @ SV20 ) @ ( cartesian_product2 @ SV34 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(470,plain,
! [SV5: $i,SV21: $i] :
( ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV21 )
= $true )
| ( ( in @ ( sK5_SY130 @ SV21 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = SV21 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(471,plain,
! [SV6: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY131 @ SV22 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK15_SY131 @ SV22 @ SV6 ) @ SV22 ) ) )
= $true )
| ( ( disjoint @ SV6 @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(472,plain,
! [SV22: $i,SV6: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ SV6 )
| ~ ( in @ SV50 @ SV22 ) )
= $true )
| ( ( ~ ( disjoint @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(473,plain,
! [SV8: $i,SV24: $i,SV42: $i] :
( ( ( in @ SV42 @ SV24 )
= $false )
| ( ( SV42 = SV8 )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(474,plain,
! [SV24: $i,SV8: $i,SV42: $i] :
( ( ( SV42 = SV8 )
= $false )
| ( ( in @ SV42 @ SV24 )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(475,plain,
! [SV24: $i,SV8: $i] :
( ( ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 )
= $true )
| ( ( ~ ( ( ( sK7_SY136 @ SV8 @ SV24 )
!= SV8 )
| ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 ) ) )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(476,plain,
! [SV24: $i,SV8: $i] :
( ( ( ( ( sK7_SY136 @ SV8 @ SV24 )
!= SV8 )
| ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 ) )
= $false )
| ( ( ( sK7_SY136 @ SV8 @ SV24 )
= SV8 )
= $false )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(477,plain,
! [SV26: $i,SV11: $i,SV36: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV36 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(478,plain,
! [SV36: $i,SV26: $i,SV11: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) ) )
= $true )
| ( ( in @ SV47 @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(479,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(480,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(481,plain,
! [SV27: $i,SV12: $i,SV37: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV37 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(482,plain,
! [SV37: $i,SV27: $i,SV12: $i,SV48: $i] :
( ( ( ~ ~ ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) ) )
= $true )
| ( ( in @ SV48 @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(483,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(484,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[453]) ).
thf(485,plain,
! [SV13: $i,SV28: $i,SV43: $i] :
( ( ( in @ SV43 @ SV28 )
= $false )
| ( ( ~ ! [SY182: $i] :
~ ~ ( ~ ( in @ SV43 @ SY182 )
| ~ ( in @ SY182 @ SV13 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(486,plain,
! [SV28: $i,SV13: $i,SV43: $i] :
( ( ( ~ ! [SY183: $i] :
~ ~ ( ~ ( in @ SV43 @ SY183 )
| ~ ( in @ SY183 @ SV13 ) ) )
= $false )
| ( ( in @ SV43 @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(487,plain,
! [SV28: $i,SV13: $i] :
( ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[456]) ).
thf(488,plain,
! [SV28: $i,SV13: $i] :
( ( ( ! [SY184: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY184 )
| ~ ( in @ SY184 @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(489,plain,
! [SV30: $i,SV15: $i,SV38: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV38 ) )
= $true )
| ( ( ~ ! [SY186: $i] :
~ ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY186 @ SV15 )
| ~ ( in @ SY187 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY186 @ SY187 ) ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(490,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV15: $i] :
( ( ( ~ ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY188 @ SV15 )
| ~ ( in @ SY189 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY188 @ SY189 ) ) ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(491,plain,
! [SV38: $i,SV15: $i,SV30: $i] :
( ( ( ~ ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(492,plain,
! [SV38: $i,SV30: $i,SV15: $i] :
( ( ( ~ ! [SY190: $i] :
~ ~ ! [SY191: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ SV15 )
| ~ ( in @ SY191 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY190 @ SY191 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(493,plain,
! [SV18: $i,SV2: $i,SV32: $i,SV45: $i] :
( ( ( in @ SV45 @ SV32 )
= $false )
| ( ( ( in @ SV45 @ SV2 )
| ( in @ SV45 @ SV18 ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(494,plain,
! [SV32: $i,SV18: $i,SV2: $i,SV45: $i] :
( ( ( ( in @ SV45 @ SV2 )
| ( in @ SV45 @ SV18 ) )
= $false )
| ( ( in @ SV45 @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(495,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(496,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(497,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) ) )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[464]) ).
thf(498,plain,
! [SV19: $i,SV3: $i,SV33: $i,SV46: $i] :
( ( ( in @ SV46 @ SV33 )
= $false )
| ( ( ( SV46 = SV3 )
| ( SV46 = SV19 ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(499,plain,
! [SV33: $i,SV19: $i,SV3: $i,SV46: $i] :
( ( ( ( SV46 = SV3 )
| ( SV46 = SV19 ) )
= $false )
| ( ( in @ SV46 @ SV33 )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(500,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
= $true )
| ( ( ~ ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(501,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
= $false )
| ( ( ~ ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(502,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 )
= $false )
| ( ( ~ ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[468]) ).
thf(503,plain,
! [SV6: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK15_SY131 @ SV22 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK15_SY131 @ SV22 @ SV6 ) @ SV22 ) )
= $false )
| ( ( disjoint @ SV6 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(504,plain,
! [SV22: $i,SV6: $i,SV50: $i] :
( ( ( ~ ( in @ SV50 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV50 @ SV22 ) )
= $true )
| ( ( ~ ( disjoint @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(505,plain,
! [SV24: $i,SV8: $i] :
( ( ( ( ( sK7_SY136 @ SV8 @ SV24 )
!= SV8 )
| ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 ) )
= $false )
| ( ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(506,plain,
! [SV24: $i,SV8: $i] :
( ( ( ( sK7_SY136 @ SV8 @ SV24 )
!= SV8 )
= $false )
| ( ( ( sK7_SY136 @ SV8 @ SV24 )
= SV8 )
= $false )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(507,plain,
! [SV24: $i,SV8: $i] :
( ( ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 )
= $false )
| ( ( ( sK7_SY136 @ SV8 @ SV24 )
= SV8 )
= $false )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(508,plain,
! [SV26: $i,SV11: $i,SV36: $i,SV47: $i] :
( ( ( in @ SV47 @ SV36 )
= $false )
| ( ( ~ ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(509,plain,
! [SV36: $i,SV26: $i,SV11: $i,SV47: $i] :
( ( ( ~ ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) ) )
= $false )
| ( ( in @ SV47 @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(510,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(511,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(512,plain,
! [SV27: $i,SV12: $i,SV37: $i,SV48: $i] :
( ( ( in @ SV48 @ SV37 )
= $false )
| ( ( ~ ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(513,plain,
! [SV37: $i,SV27: $i,SV12: $i,SV48: $i] :
( ( ( ~ ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) ) )
= $false )
| ( ( in @ SV48 @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(514,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(515,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(516,plain,
! [SV28: $i,SV13: $i,SV43: $i] :
( ( ( ! [SY182: $i] :
~ ~ ( ~ ( in @ SV43 @ SY182 )
| ~ ( in @ SY182 @ SV13 ) ) )
= $false )
| ( ( in @ SV43 @ SV28 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(517,plain,
! [SV28: $i,SV13: $i,SV43: $i] :
( ( ( ! [SY183: $i] :
~ ~ ( ~ ( in @ SV43 @ SY183 )
| ~ ( in @ SY183 @ SV13 ) ) )
= $true )
| ( ( in @ SV43 @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(518,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(519,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
| ~ ( in @ SV51 @ SV13 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(520,plain,
! [SV30: $i,SV15: $i,SV38: $i,SV49: $i] :
( ( ( in @ SV49 @ SV38 )
= $false )
| ( ( ~ ! [SY186: $i] :
~ ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY186 @ SV15 )
| ~ ( in @ SY187 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY186 @ SY187 ) ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(521,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV15: $i] :
( ( ( ~ ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY188 @ SV15 )
| ~ ( in @ SY189 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY188 @ SY189 ) ) ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(522,plain,
! [SV38: $i,SV15: $i,SV30: $i] :
( ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(523,plain,
! [SV38: $i,SV30: $i,SV15: $i] :
( ( ( ! [SY190: $i] :
~ ~ ! [SY191: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY190 @ SV15 )
| ~ ( in @ SY191 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY190 @ SY191 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(524,plain,
! [SV32: $i,SV18: $i,SV2: $i,SV45: $i] :
( ( ( in @ SV45 @ SV2 )
= $true )
| ( ( in @ SV45 @ SV18 )
= $true )
| ( ( in @ SV45 @ SV32 )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(525,plain,
! [SV18: $i,SV32: $i,SV2: $i,SV45: $i] :
( ( ( in @ SV45 @ SV2 )
= $false )
| ( ( in @ SV45 @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(526,plain,
! [SV2: $i,SV32: $i,SV18: $i,SV45: $i] :
( ( ( in @ SV45 @ SV18 )
= $false )
| ( ( in @ SV45 @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(527,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) )
= $false )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(528,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) )
= $false )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(529,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 ) )
= $false )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(530,plain,
! [SV33: $i,SV19: $i,SV3: $i,SV46: $i] :
( ( ( SV46 = SV3 )
= $true )
| ( ( SV46 = SV19 )
= $true )
| ( ( in @ SV46 @ SV33 )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(531,plain,
! [SV19: $i,SV33: $i,SV3: $i,SV46: $i] :
( ( ( SV46 = SV3 )
= $false )
| ( ( in @ SV46 @ SV33 )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(532,plain,
! [SV3: $i,SV33: $i,SV19: $i,SV46: $i] :
( ( ( SV46 = SV19 )
= $false )
| ( ( in @ SV46 @ SV33 )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(533,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(534,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) )
= $false )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(535,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
| ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 ) )
= $false )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(536,plain,
! [SV6: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK15_SY131 @ SV22 @ SV6 ) @ SV6 ) )
= $false )
| ( ( disjoint @ SV6 @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[503]) ).
thf(537,plain,
! [SV6: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK15_SY131 @ SV22 @ SV6 ) @ SV22 ) )
= $false )
| ( ( disjoint @ SV6 @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[503]) ).
thf(538,plain,
! [SV22: $i,SV6: $i,SV50: $i] :
( ( ( in @ SV50 @ SV6 )
= $false )
| ( ( ~ ( in @ SV50 @ SV22 ) )
= $true )
| ( ( ~ ( disjoint @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(539,plain,
! [SV24: $i,SV8: $i] :
( ( ( ( sK7_SY136 @ SV8 @ SV24 )
!= SV8 )
= $false )
| ( ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(540,plain,
! [SV24: $i,SV8: $i] :
( ( ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 )
= $false )
| ( ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(541,plain,
! [SV24: $i,SV8: $i] :
( ( ( ( sK7_SY136 @ SV8 @ SV24 )
= SV8 )
= $true )
| ( ( ( sK7_SY136 @ SV8 @ SV24 )
= SV8 )
= $false )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(542,plain,
! [SV36: $i,SV26: $i,SV11: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) )
= $false )
| ( ( in @ SV47 @ SV36 )
= $false )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(543,plain,
! [SV36: $i,SV26: $i,SV11: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV11 )
| ~ ~ ( in @ SV47 @ SV26 ) )
= $true )
| ( ( in @ SV47 @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(544,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(545,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(546,plain,
! [SV37: $i,SV27: $i,SV12: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) )
= $false )
| ( ( in @ SV48 @ SV37 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(547,plain,
! [SV37: $i,SV27: $i,SV12: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV12 )
| ~ ( in @ SV48 @ SV27 ) )
= $true )
| ( ( in @ SV48 @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(548,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(549,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 ) )
= $true )
| ( ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(550,plain,
! [SV13: $i,SV28: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( in @ SV43 @ ( sK16_SY182 @ SV28 @ SV13 @ SV43 ) )
| ~ ( in @ ( sK16_SY182 @ SV28 @ SV13 @ SV43 ) @ SV13 ) ) )
= $false )
| ( ( in @ SV43 @ SV28 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[516]) ).
thf(551,plain,
! [SV28: $i,SV13: $i,SV52: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( in @ SV43 @ SV52 )
| ~ ( in @ SV52 @ SV13 ) ) )
= $true )
| ( ( in @ SV43 @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(552,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(553,plain,
! [SV28: $i,SV13: $i] :
( ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(554,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
| ~ ( in @ SV51 @ SV13 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(555,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV15: $i] :
( ( ( ! [SY186: $i] :
~ ~ ! [SY187: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY186 @ SV15 )
| ~ ( in @ SY187 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY186 @ SY187 ) ) ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(556,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV15: $i] :
( ( ( ! [SY188: $i] :
~ ~ ! [SY189: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY188 @ SV15 )
| ~ ( in @ SY189 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SY188 @ SY189 ) ) ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(557,plain,
! [SV38: $i,SV30: $i,SV15: $i] :
( ( ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(558,plain,
! [SV38: $i,SV30: $i,SV15: $i,SV53: $i] :
( ( ( ~ ~ ! [SY194: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV53 @ SV15 )
| ~ ( in @ SY194 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SV53 @ SY194 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(559,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) ) )
= $false )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[527]) ).
thf(560,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
= $false )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[527]) ).
thf(561,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) ) )
= $false )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(562,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
= $false )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(563,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ~ ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) ) )
= $false )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(564,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
= $false )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[529]) ).
thf(565,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) ) )
= $false )
| ( ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(566,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
= $false )
| ( ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(567,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) ) )
= $false )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(568,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
= $false )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[534]) ).
thf(569,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ~ ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) ) )
= $false )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(570,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
= $false )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[535]) ).
thf(571,plain,
! [SV6: $i,SV22: $i] :
( ( ( in @ ( sK15_SY131 @ SV22 @ SV6 ) @ SV6 )
= $true )
| ( ( disjoint @ SV6 @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(572,plain,
! [SV6: $i,SV22: $i] :
( ( ( in @ ( sK15_SY131 @ SV22 @ SV6 ) @ SV22 )
= $true )
| ( ( disjoint @ SV6 @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(573,plain,
! [SV6: $i,SV22: $i,SV50: $i] :
( ( ( in @ SV50 @ SV22 )
= $false )
| ( ( in @ SV50 @ SV6 )
= $false )
| ( ( ~ ( disjoint @ SV6 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(574,plain,
! [SV24: $i,SV8: $i] :
( ( ( ( sK7_SY136 @ SV8 @ SV24 )
= SV8 )
= $true )
| ( ( in @ ( sK7_SY136 @ SV8 @ SV24 ) @ SV24 )
= $true )
| ( ( SV24
= ( singleton @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(575,plain,
! [SV26: $i,SV36: $i,SV11: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV11 ) )
= $false )
| ( ( in @ SV47 @ SV36 )
= $false )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(576,plain,
! [SV11: $i,SV36: $i,SV26: $i,SV47: $i] :
( ( ( ~ ~ ( in @ SV47 @ SV26 ) )
= $false )
| ( ( in @ SV47 @ SV36 )
= $false )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(577,plain,
! [SV36: $i,SV26: $i,SV11: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV11 ) )
= $true )
| ( ( ~ ~ ( in @ SV47 @ SV26 ) )
= $true )
| ( ( in @ SV47 @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(578,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) ) )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(579,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(580,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(581,plain,
! [SV27: $i,SV37: $i,SV12: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV12 ) )
= $false )
| ( ( in @ SV48 @ SV37 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(582,plain,
! [SV12: $i,SV37: $i,SV27: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV27 ) )
= $false )
| ( ( in @ SV48 @ SV37 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(583,plain,
! [SV37: $i,SV27: $i,SV12: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV12 ) )
= $true )
| ( ( ~ ( in @ SV48 @ SV27 ) )
= $true )
| ( ( in @ SV48 @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(584,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) ) )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(585,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(586,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $false )
| ( ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(587,plain,
! [SV13: $i,SV28: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ SV43 @ ( sK16_SY182 @ SV28 @ SV13 @ SV43 ) )
| ~ ( in @ ( sK16_SY182 @ SV28 @ SV13 @ SV43 ) @ SV13 ) ) )
= $true )
| ( ( in @ SV43 @ SV28 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(588,plain,
! [SV28: $i,SV13: $i,SV52: $i,SV43: $i] :
( ( ( ~ ( ~ ( in @ SV43 @ SV52 )
| ~ ( in @ SV52 @ SV13 ) ) )
= $false )
| ( ( in @ SV43 @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(589,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) ) )
= $true )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(590,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
| ~ ( in @ SV51 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(591,plain,
! [SV15: $i,SV30: $i,SV49: $i,SV38: $i] :
( ( ( ~ ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ SY195 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SY195 ) ) ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[555]) ).
thf(592,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV15: $i,SV54: $i] :
( ( ( ~ ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV54 @ SV15 )
| ~ ( in @ SY196 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SV54 @ SY196 ) ) ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(593,plain,
! [SV38: $i,SV30: $i,SV15: $i] :
( ( ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(594,plain,
! [SV38: $i,SV15: $i,SV30: $i] :
( ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(595,plain,
! [SV38: $i,SV30: $i,SV15: $i,SV53: $i] :
( ( ( ~ ! [SY194: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV53 @ SV15 )
| ~ ( in @ SY194 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SV53 @ SY194 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(596,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
= $true )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(597,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
= $true )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(598,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
| ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 ) )
= $true )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[563]) ).
thf(599,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
= $true )
| ( ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[565]) ).
thf(600,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
= $true )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(601,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
| ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 ) )
= $true )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(602,plain,
! [SV50: $i,SV22: $i,SV6: $i] :
( ( ( disjoint @ SV6 @ SV22 )
= $false )
| ( ( in @ SV50 @ SV6 )
= $false )
| ( ( in @ SV50 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(603,plain,
! [SV26: $i,SV36: $i,SV11: $i,SV47: $i] :
( ( ( in @ SV47 @ SV11 )
= $true )
| ( ( in @ SV47 @ SV36 )
= $false )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[575]) ).
thf(604,plain,
! [SV11: $i,SV36: $i,SV26: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV26 ) )
= $true )
| ( ( in @ SV47 @ SV36 )
= $false )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[576]) ).
thf(605,plain,
! [SV36: $i,SV26: $i,SV11: $i,SV47: $i] :
( ( ( in @ SV47 @ SV11 )
= $false )
| ( ( ~ ~ ( in @ SV47 @ SV26 ) )
= $true )
| ( ( in @ SV47 @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(606,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) ) )
= $true )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(607,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(608,plain,
! [SV27: $i,SV37: $i,SV12: $i,SV48: $i] :
( ( ( in @ SV48 @ SV12 )
= $true )
| ( ( in @ SV48 @ SV37 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(609,plain,
! [SV12: $i,SV37: $i,SV27: $i,SV48: $i] :
( ( ( in @ SV48 @ SV27 )
= $true )
| ( ( in @ SV48 @ SV37 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(610,plain,
! [SV37: $i,SV27: $i,SV12: $i,SV48: $i] :
( ( ( in @ SV48 @ SV12 )
= $false )
| ( ( ~ ( in @ SV48 @ SV27 ) )
= $true )
| ( ( in @ SV48 @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(611,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) ) )
= $true )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(612,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) ) )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(613,plain,
! [SV13: $i,SV28: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ ( sK16_SY182 @ SV28 @ SV13 @ SV43 ) )
| ~ ( in @ ( sK16_SY182 @ SV28 @ SV13 @ SV43 ) @ SV13 ) )
= $false )
| ( ( in @ SV43 @ SV28 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(614,plain,
! [SV28: $i,SV13: $i,SV52: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ SV52 )
| ~ ( in @ SV52 @ SV13 ) )
= $true )
| ( ( in @ SV43 @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(615,plain,
! [SV28: $i,SV13: $i] :
( ( ( ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(616,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 ) )
= $true )
| ( ( ~ ( in @ SV51 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(617,plain,
! [SV15: $i,SV30: $i,SV49: $i,SV38: $i] :
( ( ( ~ ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ SY195 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SY195 ) ) ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(618,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV15: $i,SV54: $i] :
( ( ( ~ ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV54 @ SV15 )
| ~ ( in @ SY196 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SV54 @ SY196 ) ) ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(619,plain,
! [SV38: $i,SV30: $i,SV15: $i] :
( ( ( ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) ) )
= $true )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(620,plain,
! [SV38: $i,SV30: $i,SV15: $i,SV53: $i] :
( ( ( ! [SY194: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV53 @ SV15 )
| ~ ( in @ SY194 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SV53 @ SY194 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(621,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
= $true )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 )
= $true )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV32 )
= $true )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(622,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
= $true )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 )
= $true )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(623,plain,
! [SV32: $i,SV2: $i,SV18: $i] :
( ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV2 )
= $true )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 )
= $true )
| ( ( in @ ( sK10_SY163 @ SV18 @ SV2 @ SV32 ) @ SV18 )
= $false )
| ( ( SV32
= ( set_union2 @ SV2 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(624,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
= $true )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 )
= $true )
| ( ( in @ ( sK11_SY165 @ SV19 @ SV3 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(625,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
= $true )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 )
= $true )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(626,plain,
! [SV33: $i,SV3: $i,SV19: $i] :
( ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV3 )
= $true )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 )
= $true )
| ( ( ( sK11_SY165 @ SV19 @ SV3 @ SV33 )
= SV19 )
= $false )
| ( ( SV33
= ( unordered_pair @ SV3 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(627,plain,
! [SV11: $i,SV36: $i,SV26: $i,SV47: $i] :
( ( ( in @ SV47 @ SV26 )
= $false )
| ( ( in @ SV47 @ SV36 )
= $false )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(628,plain,
! [SV36: $i,SV11: $i,SV26: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV26 ) )
= $false )
| ( ( in @ SV47 @ SV11 )
= $false )
| ( ( in @ SV47 @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(629,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(630,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $true )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) ) )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(631,plain,
! [SV37: $i,SV12: $i,SV27: $i,SV48: $i] :
( ( ( in @ SV48 @ SV27 )
= $false )
| ( ( in @ SV48 @ SV12 )
= $false )
| ( ( in @ SV48 @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(632,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(633,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
| ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 ) )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(634,plain,
! [SV13: $i,SV28: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ ( sK16_SY182 @ SV28 @ SV13 @ SV43 ) ) )
= $false )
| ( ( in @ SV43 @ SV28 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(635,plain,
! [SV43: $i,SV13: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK16_SY182 @ SV28 @ SV13 @ SV43 ) @ SV13 ) )
= $false )
| ( ( in @ SV43 @ SV28 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[613]) ).
thf(636,plain,
! [SV28: $i,SV13: $i,SV52: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ SV52 ) )
= $true )
| ( ( ~ ( in @ SV52 @ SV13 ) )
= $true )
| ( ( in @ SV43 @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(637,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ ( sK18_SY185 @ SV28 @ SV13 ) )
| ~ ( in @ ( sK18_SY185 @ SV28 @ SV13 ) @ SV13 ) ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[615]) ).
thf(638,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( ~ ( in @ SV51 @ SV13 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(639,plain,
! [SV15: $i,SV30: $i,SV49: $i,SV38: $i] :
( ( ( ! [SY195: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ SY195 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SY195 ) ) ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(640,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV15: $i,SV54: $i] :
( ( ( ! [SY196: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV54 @ SV15 )
| ~ ( in @ SY196 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SV54 @ SY196 ) ) ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[618]) ).
thf(641,plain,
! [SV38: $i,SV30: $i,SV15: $i] :
( ( ( ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(642,plain,
! [SV38: $i,SV30: $i,SV55: $i,SV15: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV53 @ SV15 )
| ~ ( in @ SV55 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SV53 @ SV55 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(643,plain,
! [SV36: $i,SV11: $i,SV26: $i,SV47: $i] :
( ( ( in @ SV47 @ SV26 )
= $true )
| ( ( in @ SV47 @ SV11 )
= $false )
| ( ( in @ SV47 @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(644,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(645,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[629]) ).
thf(646,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
| ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 ) )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(647,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 ) )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(648,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[632]) ).
thf(649,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) ) )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(650,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[633]) ).
thf(651,plain,
! [SV13: $i,SV28: $i,SV43: $i] :
( ( ( in @ SV43 @ ( sK16_SY182 @ SV28 @ SV13 @ SV43 ) )
= $true )
| ( ( in @ SV43 @ SV28 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[634]) ).
thf(652,plain,
! [SV43: $i,SV13: $i,SV28: $i] :
( ( ( in @ ( sK16_SY182 @ SV28 @ SV13 @ SV43 ) @ SV13 )
= $true )
| ( ( in @ SV43 @ SV28 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[635]) ).
thf(653,plain,
! [SV28: $i,SV13: $i,SV52: $i,SV43: $i] :
( ( ( in @ SV43 @ SV52 )
= $false )
| ( ( ~ ( in @ SV52 @ SV13 ) )
= $true )
| ( ( in @ SV43 @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(654,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ ( sK18_SY185 @ SV28 @ SV13 ) )
| ~ ( in @ ( sK18_SY185 @ SV28 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(655,plain,
! [SV28: $i,SV13: $i,SV51: $i] :
( ( ( in @ SV51 @ SV13 )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( ~ ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) ) )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[638]) ).
thf(656,plain,
! [SV15: $i,SV30: $i,SV49: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) @ SV30 ) )
| ( SV49
!= ( ordered_pair @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) ) ) ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[639]) ).
thf(657,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV56: $i,SV15: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV54 @ SV15 )
| ~ ( in @ SV56 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SV54 @ SV56 ) ) ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(658,plain,
! [SV15: $i,SV30: $i,SV38: $i] :
( ( ( ~ ~ ! [SY197: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ SY197 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SY197 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[641]) ).
thf(659,plain,
! [SV38: $i,SV30: $i,SV55: $i,SV15: $i,SV53: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV53 @ SV15 )
| ~ ( in @ SV55 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SV53 @ SV55 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(660,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $true )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(661,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
= $true )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[645]) ).
thf(662,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) ) )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(663,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[646]) ).
thf(664,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $true )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[647]) ).
thf(665,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 )
= $true )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV37 )
= $true )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(666,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) ) )
= $true )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[649]) ).
thf(667,plain,
! [SV28: $i,SV43: $i,SV13: $i,SV52: $i] :
( ( ( in @ SV52 @ SV13 )
= $false )
| ( ( in @ SV43 @ SV52 )
= $false )
| ( ( in @ SV43 @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(668,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ ( sK18_SY185 @ SV28 @ SV13 ) )
| ~ ( in @ ( sK18_SY185 @ SV28 @ SV13 ) @ SV13 ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(669,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) )
| ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( in @ SV51 @ SV13 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(670,plain,
! [SV15: $i,SV30: $i,SV49: $i,SV38: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) @ SV30 ) )
| ( SV49
!= ( ordered_pair @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) ) ) ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[656]) ).
thf(671,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV56: $i,SV15: $i,SV54: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV54 @ SV15 )
| ~ ( in @ SV56 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SV54 @ SV56 ) ) ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(672,plain,
! [SV15: $i,SV30: $i,SV38: $i] :
( ( ( ~ ! [SY197: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ SY197 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SY197 ) ) ) )
= $true )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[658]) ).
thf(673,plain,
! [SV38: $i,SV30: $i,SV55: $i,SV15: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ( in @ SV53 @ SV15 )
| ~ ( in @ SV55 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SV53 @ SV55 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[659]) ).
thf(674,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV36 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(675,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) ) )
= $true )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[662]) ).
thf(676,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
| ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(677,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ ( sK18_SY185 @ SV28 @ SV13 ) ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[668]) ).
thf(678,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK18_SY185 @ SV28 @ SV13 ) @ SV13 ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[668]) ).
thf(679,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( ~ ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( in @ SV51 @ SV13 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[669]) ).
thf(680,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( in @ SV51 @ SV13 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[669]) ).
thf(681,plain,
! [SV15: $i,SV30: $i,SV49: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) @ SV30 ) )
| ( SV49
!= ( ordered_pair @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) ) ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(682,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV56: $i,SV15: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ( in @ SV54 @ SV15 )
| ~ ( in @ SV56 @ SV30 ) )
| ( SV49
!= ( ordered_pair @ SV54 @ SV56 ) ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[671]) ).
thf(683,plain,
! [SV15: $i,SV30: $i,SV38: $i] :
( ( ( ! [SY197: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ SY197 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SY197 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(684,plain,
! [SV38: $i,SV30: $i,SV55: $i,SV15: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ( in @ SV53 @ SV15 )
| ~ ( in @ SV55 @ SV30 ) ) )
= $true )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SV53 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(685,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
| ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(686,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 ) )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(687,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 ) )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[676]) ).
thf(688,plain,
! [SV28: $i,SV13: $i] :
( ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ ( sK18_SY185 @ SV28 @ SV13 ) )
= $true )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[677]) ).
thf(689,plain,
! [SV13: $i,SV28: $i] :
( ( ( in @ ( sK18_SY185 @ SV28 @ SV13 ) @ SV13 )
= $true )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV28 )
= $true )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[678]) ).
thf(690,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( ~ ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) ) )
= $true )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( in @ SV51 @ SV13 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[679]) ).
thf(691,plain,
! [SV15: $i,SV30: $i,SV49: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) @ SV30 ) ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(692,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV49: $i] :
( ( ( SV49
!= ( ordered_pair @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[681]) ).
thf(693,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV56: $i,SV15: $i,SV54: $i] :
( ( ( ~ ~ ( ~ ( in @ SV54 @ SV15 )
| ~ ( in @ SV56 @ SV30 ) ) )
= $true )
| ( ( SV49
!= ( ordered_pair @ SV54 @ SV56 ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(694,plain,
! [SV15: $i,SV30: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) ) ) ) )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[683]) ).
thf(695,plain,
! [SV38: $i,SV30: $i,SV55: $i,SV15: $i,SV53: $i] :
( ( ( ~ ( ~ ( in @ SV53 @ SV15 )
| ~ ( in @ SV55 @ SV30 ) ) )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SV53 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(696,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(697,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[685]) ).
thf(698,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $true )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[686]) ).
thf(699,plain,
! [SV37: $i,SV12: $i,SV27: $i] :
( ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 )
= $true )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV12 )
= $false )
| ( ( in @ ( sK13_SY171 @ SV27 @ SV12 @ SV37 ) @ SV27 )
= $false )
| ( ( SV37
= ( set_intersection2 @ SV12 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(700,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( ! [SY185: $i] :
~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SY185 )
| ~ ( in @ SY185 @ SV13 ) ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( in @ SV51 @ SV13 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(701,plain,
! [SV15: $i,SV30: $i,SV49: $i,SV38: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) @ SV30 ) ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(702,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV49: $i] :
( ( ( SV49
= ( ordered_pair @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(703,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV56: $i,SV15: $i,SV54: $i] :
( ( ( ~ ( ~ ( in @ SV54 @ SV15 )
| ~ ( in @ SV56 @ SV30 ) ) )
= $false )
| ( ( SV49
!= ( ordered_pair @ SV54 @ SV56 ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(704,plain,
! [SV15: $i,SV30: $i,SV38: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) ) ) ) )
= $true )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[694]) ).
thf(705,plain,
! [SV38: $i,SV30: $i,SV55: $i,SV15: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV15 )
| ~ ( in @ SV55 @ SV30 ) )
= $true )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SV53 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[695]) ).
thf(706,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $true )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[696]) ).
thf(707,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 ) )
= $true )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[697]) ).
thf(708,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ ( sK22_SY185 @ SV51 @ SV28 @ SV13 ) )
| ~ ( in @ ( sK22_SY185 @ SV51 @ SV28 @ SV13 ) @ SV13 ) ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( in @ SV51 @ SV13 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[700]) ).
thf(709,plain,
! [SV15: $i,SV30: $i,SV49: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) @ SV30 ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(710,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV56: $i,SV15: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV15 )
| ~ ( in @ SV56 @ SV30 ) )
= $true )
| ( ( SV49
!= ( ordered_pair @ SV54 @ SV56 ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[703]) ).
thf(711,plain,
! [SV15: $i,SV30: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) ) ) )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(712,plain,
! [SV38: $i,SV30: $i,SV55: $i,SV15: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV15 ) )
= $true )
| ( ( ~ ( in @ SV55 @ SV30 ) )
= $true )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SV53 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(713,plain,
! [SV36: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV11 )
= $false )
| ( ( in @ ( sK12_SY169 @ SV26 @ SV11 @ SV36 ) @ SV26 )
= $true )
| ( ( SV36
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(714,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ ( sK22_SY185 @ SV51 @ SV28 @ SV13 ) )
| ~ ( in @ ( sK22_SY185 @ SV51 @ SV28 @ SV13 ) @ SV13 ) ) )
= $true )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( in @ SV51 @ SV13 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(715,plain,
! [SV15: $i,SV30: $i,SV49: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(716,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) @ SV30 ) )
= $false )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(717,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV56: $i,SV15: $i,SV54: $i] :
( ( ( ~ ( in @ SV54 @ SV15 ) )
= $true )
| ( ( ~ ( in @ SV56 @ SV30 ) )
= $true )
| ( ( SV49
!= ( ordered_pair @ SV54 @ SV56 ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[710]) ).
thf(718,plain,
! [SV15: $i,SV30: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) @ SV30 ) ) )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(719,plain,
! [SV38: $i,SV15: $i,SV30: $i] :
( ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) ) )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[711]) ).
thf(720,plain,
! [SV38: $i,SV30: $i,SV55: $i,SV15: $i,SV53: $i] :
( ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ~ ( in @ SV55 @ SV30 ) )
= $true )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SV53 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(721,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ ( sK22_SY185 @ SV51 @ SV28 @ SV13 ) )
| ~ ( in @ ( sK22_SY185 @ SV51 @ SV28 @ SV13 ) @ SV13 ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( in @ SV51 @ SV13 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(722,plain,
! [SV15: $i,SV30: $i,SV49: $i,SV38: $i] :
( ( ( in @ ( sK17_SY186 @ SV38 @ SV49 @ SV30 @ SV15 ) @ SV15 )
= $true )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[715]) ).
thf(723,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV15: $i] :
( ( ( in @ ( sK19_SY195 @ SV15 @ SV30 @ SV49 @ SV38 ) @ SV30 )
= $true )
| ( ( in @ SV49 @ SV38 )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[716]) ).
thf(724,plain,
! [SV38: $i,SV49: $i,SV30: $i,SV56: $i,SV15: $i,SV54: $i] :
( ( ( in @ SV54 @ SV15 )
= $false )
| ( ( ~ ( in @ SV56 @ SV30 ) )
= $true )
| ( ( SV49
!= ( ordered_pair @ SV54 @ SV56 ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(725,plain,
! [SV15: $i,SV30: $i,SV38: $i] :
( ( ( ~ ( ~ ( in @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) @ SV30 ) ) )
= $true )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(726,plain,
! [SV38: $i,SV15: $i,SV30: $i] :
( ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) ) )
= $true )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[719]) ).
thf(727,plain,
! [SV38: $i,SV15: $i,SV53: $i,SV30: $i,SV55: $i] :
( ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SV53 @ SV55 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(728,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( ~ ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ ( sK22_SY185 @ SV51 @ SV28 @ SV13 ) ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( in @ SV51 @ SV13 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(729,plain,
! [SV13: $i,SV28: $i,SV51: $i] :
( ( ( ~ ( in @ ( sK22_SY185 @ SV51 @ SV28 @ SV13 ) @ SV13 ) )
= $false )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( in @ SV51 @ SV13 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(730,plain,
! [SV38: $i,SV49: $i,SV15: $i,SV54: $i,SV30: $i,SV56: $i] :
( ( ( in @ SV56 @ SV30 )
= $false )
| ( ( in @ SV54 @ SV15 )
= $false )
| ( ( SV49
!= ( ordered_pair @ SV54 @ SV56 ) )
= $true )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(731,plain,
! [SV15: $i,SV30: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) @ SV30 ) )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(732,plain,
! [SV55: $i,SV53: $i,SV38: $i,SV15: $i,SV30: $i] :
( ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( ~ ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) ) )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(733,plain,
! [SV51: $i,SV28: $i,SV13: $i] :
( ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ ( sK22_SY185 @ SV51 @ SV28 @ SV13 ) )
= $true )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( in @ SV51 @ SV13 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(734,plain,
! [SV13: $i,SV28: $i,SV51: $i] :
( ( ( in @ ( sK22_SY185 @ SV51 @ SV28 @ SV13 ) @ SV13 )
= $true )
| ( ( in @ ( sK8_SY146 @ SV13 @ SV28 ) @ SV51 )
= $false )
| ( ( in @ SV51 @ SV13 )
= $false )
| ( ( SV28
= ( union @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(735,plain,
! [SV38: $i,SV30: $i,SV15: $i,SV56: $i,SV54: $i,SV49: $i] :
( ( ( SV49
= ( ordered_pair @ SV54 @ SV56 ) )
= $false )
| ( ( in @ SV54 @ SV15 )
= $false )
| ( ( in @ SV56 @ SV30 )
= $false )
| ( ( in @ SV49 @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(736,plain,
! [SV15: $i,SV30: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(737,plain,
! [SV38: $i,SV30: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) @ SV30 ) )
= $false )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[731]) ).
thf(738,plain,
! [SV53: $i,SV55: $i,SV38: $i,SV30: $i,SV15: $i] :
( ( ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) )
| ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 ) )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(739,plain,
! [SV15: $i,SV30: $i,SV38: $i] :
( ( ( in @ ( sK20_SY192 @ SV38 @ SV30 @ SV15 ) @ SV15 )
= $true )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(740,plain,
! [SV38: $i,SV30: $i,SV15: $i] :
( ( ( in @ ( sK21_SY197 @ SV15 @ SV30 @ SV38 ) @ SV30 )
= $true )
| ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $true )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(741,plain,
! [SV53: $i,SV55: $i,SV38: $i,SV30: $i,SV15: $i] :
( ( ( ~ ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) ) )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[738]) ).
thf(742,plain,
! [SV53: $i,SV55: $i,SV38: $i,SV15: $i,SV30: $i] :
( ( ( in @ ( sK14_SY177 @ SV30 @ SV15 @ SV38 ) @ SV38 )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[738]) ).
thf(743,plain,
! [SV53: $i,SV55: $i,SV38: $i,SV30: $i,SV15: $i] :
( ( ( ~ ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) ) )
= $true )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[741]) ).
thf(744,plain,
! [SV53: $i,SV55: $i,SV38: $i,SV30: $i,SV15: $i] :
( ( ( ! [SY192: $i] :
~ ~ ! [SY193: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY192 @ SV15 )
| ~ ( in @ SY193 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ SY192 @ SY193 ) ) ) )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(745,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV55: $i,SV53: $i] :
( ( ( ~ ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ SY198 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SY198 ) ) ) )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[744]) ).
thf(746,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV55: $i,SV53: $i] :
( ( ( ~ ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ SY198 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SY198 ) ) ) )
= $true )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(747,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV55: $i,SV53: $i] :
( ( ( ! [SY198: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ SY198 @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SY198 ) ) ) )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(748,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV55: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) ) ) ) )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[747]) ).
thf(749,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV55: $i,SV53: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) ) ) ) )
= $true )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[748]) ).
thf(750,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV55: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) @ SV30 ) )
| ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) ) ) )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(751,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV55: $i,SV53: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) @ SV30 ) ) )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(752,plain,
! [SV55: $i,SV53: $i,SV38: $i,SV15: $i,SV30: $i] :
( ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
!= ( ordered_pair @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) ) )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[750]) ).
thf(753,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV55: $i,SV53: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) @ SV30 ) ) )
= $true )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(754,plain,
! [SV55: $i,SV53: $i,SV38: $i,SV15: $i,SV30: $i] :
( ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) ) )
= $true )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(755,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV55: $i,SV53: $i] :
( ( ( ~ ( in @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SV15 )
| ~ ( in @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) @ SV30 ) )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(756,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV55: $i,SV53: $i] :
( ( ( ~ ( in @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[755]) ).
thf(757,plain,
! [SV53: $i,SV55: $i,SV38: $i,SV30: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) @ SV30 ) )
= $false )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[755]) ).
thf(758,plain,
! [SV15: $i,SV30: $i,SV38: $i,SV55: $i,SV53: $i] :
( ( ( in @ ( sK23_SY192 @ SV53 @ SV55 @ SV38 @ SV30 @ SV15 ) @ SV15 )
= $true )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(759,plain,
! [SV53: $i,SV55: $i,SV38: $i,SV30: $i,SV15: $i] :
( ( ( in @ ( sK24_SY198 @ SV15 @ SV30 @ SV38 @ SV55 @ SV53 ) @ SV30 )
= $true )
| ( ( in @ SV55 @ SV30 )
= $false )
| ( ( in @ SV53 @ SV15 )
= $false )
| ( ( ( sK14_SY177 @ SV30 @ SV15 @ SV38 )
= ( ordered_pair @ SV53 @ SV55 ) )
= $false )
| ( ( SV38
= ( cartesian_product2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[757]) ).
thf(760,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[145,759,758,754,742,740,739,735,734,733,726,723,722,713,706,702,699,698,689,688,680,674,667,665,664,663,660,652,651,650,643,631,627,626,625,624,623,622,621,609,608,603,602,594,585,579,574,572,571,570,568,566,564,562,560,553,541,540,532,531,530,526,525,524,507,474,473,470,469,441,440,437,436,412,400,399,376,363,362,341,340,314,280,271,213,210,154,153,152,151,150,149,148,147,146]) ).
thf(761,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(copy,[status(thm)],[123]) ).
thf(762,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(763,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(764,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(765,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(766,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(767,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(768,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(769,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(copy,[status(thm)],[115]) ).
thf(770,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(771,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(772,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(773,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(774,plain,
$true = $true,
inference(copy,[status(thm)],[110]) ).
thf(775,plain,
$true = $true,
inference(copy,[status(thm)],[109]) ).
thf(776,plain,
$true = $true,
inference(copy,[status(thm)],[108]) ).
thf(777,plain,
$true = $true,
inference(copy,[status(thm)],[107]) ).
thf(778,plain,
$true = $true,
inference(copy,[status(thm)],[106]) ).
thf(779,plain,
$true = $true,
inference(copy,[status(thm)],[105]) ).
thf(780,plain,
$true = $true,
inference(copy,[status(thm)],[104]) ).
thf(781,plain,
$true = $true,
inference(copy,[status(thm)],[103]) ).
thf(782,plain,
$true = $true,
inference(copy,[status(thm)],[102]) ).
thf(783,plain,
$true = $true,
inference(copy,[status(thm)],[101]) ).
thf(784,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(785,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(786,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(787,plain,
( ( ~ ( ( ( in @ sK1_A @ sK3_SY62 )
& ( in @ sK2_SY59 @ sK4_SY64 ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(788,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[771]) ).
thf(789,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[770]) ).
thf(790,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 ) )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[769]) ).
thf(791,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) ) )
| ~ ~ ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[763]) ).
thf(792,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[768]) ).
thf(793,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[785]) ).
thf(794,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[786]) ).
thf(795,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[764]) ).
thf(796,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[773]) ).
thf(797,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) )
| ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX2 )
| ~ ( in @ SX1 @ SX3 ) )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ ( cartesian_product2 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[761]) ).
thf(798,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( union @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX2 @ SX3 )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( union @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[772]) ).
thf(799,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[766]) ).
thf(800,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[765]) ).
thf(801,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( ordered_pair @ SX0 @ SX1 )
!= ( ordered_pair @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[762]) ).
thf(802,plain,
( ( ~ ( ~ ~ ( ~ ( in @ sK1_A @ sK3_SY62 )
| ~ ( in @ sK2_SY59 @ sK4_SY64 ) )
| ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[787]) ).
thf(803,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[767]) ).
thf(804,plain,
! [SV57: $i] :
( ( ! [SY199: $i] :
~ ( empty @ ( ordered_pair @ SV57 @ SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(805,plain,
! [SV58: $i] :
( ( ! [SY200: $i,SY201: $i] :
~ ( ~ ( ( SY201
!= ( set_intersection2 @ SV58 @ SY200 ) )
| ! [SY202: $i] :
~ ( ~ ( ~ ( in @ SY202 @ SY201 )
| ~ ( ~ ( in @ SY202 @ SV58 )
| ~ ( in @ SY202 @ SY200 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY202 @ SV58 )
| ~ ( in @ SY202 @ SY200 ) )
| ( in @ SY202 @ SY201 ) ) ) )
| ~ ( ~ ! [SY203: $i] :
~ ( ~ ( ~ ( in @ SY203 @ SY201 )
| ~ ( ~ ( in @ SY203 @ SV58 )
| ~ ( in @ SY203 @ SY200 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY203 @ SV58 )
| ~ ( in @ SY203 @ SY200 ) )
| ( in @ SY203 @ SY201 ) ) )
| ( SY201
= ( set_intersection2 @ SV58 @ SY200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(806,plain,
! [SV59: $i] :
( ( ! [SY204: $i] :
~ ( ~ ( ~ ( subset @ SV59 @ SY204 )
| ! [SY205: $i] :
( ~ ( in @ SY205 @ SV59 )
| ( in @ SY205 @ SY204 ) ) )
| ~ ( ~ ! [SY206: $i] :
( ~ ( in @ SY206 @ SV59 )
| ( in @ SY206 @ SY204 ) )
| ( subset @ SV59 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(807,plain,
! [SV60: $i] :
( ( ! [SY207: $i,SY208: $i] :
~ ( ~ ( ( SY208
!= ( cartesian_product2 @ SV60 @ SY207 ) )
| ! [SY209: $i] :
~ ( ~ ( ~ ( in @ SY209 @ SY208 )
| ~ ! [SY210: $i] :
~ ~ ! [SY211: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY210 @ SV60 )
| ~ ( in @ SY211 @ SY207 ) )
| ( SY209
!= ( ordered_pair @ SY210 @ SY211 ) ) ) )
| ~ ( ~ ~ ! [SY212: $i] :
~ ~ ! [SY213: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY212 @ SV60 )
| ~ ( in @ SY213 @ SY207 ) )
| ( SY209
!= ( ordered_pair @ SY212 @ SY213 ) ) )
| ( in @ SY209 @ SY208 ) ) ) )
| ~ ( ~ ! [SY214: $i] :
~ ( ~ ( ~ ( in @ SY214 @ SY208 )
| ~ ! [SY215: $i] :
~ ~ ! [SY216: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY215 @ SV60 )
| ~ ( in @ SY216 @ SY207 ) )
| ( SY214
!= ( ordered_pair @ SY215 @ SY216 ) ) ) )
| ~ ( ~ ~ ! [SY217: $i] :
~ ~ ! [SY218: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY217 @ SV60 )
| ~ ( in @ SY218 @ SY207 ) )
| ( SY214
!= ( ordered_pair @ SY217 @ SY218 ) ) )
| ( in @ SY214 @ SY208 ) ) )
| ( SY208
= ( cartesian_product2 @ SV60 @ SY207 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(808,plain,
! [SV61: $i] :
( ( ! [SY219: $i] :
~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV61 @ SY219 )
| ~ ! [SY220: $i] :
~ ~ ( ~ ( in @ SY220 @ SV61 )
| ~ ( in @ SY220 @ SY219 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY221: $i] :
~ ~ ( ~ ( in @ SY221 @ SV61 )
| ~ ( in @ SY221 @ SY219 ) )
| ~ ( disjoint @ SV61 @ SY219 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(809,plain,
! [SV62: $i] :
( ( ! [SY222: $i,SY223: $i] :
~ ( ~ ( ( SY223
!= ( set_union2 @ SV62 @ SY222 ) )
| ! [SY224: $i] :
~ ( ~ ( ~ ( in @ SY224 @ SY223 )
| ( in @ SY224 @ SV62 )
| ( in @ SY224 @ SY222 ) )
| ~ ( ~ ( ( in @ SY224 @ SV62 )
| ( in @ SY224 @ SY222 ) )
| ( in @ SY224 @ SY223 ) ) ) )
| ~ ( ~ ! [SY225: $i] :
~ ( ~ ( ~ ( in @ SY225 @ SY223 )
| ( in @ SY225 @ SV62 )
| ( in @ SY225 @ SY222 ) )
| ~ ( ~ ( ( in @ SY225 @ SV62 )
| ( in @ SY225 @ SY222 ) )
| ( in @ SY225 @ SY223 ) ) )
| ( SY223
= ( set_union2 @ SV62 @ SY222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(810,plain,
! [SV63: $i] :
( ( ! [SY226: $i] :
( ~ ! [SY227: $i] :
~ ( ~ ( ~ ( in @ SY227 @ SV63 )
| ( in @ SY227 @ SY226 ) )
| ~ ( ~ ( in @ SY227 @ SY226 )
| ( in @ SY227 @ SV63 ) ) )
| ( SV63 = SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(811,plain,
! [SV64: $i] :
( ( ! [SY228: $i] :
~ ~ ( ~ ( in @ SV64 @ SY228 )
| ~ ( empty @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(812,plain,
! [SV65: $i] :
( ( ! [SY229: $i] :
( ~ ( in @ SV65 @ SY229 )
| ~ ( in @ SY229 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(813,plain,
! [SV66: $i] :
( ( ! [SY230: $i,SY231: $i] :
~ ( ~ ( ( SY231
!= ( set_difference @ SV66 @ SY230 ) )
| ! [SY232: $i] :
~ ( ~ ( ~ ( in @ SY232 @ SY231 )
| ~ ( ~ ( in @ SY232 @ SV66 )
| ~ ~ ( in @ SY232 @ SY230 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY232 @ SV66 )
| ~ ~ ( in @ SY232 @ SY230 ) )
| ( in @ SY232 @ SY231 ) ) ) )
| ~ ( ~ ! [SY233: $i] :
~ ( ~ ( ~ ( in @ SY233 @ SY231 )
| ~ ( ~ ( in @ SY233 @ SV66 )
| ~ ~ ( in @ SY233 @ SY230 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY233 @ SV66 )
| ~ ~ ( in @ SY233 @ SY230 ) )
| ( in @ SY233 @ SY231 ) ) )
| ( SY231
= ( set_difference @ SV66 @ SY230 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(814,plain,
! [SV67: $i] :
( ( ! [SY234: $i,SY235: $i,SY236: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV67 @ SY234 ) @ ( cartesian_product2 @ SY235 @ SY236 ) )
| ~ ( ~ ( in @ SV67 @ SY235 )
| ~ ( in @ SY234 @ SY236 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV67 @ SY235 )
| ~ ( in @ SY234 @ SY236 ) )
| ( in @ ( ordered_pair @ SV67 @ SY234 ) @ ( cartesian_product2 @ SY235 @ SY236 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(815,plain,
! [SV68: $i] :
( ( ! [SY237: $i] :
~ ( ~ ( ( SY237
!= ( union @ SV68 ) )
| ! [SY238: $i] :
~ ( ~ ( ~ ( in @ SY238 @ SY237 )
| ~ ! [SY239: $i] :
~ ~ ( ~ ( in @ SY238 @ SY239 )
| ~ ( in @ SY239 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY238 @ SY240 )
| ~ ( in @ SY240 @ SV68 ) )
| ( in @ SY238 @ SY237 ) ) ) )
| ~ ( ~ ! [SY241: $i] :
~ ( ~ ( ~ ( in @ SY241 @ SY237 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( in @ SY241 @ SY242 )
| ~ ( in @ SY242 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( in @ SY241 @ SY243 )
| ~ ( in @ SY243 @ SV68 ) )
| ( in @ SY241 @ SY237 ) ) )
| ( SY237
= ( union @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(816,plain,
! [SV69: $i] :
( ( ~ ( ~ ( ( SV69 != empty_set )
| ! [SY244: $i] :
~ ( in @ SY244 @ SV69 ) )
| ~ ( ~ ! [SY245: $i] :
~ ( in @ SY245 @ SV69 )
| ( SV69 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(817,plain,
! [SV70: $i] :
( ( ! [SY246: $i] :
~ ( ~ ( ( SY246
!= ( singleton @ SV70 ) )
| ! [SY247: $i] :
~ ( ~ ( ~ ( in @ SY247 @ SY246 )
| ( SY247 = SV70 ) )
| ~ ( ( SY247 != SV70 )
| ( in @ SY247 @ SY246 ) ) ) )
| ~ ( ~ ! [SY248: $i] :
~ ( ~ ( ~ ( in @ SY248 @ SY246 )
| ( SY248 = SV70 ) )
| ~ ( ( SY248 != SV70 )
| ( in @ SY248 @ SY246 ) ) )
| ( SY246
= ( singleton @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(818,plain,
! [SV71: $i] :
( ( ! [SY249: $i,SY250: $i,SY251: $i] :
( ( ( ordered_pair @ SV71 @ SY249 )
!= ( ordered_pair @ SY250 @ SY251 ) )
| ~ ( ( SV71 != SY250 )
| ( SY249 != SY251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(819,plain,
( ( ~ ~ ( ~ ( in @ sK1_A @ sK3_SY62 )
| ~ ( in @ sK2_SY59 @ sK4_SY64 ) )
| ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(820,plain,
! [SV72: $i] :
( ( ! [SY252: $i,SY253: $i] :
~ ( ~ ( ( SY253
!= ( unordered_pair @ SV72 @ SY252 ) )
| ! [SY254: $i] :
~ ( ~ ( ~ ( in @ SY254 @ SY253 )
| ( SY254 = SV72 )
| ( SY254 = SY252 ) )
| ~ ( ~ ( ( SY254 = SV72 )
| ( SY254 = SY252 ) )
| ( in @ SY254 @ SY253 ) ) ) )
| ~ ( ~ ! [SY255: $i] :
~ ( ~ ( ~ ( in @ SY255 @ SY253 )
| ( SY255 = SV72 )
| ( SY255 = SY252 ) )
| ~ ( ~ ( ( SY255 = SV72 )
| ( SY255 = SY252 ) )
| ( in @ SY255 @ SY253 ) ) )
| ( SY253
= ( unordered_pair @ SV72 @ SY252 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(821,plain,
! [SV73: $i,SV57: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV57 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(822,plain,
! [SV74: $i,SV58: $i] :
( ( ! [SY256: $i] :
~ ( ~ ( ( SY256
!= ( set_intersection2 @ SV58 @ SV74 ) )
| ! [SY257: $i] :
~ ( ~ ( ~ ( in @ SY257 @ SY256 )
| ~ ( ~ ( in @ SY257 @ SV58 )
| ~ ( in @ SY257 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY257 @ SV58 )
| ~ ( in @ SY257 @ SV74 ) )
| ( in @ SY257 @ SY256 ) ) ) )
| ~ ( ~ ! [SY258: $i] :
~ ( ~ ( ~ ( in @ SY258 @ SY256 )
| ~ ( ~ ( in @ SY258 @ SV58 )
| ~ ( in @ SY258 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY258 @ SV58 )
| ~ ( in @ SY258 @ SV74 ) )
| ( in @ SY258 @ SY256 ) ) )
| ( SY256
= ( set_intersection2 @ SV58 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(823,plain,
! [SV75: $i,SV59: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV59 @ SV75 )
| ! [SY259: $i] :
( ~ ( in @ SY259 @ SV59 )
| ( in @ SY259 @ SV75 ) ) )
| ~ ( ~ ! [SY260: $i] :
( ~ ( in @ SY260 @ SV59 )
| ( in @ SY260 @ SV75 ) )
| ( subset @ SV59 @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(824,plain,
! [SV76: $i,SV60: $i] :
( ( ! [SY261: $i] :
~ ( ~ ( ( SY261
!= ( cartesian_product2 @ SV60 @ SV76 ) )
| ! [SY262: $i] :
~ ( ~ ( ~ ( in @ SY262 @ SY261 )
| ~ ! [SY263: $i] :
~ ~ ! [SY264: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY263 @ SV60 )
| ~ ( in @ SY264 @ SV76 ) )
| ( SY262
!= ( ordered_pair @ SY263 @ SY264 ) ) ) )
| ~ ( ~ ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY265 @ SV60 )
| ~ ( in @ SY266 @ SV76 ) )
| ( SY262
!= ( ordered_pair @ SY265 @ SY266 ) ) )
| ( in @ SY262 @ SY261 ) ) ) )
| ~ ( ~ ! [SY267: $i] :
~ ( ~ ( ~ ( in @ SY267 @ SY261 )
| ~ ! [SY268: $i] :
~ ~ ! [SY269: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY268 @ SV60 )
| ~ ( in @ SY269 @ SV76 ) )
| ( SY267
!= ( ordered_pair @ SY268 @ SY269 ) ) ) )
| ~ ( ~ ~ ! [SY270: $i] :
~ ~ ! [SY271: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY270 @ SV60 )
| ~ ( in @ SY271 @ SV76 ) )
| ( SY267
!= ( ordered_pair @ SY270 @ SY271 ) ) )
| ( in @ SY267 @ SY261 ) ) )
| ( SY261
= ( cartesian_product2 @ SV60 @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(825,plain,
! [SV77: $i,SV61: $i] :
( ( ~ ( ~ ~ ~ ( ~ ~ ( disjoint @ SV61 @ SV77 )
| ~ ! [SY272: $i] :
~ ~ ( ~ ( in @ SY272 @ SV61 )
| ~ ( in @ SY272 @ SV77 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY273: $i] :
~ ~ ( ~ ( in @ SY273 @ SV61 )
| ~ ( in @ SY273 @ SV77 ) )
| ~ ( disjoint @ SV61 @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(826,plain,
! [SV78: $i,SV62: $i] :
( ( ! [SY274: $i] :
~ ( ~ ( ( SY274
!= ( set_union2 @ SV62 @ SV78 ) )
| ! [SY275: $i] :
~ ( ~ ( ~ ( in @ SY275 @ SY274 )
| ( in @ SY275 @ SV62 )
| ( in @ SY275 @ SV78 ) )
| ~ ( ~ ( ( in @ SY275 @ SV62 )
| ( in @ SY275 @ SV78 ) )
| ( in @ SY275 @ SY274 ) ) ) )
| ~ ( ~ ! [SY276: $i] :
~ ( ~ ( ~ ( in @ SY276 @ SY274 )
| ( in @ SY276 @ SV62 )
| ( in @ SY276 @ SV78 ) )
| ~ ( ~ ( ( in @ SY276 @ SV62 )
| ( in @ SY276 @ SV78 ) )
| ( in @ SY276 @ SY274 ) ) )
| ( SY274
= ( set_union2 @ SV62 @ SV78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(827,plain,
! [SV79: $i,SV63: $i] :
( ( ~ ! [SY277: $i] :
~ ( ~ ( ~ ( in @ SY277 @ SV63 )
| ( in @ SY277 @ SV79 ) )
| ~ ( ~ ( in @ SY277 @ SV79 )
| ( in @ SY277 @ SV63 ) ) )
| ( SV63 = SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(828,plain,
! [SV80: $i,SV64: $i] :
( ( ~ ~ ( ~ ( in @ SV64 @ SV80 )
| ~ ( empty @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(829,plain,
! [SV81: $i,SV65: $i] :
( ( ~ ( in @ SV65 @ SV81 )
| ~ ( in @ SV81 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(830,plain,
! [SV82: $i,SV66: $i] :
( ( ! [SY278: $i] :
~ ( ~ ( ( SY278
!= ( set_difference @ SV66 @ SV82 ) )
| ! [SY279: $i] :
~ ( ~ ( ~ ( in @ SY279 @ SY278 )
| ~ ( ~ ( in @ SY279 @ SV66 )
| ~ ~ ( in @ SY279 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY279 @ SV66 )
| ~ ~ ( in @ SY279 @ SV82 ) )
| ( in @ SY279 @ SY278 ) ) ) )
| ~ ( ~ ! [SY280: $i] :
~ ( ~ ( ~ ( in @ SY280 @ SY278 )
| ~ ( ~ ( in @ SY280 @ SV66 )
| ~ ~ ( in @ SY280 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY280 @ SV66 )
| ~ ~ ( in @ SY280 @ SV82 ) )
| ( in @ SY280 @ SY278 ) ) )
| ( SY278
= ( set_difference @ SV66 @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(831,plain,
! [SV83: $i,SV67: $i] :
( ( ! [SY281: $i,SY282: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SY281 @ SY282 ) )
| ~ ( ~ ( in @ SV67 @ SY281 )
| ~ ( in @ SV83 @ SY282 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV67 @ SY281 )
| ~ ( in @ SV83 @ SY282 ) )
| ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SY281 @ SY282 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(832,plain,
! [SV68: $i,SV84: $i] :
( ( ~ ( ~ ( ( SV84
!= ( union @ SV68 ) )
| ! [SY283: $i] :
~ ( ~ ( ~ ( in @ SY283 @ SV84 )
| ~ ! [SY239: $i] :
~ ~ ( ~ ( in @ SY283 @ SY239 )
| ~ ( in @ SY239 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY283 @ SY240 )
| ~ ( in @ SY240 @ SV68 ) )
| ( in @ SY283 @ SV84 ) ) ) )
| ~ ( ~ ! [SY286: $i] :
~ ( ~ ( ~ ( in @ SY286 @ SV84 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( in @ SY286 @ SY242 )
| ~ ( in @ SY242 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( in @ SY286 @ SY243 )
| ~ ( in @ SY243 @ SV68 ) )
| ( in @ SY286 @ SV84 ) ) )
| ( SV84
= ( union @ SV68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(833,plain,
! [SV69: $i] :
( ( ~ ( ( SV69 != empty_set )
| ! [SY244: $i] :
~ ( in @ SY244 @ SV69 ) )
| ~ ( ~ ! [SY245: $i] :
~ ( in @ SY245 @ SV69 )
| ( SV69 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(834,plain,
! [SV70: $i,SV85: $i] :
( ( ~ ( ~ ( ( SV85
!= ( singleton @ SV70 ) )
| ! [SY289: $i] :
~ ( ~ ( ~ ( in @ SY289 @ SV85 )
| ( SY289 = SV70 ) )
| ~ ( ( SY289 != SV70 )
| ( in @ SY289 @ SV85 ) ) ) )
| ~ ( ~ ! [SY290: $i] :
~ ( ~ ( ~ ( in @ SY290 @ SV85 )
| ( SY290 = SV70 ) )
| ~ ( ( SY290 != SV70 )
| ( in @ SY290 @ SV85 ) ) )
| ( SV85
= ( singleton @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(835,plain,
! [SV86: $i,SV71: $i] :
( ( ! [SY291: $i,SY292: $i] :
( ( ( ordered_pair @ SV71 @ SV86 )
!= ( ordered_pair @ SY291 @ SY292 ) )
| ~ ( ( SV71 != SY291 )
| ( SV86 != SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(836,plain,
( ( ~ ~ ( ~ ( in @ sK1_A @ sK3_SY62 )
| ~ ( in @ sK2_SY59 @ sK4_SY64 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(837,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY59 ) @ ( cartesian_product2 @ sK3_SY62 @ sK4_SY64 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[819]) ).
thf(838,plain,
! [SV87: $i,SV72: $i] :
( ( ! [SY293: $i] :
~ ( ~ ( ( SY293
!= ( unordered_pair @ SV72 @ SV87 ) )
| ! [SY294: $i] :
~ ( ~ ( ~ ( in @ SY294 @ SY293 )
| ( SY294 = SV72 )
| ( SY294 = SV87 ) )
| ~ ( ~ ( ( SY294 = SV72 )
| ( SY294 = SV87 ) )
| ( in @ SY294 @ SY293 ) ) ) )
| ~ ( ~ ! [SY295: $i] :
~ ( ~ ( ~ ( in @ SY295 @ SY293 )
| ( SY295 = SV72 )
| ( SY295 = SV87 ) )
| ~ ( ~ ( ( SY295 = SV72 )
| ( SY295 = SV87 ) )
| ( in @ SY295 @ SY293 ) ) )
| ( SY293
= ( unordered_pair @ SV72 @ SV87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(839,plain,
! [SV73: $i,SV57: $i] :
( ( empty @ ( ordered_pair @ SV57 @ SV73 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(840,plain,
! [SV74: $i,SV58: $i,SV88: $i] :
( ( ~ ( ~ ( ( SV88
!= ( set_intersection2 @ SV58 @ SV74 ) )
| ! [SY296: $i] :
~ ( ~ ( ~ ( in @ SY296 @ SV88 )
| ~ ( ~ ( in @ SY296 @ SV58 )
| ~ ( in @ SY296 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY296 @ SV58 )
| ~ ( in @ SY296 @ SV74 ) )
| ( in @ SY296 @ SV88 ) ) ) )
| ~ ( ~ ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SV88 )
| ~ ( ~ ( in @ SY297 @ SV58 )
| ~ ( in @ SY297 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY297 @ SV58 )
| ~ ( in @ SY297 @ SV74 ) )
| ( in @ SY297 @ SV88 ) ) )
| ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(841,plain,
! [SV75: $i,SV59: $i] :
( ( ~ ( ~ ( subset @ SV59 @ SV75 )
| ! [SY259: $i] :
( ~ ( in @ SY259 @ SV59 )
| ( in @ SY259 @ SV75 ) ) )
| ~ ( ~ ! [SY260: $i] :
( ~ ( in @ SY260 @ SV59 )
| ( in @ SY260 @ SV75 ) )
| ( subset @ SV59 @ SV75 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(842,plain,
! [SV76: $i,SV60: $i,SV89: $i] :
( ( ~ ( ~ ( ( SV89
!= ( cartesian_product2 @ SV60 @ SV76 ) )
| ! [SY298: $i] :
~ ( ~ ( ~ ( in @ SY298 @ SV89 )
| ~ ! [SY263: $i] :
~ ~ ! [SY264: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY263 @ SV60 )
| ~ ( in @ SY264 @ SV76 ) )
| ( SY298
!= ( ordered_pair @ SY263 @ SY264 ) ) ) )
| ~ ( ~ ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY265 @ SV60 )
| ~ ( in @ SY266 @ SV76 ) )
| ( SY298
!= ( ordered_pair @ SY265 @ SY266 ) ) )
| ( in @ SY298 @ SV89 ) ) ) )
| ~ ( ~ ! [SY303: $i] :
~ ( ~ ( ~ ( in @ SY303 @ SV89 )
| ~ ! [SY268: $i] :
~ ~ ! [SY269: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY268 @ SV60 )
| ~ ( in @ SY269 @ SV76 ) )
| ( SY303
!= ( ordered_pair @ SY268 @ SY269 ) ) ) )
| ~ ( ~ ~ ! [SY270: $i] :
~ ~ ! [SY271: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY270 @ SV60 )
| ~ ( in @ SY271 @ SV76 ) )
| ( SY303
!= ( ordered_pair @ SY270 @ SY271 ) ) )
| ( in @ SY303 @ SV89 ) ) )
| ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(843,plain,
! [SV77: $i,SV61: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV61 @ SV77 )
| ~ ! [SY272: $i] :
~ ~ ( ~ ( in @ SY272 @ SV61 )
| ~ ( in @ SY272 @ SV77 ) ) )
| ~ ~ ~ ( ~ ~ ! [SY273: $i] :
~ ~ ( ~ ( in @ SY273 @ SV61 )
| ~ ( in @ SY273 @ SV77 ) )
| ~ ( disjoint @ SV61 @ SV77 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(844,plain,
! [SV78: $i,SV62: $i,SV90: $i] :
( ( ~ ( ~ ( ( SV90
!= ( set_union2 @ SV62 @ SV78 ) )
| ! [SY308: $i] :
~ ( ~ ( ~ ( in @ SY308 @ SV90 )
| ( in @ SY308 @ SV62 )
| ( in @ SY308 @ SV78 ) )
| ~ ( ~ ( ( in @ SY308 @ SV62 )
| ( in @ SY308 @ SV78 ) )
| ( in @ SY308 @ SV90 ) ) ) )
| ~ ( ~ ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SV90 )
| ( in @ SY309 @ SV62 )
| ( in @ SY309 @ SV78 ) )
| ~ ( ~ ( ( in @ SY309 @ SV62 )
| ( in @ SY309 @ SV78 ) )
| ( in @ SY309 @ SV90 ) ) )
| ( SV90
= ( set_union2 @ SV62 @ SV78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(845,plain,
! [SV79: $i,SV63: $i] :
( ( ( ~ ! [SY277: $i] :
~ ( ~ ( ~ ( in @ SY277 @ SV63 )
| ( in @ SY277 @ SV79 ) )
| ~ ( ~ ( in @ SY277 @ SV79 )
| ( in @ SY277 @ SV63 ) ) ) )
= $true )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(846,plain,
! [SV80: $i,SV64: $i] :
( ( ~ ( ~ ( in @ SV64 @ SV80 )
| ~ ( empty @ SV80 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(847,plain,
! [SV81: $i,SV65: $i] :
( ( ( ~ ( in @ SV65 @ SV81 ) )
= $true )
| ( ( ~ ( in @ SV81 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(848,plain,
! [SV82: $i,SV66: $i,SV91: $i] :
( ( ~ ( ~ ( ( SV91
!= ( set_difference @ SV66 @ SV82 ) )
| ! [SY310: $i] :
~ ( ~ ( ~ ( in @ SY310 @ SV91 )
| ~ ( ~ ( in @ SY310 @ SV66 )
| ~ ~ ( in @ SY310 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY310 @ SV66 )
| ~ ~ ( in @ SY310 @ SV82 ) )
| ( in @ SY310 @ SV91 ) ) ) )
| ~ ( ~ ! [SY311: $i] :
~ ( ~ ( ~ ( in @ SY311 @ SV91 )
| ~ ( ~ ( in @ SY311 @ SV66 )
| ~ ~ ( in @ SY311 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY311 @ SV66 )
| ~ ~ ( in @ SY311 @ SV82 ) )
| ( in @ SY311 @ SV91 ) ) )
| ( SV91
= ( set_difference @ SV66 @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(849,plain,
! [SV92: $i,SV83: $i,SV67: $i] :
( ( ! [SY312: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SY312 ) )
| ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SY312 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SY312 ) )
| ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SY312 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(850,plain,
! [SV68: $i,SV84: $i] :
( ( ~ ( ( SV84
!= ( union @ SV68 ) )
| ! [SY283: $i] :
~ ( ~ ( ~ ( in @ SY283 @ SV84 )
| ~ ! [SY239: $i] :
~ ~ ( ~ ( in @ SY283 @ SY239 )
| ~ ( in @ SY239 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY283 @ SY240 )
| ~ ( in @ SY240 @ SV68 ) )
| ( in @ SY283 @ SV84 ) ) ) )
| ~ ( ~ ! [SY286: $i] :
~ ( ~ ( ~ ( in @ SY286 @ SV84 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( in @ SY286 @ SY242 )
| ~ ( in @ SY242 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( in @ SY286 @ SY243 )
| ~ ( in @ SY243 @ SV68 ) )
| ( in @ SY286 @ SV84 ) ) )
| ( SV84
= ( union @ SV68 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(851,plain,
! [SV69: $i] :
( ( ~ ( ( SV69 != empty_set )
| ! [SY244: $i] :
~ ( in @ SY244 @ SV69 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(852,plain,
! [SV69: $i] :
( ( ~ ( ~ ! [SY245: $i] :
~ ( in @ SY245 @ SV69 )
| ( SV69 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(853,plain,
! [SV70: $i,SV85: $i] :
( ( ~ ( ( SV85
!= ( singleton @ SV70 ) )
| ! [SY289: $i] :
~ ( ~ ( ~ ( in @ SY289 @ SV85 )
| ( SY289 = SV70 ) )
| ~ ( ( SY289 != SV70 )
| ( in @ SY289 @ SV85 ) ) ) )
| ~ ( ~ ! [SY290: $i] :
~ ( ~ ( ~ ( in @ SY290 @ SV85 )
| ( SY290 = SV70 ) )
| ~ ( ( SY290 != SV70 )
| ( in @ SY290 @ SV85 ) ) )
| ( SV85
= ( singleton @ SV70 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(854,plain,
! [SV93: $i,SV86: $i,SV71: $i] :
( ( ! [SY313: $i] :
( ( ( ordered_pair @ SV71 @ SV86 )
!= ( ordered_pair @ SV93 @ SY313 ) )
| ~ ( ( SV71 != SV93 )
| ( SV86 != SY313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(855,plain,
( ( ~ ( ~ ( in @ sK1_A @ sK3_SY62 )
| ~ ( in @ sK2_SY59 @ sK4_SY64 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(856,plain,
! [SV87: $i,SV72: $i,SV94: $i] :
( ( ~ ( ~ ( ( SV94
!= ( unordered_pair @ SV72 @ SV87 ) )
| ! [SY314: $i] :
~ ( ~ ( ~ ( in @ SY314 @ SV94 )
| ( SY314 = SV72 )
| ( SY314 = SV87 ) )
| ~ ( ~ ( ( SY314 = SV72 )
| ( SY314 = SV87 ) )
| ( in @ SY314 @ SV94 ) ) ) )
| ~ ( ~ ! [SY315: $i] :
~ ( ~ ( ~ ( in @ SY315 @ SV94 )
| ( SY315 = SV72 )
| ( SY315 = SV87 ) )
| ~ ( ~ ( ( SY315 = SV72 )
| ( SY315 = SV87 ) )
| ( in @ SY315 @ SV94 ) ) )
| ( SV94
= ( unordered_pair @ SV72 @ SV87 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(857,plain,
! [SV74: $i,SV58: $i,SV88: $i] :
( ( ~ ( ( SV88
!= ( set_intersection2 @ SV58 @ SV74 ) )
| ! [SY296: $i] :
~ ( ~ ( ~ ( in @ SY296 @ SV88 )
| ~ ( ~ ( in @ SY296 @ SV58 )
| ~ ( in @ SY296 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY296 @ SV58 )
| ~ ( in @ SY296 @ SV74 ) )
| ( in @ SY296 @ SV88 ) ) ) )
| ~ ( ~ ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SV88 )
| ~ ( ~ ( in @ SY297 @ SV58 )
| ~ ( in @ SY297 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY297 @ SV58 )
| ~ ( in @ SY297 @ SV74 ) )
| ( in @ SY297 @ SV88 ) ) )
| ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(858,plain,
! [SV75: $i,SV59: $i] :
( ( ~ ( ~ ( subset @ SV59 @ SV75 )
| ! [SY259: $i] :
( ~ ( in @ SY259 @ SV59 )
| ( in @ SY259 @ SV75 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[841]) ).
thf(859,plain,
! [SV75: $i,SV59: $i] :
( ( ~ ( ~ ! [SY260: $i] :
( ~ ( in @ SY260 @ SV59 )
| ( in @ SY260 @ SV75 ) )
| ( subset @ SV59 @ SV75 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[841]) ).
thf(860,plain,
! [SV76: $i,SV60: $i,SV89: $i] :
( ( ~ ( ( SV89
!= ( cartesian_product2 @ SV60 @ SV76 ) )
| ! [SY298: $i] :
~ ( ~ ( ~ ( in @ SY298 @ SV89 )
| ~ ! [SY263: $i] :
~ ~ ! [SY264: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY263 @ SV60 )
| ~ ( in @ SY264 @ SV76 ) )
| ( SY298
!= ( ordered_pair @ SY263 @ SY264 ) ) ) )
| ~ ( ~ ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY265 @ SV60 )
| ~ ( in @ SY266 @ SV76 ) )
| ( SY298
!= ( ordered_pair @ SY265 @ SY266 ) ) )
| ( in @ SY298 @ SV89 ) ) ) )
| ~ ( ~ ! [SY303: $i] :
~ ( ~ ( ~ ( in @ SY303 @ SV89 )
| ~ ! [SY268: $i] :
~ ~ ! [SY269: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY268 @ SV60 )
| ~ ( in @ SY269 @ SV76 ) )
| ( SY303
!= ( ordered_pair @ SY268 @ SY269 ) ) ) )
| ~ ( ~ ~ ! [SY270: $i] :
~ ~ ! [SY271: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY270 @ SV60 )
| ~ ( in @ SY271 @ SV76 ) )
| ( SY303
!= ( ordered_pair @ SY270 @ SY271 ) ) )
| ( in @ SY303 @ SV89 ) ) )
| ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(861,plain,
! [SV77: $i,SV61: $i] :
( ( ~ ~ ~ ( ~ ~ ( disjoint @ SV61 @ SV77 )
| ~ ! [SY272: $i] :
~ ~ ( ~ ( in @ SY272 @ SV61 )
| ~ ( in @ SY272 @ SV77 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[843]) ).
thf(862,plain,
! [SV77: $i,SV61: $i] :
( ( ~ ~ ~ ( ~ ~ ! [SY273: $i] :
~ ~ ( ~ ( in @ SY273 @ SV61 )
| ~ ( in @ SY273 @ SV77 ) )
| ~ ( disjoint @ SV61 @ SV77 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[843]) ).
thf(863,plain,
! [SV78: $i,SV62: $i,SV90: $i] :
( ( ~ ( ( SV90
!= ( set_union2 @ SV62 @ SV78 ) )
| ! [SY308: $i] :
~ ( ~ ( ~ ( in @ SY308 @ SV90 )
| ( in @ SY308 @ SV62 )
| ( in @ SY308 @ SV78 ) )
| ~ ( ~ ( ( in @ SY308 @ SV62 )
| ( in @ SY308 @ SV78 ) )
| ( in @ SY308 @ SV90 ) ) ) )
| ~ ( ~ ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SV90 )
| ( in @ SY309 @ SV62 )
| ( in @ SY309 @ SV78 ) )
| ~ ( ~ ( ( in @ SY309 @ SV62 )
| ( in @ SY309 @ SV78 ) )
| ( in @ SY309 @ SV90 ) ) )
| ( SV90
= ( set_union2 @ SV62 @ SV78 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(864,plain,
! [SV79: $i,SV63: $i] :
( ( ( ! [SY277: $i] :
~ ( ~ ( ~ ( in @ SY277 @ SV63 )
| ( in @ SY277 @ SV79 ) )
| ~ ( ~ ( in @ SY277 @ SV79 )
| ( in @ SY277 @ SV63 ) ) ) )
= $false )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(865,plain,
! [SV80: $i,SV64: $i] :
( ( ~ ( in @ SV64 @ SV80 )
| ~ ( empty @ SV80 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(866,plain,
! [SV81: $i,SV65: $i] :
( ( ( in @ SV65 @ SV81 )
= $false )
| ( ( ~ ( in @ SV81 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[847]) ).
thf(867,plain,
! [SV82: $i,SV66: $i,SV91: $i] :
( ( ~ ( ( SV91
!= ( set_difference @ SV66 @ SV82 ) )
| ! [SY310: $i] :
~ ( ~ ( ~ ( in @ SY310 @ SV91 )
| ~ ( ~ ( in @ SY310 @ SV66 )
| ~ ~ ( in @ SY310 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY310 @ SV66 )
| ~ ~ ( in @ SY310 @ SV82 ) )
| ( in @ SY310 @ SV91 ) ) ) )
| ~ ( ~ ! [SY311: $i] :
~ ( ~ ( ~ ( in @ SY311 @ SV91 )
| ~ ( ~ ( in @ SY311 @ SV66 )
| ~ ~ ( in @ SY311 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY311 @ SV66 )
| ~ ~ ( in @ SY311 @ SV82 ) )
| ( in @ SY311 @ SV91 ) ) )
| ( SV91
= ( set_difference @ SV66 @ SV82 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(868,plain,
! [SV95: $i,SV92: $i,SV83: $i,SV67: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
| ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) )
| ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(869,plain,
! [SV68: $i,SV84: $i] :
( ( ~ ( ( SV84
!= ( union @ SV68 ) )
| ! [SY283: $i] :
~ ( ~ ( ~ ( in @ SY283 @ SV84 )
| ~ ! [SY239: $i] :
~ ~ ( ~ ( in @ SY283 @ SY239 )
| ~ ( in @ SY239 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY283 @ SY240 )
| ~ ( in @ SY240 @ SV68 ) )
| ( in @ SY283 @ SV84 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(870,plain,
! [SV68: $i,SV84: $i] :
( ( ~ ( ~ ! [SY286: $i] :
~ ( ~ ( ~ ( in @ SY286 @ SV84 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( in @ SY286 @ SY242 )
| ~ ( in @ SY242 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( in @ SY286 @ SY243 )
| ~ ( in @ SY243 @ SV68 ) )
| ( in @ SY286 @ SV84 ) ) )
| ( SV84
= ( union @ SV68 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[850]) ).
thf(871,plain,
! [SV69: $i] :
( ( ( SV69 != empty_set )
| ! [SY244: $i] :
~ ( in @ SY244 @ SV69 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(872,plain,
! [SV69: $i] :
( ( ~ ! [SY245: $i] :
~ ( in @ SY245 @ SV69 )
| ( SV69 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[852]) ).
thf(873,plain,
! [SV70: $i,SV85: $i] :
( ( ~ ( ( SV85
!= ( singleton @ SV70 ) )
| ! [SY289: $i] :
~ ( ~ ( ~ ( in @ SY289 @ SV85 )
| ( SY289 = SV70 ) )
| ~ ( ( SY289 != SV70 )
| ( in @ SY289 @ SV85 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(874,plain,
! [SV70: $i,SV85: $i] :
( ( ~ ( ~ ! [SY290: $i] :
~ ( ~ ( ~ ( in @ SY290 @ SV85 )
| ( SY290 = SV70 ) )
| ~ ( ( SY290 != SV70 )
| ( in @ SY290 @ SV85 ) ) )
| ( SV85
= ( singleton @ SV70 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(875,plain,
! [SV96: $i,SV93: $i,SV86: $i,SV71: $i] :
( ( ( ( ordered_pair @ SV71 @ SV86 )
!= ( ordered_pair @ SV93 @ SV96 ) )
| ~ ( ( SV71 != SV93 )
| ( SV86 != SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(876,plain,
( ( ~ ( in @ sK1_A @ sK3_SY62 )
| ~ ( in @ sK2_SY59 @ sK4_SY64 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(877,plain,
! [SV87: $i,SV72: $i,SV94: $i] :
( ( ~ ( ( SV94
!= ( unordered_pair @ SV72 @ SV87 ) )
| ! [SY314: $i] :
~ ( ~ ( ~ ( in @ SY314 @ SV94 )
| ( SY314 = SV72 )
| ( SY314 = SV87 ) )
| ~ ( ~ ( ( SY314 = SV72 )
| ( SY314 = SV87 ) )
| ( in @ SY314 @ SV94 ) ) ) )
| ~ ( ~ ! [SY315: $i] :
~ ( ~ ( ~ ( in @ SY315 @ SV94 )
| ( SY315 = SV72 )
| ( SY315 = SV87 ) )
| ~ ( ~ ( ( SY315 = SV72 )
| ( SY315 = SV87 ) )
| ( in @ SY315 @ SV94 ) ) )
| ( SV94
= ( unordered_pair @ SV72 @ SV87 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(878,plain,
! [SV74: $i,SV58: $i,SV88: $i] :
( ( ~ ( ( SV88
!= ( set_intersection2 @ SV58 @ SV74 ) )
| ! [SY296: $i] :
~ ( ~ ( ~ ( in @ SY296 @ SV88 )
| ~ ( ~ ( in @ SY296 @ SV58 )
| ~ ( in @ SY296 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY296 @ SV58 )
| ~ ( in @ SY296 @ SV74 ) )
| ( in @ SY296 @ SV88 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(879,plain,
! [SV74: $i,SV58: $i,SV88: $i] :
( ( ~ ( ~ ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SV88 )
| ~ ( ~ ( in @ SY297 @ SV58 )
| ~ ( in @ SY297 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY297 @ SV58 )
| ~ ( in @ SY297 @ SV74 ) )
| ( in @ SY297 @ SV88 ) ) )
| ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[857]) ).
thf(880,plain,
! [SV75: $i,SV59: $i] :
( ( ~ ( subset @ SV59 @ SV75 )
| ! [SY259: $i] :
( ~ ( in @ SY259 @ SV59 )
| ( in @ SY259 @ SV75 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[858]) ).
thf(881,plain,
! [SV75: $i,SV59: $i] :
( ( ~ ! [SY260: $i] :
( ~ ( in @ SY260 @ SV59 )
| ( in @ SY260 @ SV75 ) )
| ( subset @ SV59 @ SV75 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[859]) ).
thf(882,plain,
! [SV76: $i,SV60: $i,SV89: $i] :
( ( ~ ( ( SV89
!= ( cartesian_product2 @ SV60 @ SV76 ) )
| ! [SY298: $i] :
~ ( ~ ( ~ ( in @ SY298 @ SV89 )
| ~ ! [SY263: $i] :
~ ~ ! [SY264: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY263 @ SV60 )
| ~ ( in @ SY264 @ SV76 ) )
| ( SY298
!= ( ordered_pair @ SY263 @ SY264 ) ) ) )
| ~ ( ~ ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY265 @ SV60 )
| ~ ( in @ SY266 @ SV76 ) )
| ( SY298
!= ( ordered_pair @ SY265 @ SY266 ) ) )
| ( in @ SY298 @ SV89 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(883,plain,
! [SV76: $i,SV60: $i,SV89: $i] :
( ( ~ ( ~ ! [SY303: $i] :
~ ( ~ ( ~ ( in @ SY303 @ SV89 )
| ~ ! [SY268: $i] :
~ ~ ! [SY269: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY268 @ SV60 )
| ~ ( in @ SY269 @ SV76 ) )
| ( SY303
!= ( ordered_pair @ SY268 @ SY269 ) ) ) )
| ~ ( ~ ~ ! [SY270: $i] :
~ ~ ! [SY271: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY270 @ SV60 )
| ~ ( in @ SY271 @ SV76 ) )
| ( SY303
!= ( ordered_pair @ SY270 @ SY271 ) ) )
| ( in @ SY303 @ SV89 ) ) )
| ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[860]) ).
thf(884,plain,
! [SV77: $i,SV61: $i] :
( ( ~ ~ ( ~ ~ ( disjoint @ SV61 @ SV77 )
| ~ ! [SY272: $i] :
~ ~ ( ~ ( in @ SY272 @ SV61 )
| ~ ( in @ SY272 @ SV77 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[861]) ).
thf(885,plain,
! [SV77: $i,SV61: $i] :
( ( ~ ~ ( ~ ~ ! [SY273: $i] :
~ ~ ( ~ ( in @ SY273 @ SV61 )
| ~ ( in @ SY273 @ SV77 ) )
| ~ ( disjoint @ SV61 @ SV77 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(886,plain,
! [SV78: $i,SV62: $i,SV90: $i] :
( ( ~ ( ( SV90
!= ( set_union2 @ SV62 @ SV78 ) )
| ! [SY308: $i] :
~ ( ~ ( ~ ( in @ SY308 @ SV90 )
| ( in @ SY308 @ SV62 )
| ( in @ SY308 @ SV78 ) )
| ~ ( ~ ( ( in @ SY308 @ SV62 )
| ( in @ SY308 @ SV78 ) )
| ( in @ SY308 @ SV90 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(887,plain,
! [SV78: $i,SV62: $i,SV90: $i] :
( ( ~ ( ~ ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SV90 )
| ( in @ SY309 @ SV62 )
| ( in @ SY309 @ SV78 ) )
| ~ ( ~ ( ( in @ SY309 @ SV62 )
| ( in @ SY309 @ SV78 ) )
| ( in @ SY309 @ SV90 ) ) )
| ( SV90
= ( set_union2 @ SV62 @ SV78 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(888,plain,
! [SV63: $i,SV79: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 ) ) ) )
= $false )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[864]) ).
thf(889,plain,
! [SV80: $i,SV64: $i] :
( ( ( ~ ( in @ SV64 @ SV80 ) )
= $true )
| ( ( ~ ( empty @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(890,plain,
! [SV65: $i,SV81: $i] :
( ( ( in @ SV81 @ SV65 )
= $false )
| ( ( in @ SV65 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[866]) ).
thf(891,plain,
! [SV82: $i,SV66: $i,SV91: $i] :
( ( ~ ( ( SV91
!= ( set_difference @ SV66 @ SV82 ) )
| ! [SY310: $i] :
~ ( ~ ( ~ ( in @ SY310 @ SV91 )
| ~ ( ~ ( in @ SY310 @ SV66 )
| ~ ~ ( in @ SY310 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY310 @ SV66 )
| ~ ~ ( in @ SY310 @ SV82 ) )
| ( in @ SY310 @ SV91 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[867]) ).
thf(892,plain,
! [SV82: $i,SV66: $i,SV91: $i] :
( ( ~ ( ~ ! [SY311: $i] :
~ ( ~ ( ~ ( in @ SY311 @ SV91 )
| ~ ( ~ ( in @ SY311 @ SV66 )
| ~ ~ ( in @ SY311 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY311 @ SV66 )
| ~ ~ ( in @ SY311 @ SV82 ) )
| ( in @ SY311 @ SV91 ) ) )
| ( SV91
= ( set_difference @ SV66 @ SV82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[867]) ).
thf(893,plain,
! [SV95: $i,SV92: $i,SV83: $i,SV67: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
| ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) )
| ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(894,plain,
! [SV68: $i,SV84: $i] :
( ( ( SV84
!= ( union @ SV68 ) )
| ! [SY283: $i] :
~ ( ~ ( ~ ( in @ SY283 @ SV84 )
| ~ ! [SY239: $i] :
~ ~ ( ~ ( in @ SY283 @ SY239 )
| ~ ( in @ SY239 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY283 @ SY240 )
| ~ ( in @ SY240 @ SV68 ) )
| ( in @ SY283 @ SV84 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(895,plain,
! [SV68: $i,SV84: $i] :
( ( ~ ! [SY286: $i] :
~ ( ~ ( ~ ( in @ SY286 @ SV84 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( in @ SY286 @ SY242 )
| ~ ( in @ SY242 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( in @ SY286 @ SY243 )
| ~ ( in @ SY243 @ SV68 ) )
| ( in @ SY286 @ SV84 ) ) )
| ( SV84
= ( union @ SV68 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[870]) ).
thf(896,plain,
! [SV69: $i] :
( ( ( SV69 != empty_set )
= $true )
| ( ( ! [SY244: $i] :
~ ( in @ SY244 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(897,plain,
! [SV69: $i] :
( ( ( ~ ! [SY245: $i] :
~ ( in @ SY245 @ SV69 ) )
= $true )
| ( ( SV69 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(898,plain,
! [SV70: $i,SV85: $i] :
( ( ( SV85
!= ( singleton @ SV70 ) )
| ! [SY289: $i] :
~ ( ~ ( ~ ( in @ SY289 @ SV85 )
| ( SY289 = SV70 ) )
| ~ ( ( SY289 != SV70 )
| ( in @ SY289 @ SV85 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[873]) ).
thf(899,plain,
! [SV70: $i,SV85: $i] :
( ( ~ ! [SY290: $i] :
~ ( ~ ( ~ ( in @ SY290 @ SV85 )
| ( SY290 = SV70 ) )
| ~ ( ( SY290 != SV70 )
| ( in @ SY290 @ SV85 ) ) )
| ( SV85
= ( singleton @ SV70 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[874]) ).
thf(900,plain,
! [SV96: $i,SV93: $i,SV86: $i,SV71: $i] :
( ( ( ( ordered_pair @ SV71 @ SV86 )
!= ( ordered_pair @ SV93 @ SV96 ) )
= $true )
| ( ( ~ ( ( SV71 != SV93 )
| ( SV86 != SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(901,plain,
( ( ~ ( in @ sK1_A @ sK3_SY62 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[876]) ).
thf(902,plain,
( ( ~ ( in @ sK2_SY59 @ sK4_SY64 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[876]) ).
thf(903,plain,
! [SV87: $i,SV72: $i,SV94: $i] :
( ( ~ ( ( SV94
!= ( unordered_pair @ SV72 @ SV87 ) )
| ! [SY314: $i] :
~ ( ~ ( ~ ( in @ SY314 @ SV94 )
| ( SY314 = SV72 )
| ( SY314 = SV87 ) )
| ~ ( ~ ( ( SY314 = SV72 )
| ( SY314 = SV87 ) )
| ( in @ SY314 @ SV94 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(904,plain,
! [SV87: $i,SV72: $i,SV94: $i] :
( ( ~ ( ~ ! [SY315: $i] :
~ ( ~ ( ~ ( in @ SY315 @ SV94 )
| ( SY315 = SV72 )
| ( SY315 = SV87 ) )
| ~ ( ~ ( ( SY315 = SV72 )
| ( SY315 = SV87 ) )
| ( in @ SY315 @ SV94 ) ) )
| ( SV94
= ( unordered_pair @ SV72 @ SV87 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(905,plain,
! [SV74: $i,SV58: $i,SV88: $i] :
( ( ( SV88
!= ( set_intersection2 @ SV58 @ SV74 ) )
| ! [SY296: $i] :
~ ( ~ ( ~ ( in @ SY296 @ SV88 )
| ~ ( ~ ( in @ SY296 @ SV58 )
| ~ ( in @ SY296 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY296 @ SV58 )
| ~ ( in @ SY296 @ SV74 ) )
| ( in @ SY296 @ SV88 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(906,plain,
! [SV74: $i,SV58: $i,SV88: $i] :
( ( ~ ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SV88 )
| ~ ( ~ ( in @ SY297 @ SV58 )
| ~ ( in @ SY297 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY297 @ SV58 )
| ~ ( in @ SY297 @ SV74 ) )
| ( in @ SY297 @ SV88 ) ) )
| ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[879]) ).
thf(907,plain,
! [SV75: $i,SV59: $i] :
( ( ( ~ ( subset @ SV59 @ SV75 ) )
= $true )
| ( ( ! [SY259: $i] :
( ~ ( in @ SY259 @ SV59 )
| ( in @ SY259 @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(908,plain,
! [SV75: $i,SV59: $i] :
( ( ( ~ ! [SY260: $i] :
( ~ ( in @ SY260 @ SV59 )
| ( in @ SY260 @ SV75 ) ) )
= $true )
| ( ( subset @ SV59 @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(909,plain,
! [SV76: $i,SV60: $i,SV89: $i] :
( ( ( SV89
!= ( cartesian_product2 @ SV60 @ SV76 ) )
| ! [SY298: $i] :
~ ( ~ ( ~ ( in @ SY298 @ SV89 )
| ~ ! [SY263: $i] :
~ ~ ! [SY264: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY263 @ SV60 )
| ~ ( in @ SY264 @ SV76 ) )
| ( SY298
!= ( ordered_pair @ SY263 @ SY264 ) ) ) )
| ~ ( ~ ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY265 @ SV60 )
| ~ ( in @ SY266 @ SV76 ) )
| ( SY298
!= ( ordered_pair @ SY265 @ SY266 ) ) )
| ( in @ SY298 @ SV89 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[882]) ).
thf(910,plain,
! [SV76: $i,SV60: $i,SV89: $i] :
( ( ~ ! [SY303: $i] :
~ ( ~ ( ~ ( in @ SY303 @ SV89 )
| ~ ! [SY268: $i] :
~ ~ ! [SY269: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY268 @ SV60 )
| ~ ( in @ SY269 @ SV76 ) )
| ( SY303
!= ( ordered_pair @ SY268 @ SY269 ) ) ) )
| ~ ( ~ ~ ! [SY270: $i] :
~ ~ ! [SY271: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY270 @ SV60 )
| ~ ( in @ SY271 @ SV76 ) )
| ( SY303
!= ( ordered_pair @ SY270 @ SY271 ) ) )
| ( in @ SY303 @ SV89 ) ) )
| ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[883]) ).
thf(911,plain,
! [SV77: $i,SV61: $i] :
( ( ~ ( ~ ~ ( disjoint @ SV61 @ SV77 )
| ~ ! [SY272: $i] :
~ ~ ( ~ ( in @ SY272 @ SV61 )
| ~ ( in @ SY272 @ SV77 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(912,plain,
! [SV77: $i,SV61: $i] :
( ( ~ ( ~ ~ ! [SY273: $i] :
~ ~ ( ~ ( in @ SY273 @ SV61 )
| ~ ( in @ SY273 @ SV77 ) )
| ~ ( disjoint @ SV61 @ SV77 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(913,plain,
! [SV78: $i,SV62: $i,SV90: $i] :
( ( ( SV90
!= ( set_union2 @ SV62 @ SV78 ) )
| ! [SY308: $i] :
~ ( ~ ( ~ ( in @ SY308 @ SV90 )
| ( in @ SY308 @ SV62 )
| ( in @ SY308 @ SV78 ) )
| ~ ( ~ ( ( in @ SY308 @ SV62 )
| ( in @ SY308 @ SV78 ) )
| ( in @ SY308 @ SV90 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[886]) ).
thf(914,plain,
! [SV78: $i,SV62: $i,SV90: $i] :
( ( ~ ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SV90 )
| ( in @ SY309 @ SV62 )
| ( in @ SY309 @ SV78 ) )
| ~ ( ~ ( ( in @ SY309 @ SV62 )
| ( in @ SY309 @ SV78 ) )
| ( in @ SY309 @ SV90 ) ) )
| ( SV90
= ( set_union2 @ SV62 @ SV78 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(915,plain,
! [SV63: $i,SV79: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 ) )
| ~ ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 ) ) )
= $true )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[888]) ).
thf(916,plain,
! [SV80: $i,SV64: $i] :
( ( ( in @ SV64 @ SV80 )
= $false )
| ( ( ~ ( empty @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(917,plain,
! [SV82: $i,SV66: $i,SV91: $i] :
( ( ( SV91
!= ( set_difference @ SV66 @ SV82 ) )
| ! [SY310: $i] :
~ ( ~ ( ~ ( in @ SY310 @ SV91 )
| ~ ( ~ ( in @ SY310 @ SV66 )
| ~ ~ ( in @ SY310 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY310 @ SV66 )
| ~ ~ ( in @ SY310 @ SV82 ) )
| ( in @ SY310 @ SV91 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[891]) ).
thf(918,plain,
! [SV82: $i,SV66: $i,SV91: $i] :
( ( ~ ! [SY311: $i] :
~ ( ~ ( ~ ( in @ SY311 @ SV91 )
| ~ ( ~ ( in @ SY311 @ SV66 )
| ~ ~ ( in @ SY311 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY311 @ SV66 )
| ~ ~ ( in @ SY311 @ SV82 ) )
| ( in @ SY311 @ SV91 ) ) )
| ( SV91
= ( set_difference @ SV66 @ SV82 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(919,plain,
! [SV95: $i,SV92: $i,SV83: $i,SV67: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
| ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(920,plain,
! [SV95: $i,SV83: $i,SV92: $i,SV67: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) )
| ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[893]) ).
thf(921,plain,
! [SV68: $i,SV84: $i] :
( ( ( SV84
!= ( union @ SV68 ) )
= $true )
| ( ( ! [SY283: $i] :
~ ( ~ ( ~ ( in @ SY283 @ SV84 )
| ~ ! [SY239: $i] :
~ ~ ( ~ ( in @ SY283 @ SY239 )
| ~ ( in @ SY239 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY283 @ SY240 )
| ~ ( in @ SY240 @ SV68 ) )
| ( in @ SY283 @ SV84 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[894]) ).
thf(922,plain,
! [SV68: $i,SV84: $i] :
( ( ( ~ ! [SY286: $i] :
~ ( ~ ( ~ ( in @ SY286 @ SV84 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( in @ SY286 @ SY242 )
| ~ ( in @ SY242 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( in @ SY286 @ SY243 )
| ~ ( in @ SY243 @ SV68 ) )
| ( in @ SY286 @ SV84 ) ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(923,plain,
! [SV69: $i] :
( ( ( SV69 = empty_set )
= $false )
| ( ( ! [SY244: $i] :
~ ( in @ SY244 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(924,plain,
! [SV69: $i] :
( ( ( ! [SY245: $i] :
~ ( in @ SY245 @ SV69 ) )
= $false )
| ( ( SV69 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(925,plain,
! [SV70: $i,SV85: $i] :
( ( ( SV85
!= ( singleton @ SV70 ) )
= $true )
| ( ( ! [SY289: $i] :
~ ( ~ ( ~ ( in @ SY289 @ SV85 )
| ( SY289 = SV70 ) )
| ~ ( ( SY289 != SV70 )
| ( in @ SY289 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(926,plain,
! [SV70: $i,SV85: $i] :
( ( ( ~ ! [SY290: $i] :
~ ( ~ ( ~ ( in @ SY290 @ SV85 )
| ( SY290 = SV70 ) )
| ~ ( ( SY290 != SV70 )
| ( in @ SY290 @ SV85 ) ) ) )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(927,plain,
! [SV96: $i,SV93: $i,SV86: $i,SV71: $i] :
( ( ( ( ordered_pair @ SV71 @ SV86 )
= ( ordered_pair @ SV93 @ SV96 ) )
= $false )
| ( ( ~ ( ( SV71 != SV93 )
| ( SV86 != SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(928,plain,
( ( in @ sK1_A @ sK3_SY62 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[901]) ).
thf(929,plain,
( ( in @ sK2_SY59 @ sK4_SY64 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[902]) ).
thf(930,plain,
! [SV87: $i,SV72: $i,SV94: $i] :
( ( ( SV94
!= ( unordered_pair @ SV72 @ SV87 ) )
| ! [SY314: $i] :
~ ( ~ ( ~ ( in @ SY314 @ SV94 )
| ( SY314 = SV72 )
| ( SY314 = SV87 ) )
| ~ ( ~ ( ( SY314 = SV72 )
| ( SY314 = SV87 ) )
| ( in @ SY314 @ SV94 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(931,plain,
! [SV87: $i,SV72: $i,SV94: $i] :
( ( ~ ! [SY315: $i] :
~ ( ~ ( ~ ( in @ SY315 @ SV94 )
| ( SY315 = SV72 )
| ( SY315 = SV87 ) )
| ~ ( ~ ( ( SY315 = SV72 )
| ( SY315 = SV87 ) )
| ( in @ SY315 @ SV94 ) ) )
| ( SV94
= ( unordered_pair @ SV72 @ SV87 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(932,plain,
! [SV74: $i,SV58: $i,SV88: $i] :
( ( ( SV88
!= ( set_intersection2 @ SV58 @ SV74 ) )
= $true )
| ( ( ! [SY296: $i] :
~ ( ~ ( ~ ( in @ SY296 @ SV88 )
| ~ ( ~ ( in @ SY296 @ SV58 )
| ~ ( in @ SY296 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY296 @ SV58 )
| ~ ( in @ SY296 @ SV74 ) )
| ( in @ SY296 @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(933,plain,
! [SV74: $i,SV58: $i,SV88: $i] :
( ( ( ~ ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SV88 )
| ~ ( ~ ( in @ SY297 @ SV58 )
| ~ ( in @ SY297 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY297 @ SV58 )
| ~ ( in @ SY297 @ SV74 ) )
| ( in @ SY297 @ SV88 ) ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(934,plain,
! [SV75: $i,SV59: $i] :
( ( ( subset @ SV59 @ SV75 )
= $false )
| ( ( ! [SY259: $i] :
( ~ ( in @ SY259 @ SV59 )
| ( in @ SY259 @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(935,plain,
! [SV75: $i,SV59: $i] :
( ( ( ! [SY260: $i] :
( ~ ( in @ SY260 @ SV59 )
| ( in @ SY260 @ SV75 ) ) )
= $false )
| ( ( subset @ SV59 @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(936,plain,
! [SV76: $i,SV60: $i,SV89: $i] :
( ( ( SV89
!= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true )
| ( ( ! [SY298: $i] :
~ ( ~ ( ~ ( in @ SY298 @ SV89 )
| ~ ! [SY263: $i] :
~ ~ ! [SY264: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY263 @ SV60 )
| ~ ( in @ SY264 @ SV76 ) )
| ( SY298
!= ( ordered_pair @ SY263 @ SY264 ) ) ) )
| ~ ( ~ ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY265 @ SV60 )
| ~ ( in @ SY266 @ SV76 ) )
| ( SY298
!= ( ordered_pair @ SY265 @ SY266 ) ) )
| ( in @ SY298 @ SV89 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(937,plain,
! [SV76: $i,SV60: $i,SV89: $i] :
( ( ( ~ ! [SY303: $i] :
~ ( ~ ( ~ ( in @ SY303 @ SV89 )
| ~ ! [SY268: $i] :
~ ~ ! [SY269: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY268 @ SV60 )
| ~ ( in @ SY269 @ SV76 ) )
| ( SY303
!= ( ordered_pair @ SY268 @ SY269 ) ) ) )
| ~ ( ~ ~ ! [SY270: $i] :
~ ~ ! [SY271: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY270 @ SV60 )
| ~ ( in @ SY271 @ SV76 ) )
| ( SY303
!= ( ordered_pair @ SY270 @ SY271 ) ) )
| ( in @ SY303 @ SV89 ) ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(938,plain,
! [SV77: $i,SV61: $i] :
( ( ~ ~ ( disjoint @ SV61 @ SV77 )
| ~ ! [SY272: $i] :
~ ~ ( ~ ( in @ SY272 @ SV61 )
| ~ ( in @ SY272 @ SV77 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[911]) ).
thf(939,plain,
! [SV77: $i,SV61: $i] :
( ( ~ ~ ! [SY273: $i] :
~ ~ ( ~ ( in @ SY273 @ SV61 )
| ~ ( in @ SY273 @ SV77 ) )
| ~ ( disjoint @ SV61 @ SV77 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[912]) ).
thf(940,plain,
! [SV78: $i,SV62: $i,SV90: $i] :
( ( ( SV90
!= ( set_union2 @ SV62 @ SV78 ) )
= $true )
| ( ( ! [SY308: $i] :
~ ( ~ ( ~ ( in @ SY308 @ SV90 )
| ( in @ SY308 @ SV62 )
| ( in @ SY308 @ SV78 ) )
| ~ ( ~ ( ( in @ SY308 @ SV62 )
| ( in @ SY308 @ SV78 ) )
| ( in @ SY308 @ SV90 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(941,plain,
! [SV78: $i,SV62: $i,SV90: $i] :
( ( ( ~ ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SV90 )
| ( in @ SY309 @ SV62 )
| ( in @ SY309 @ SV78 ) )
| ~ ( ~ ( ( in @ SY309 @ SV62 )
| ( in @ SY309 @ SV78 ) )
| ( in @ SY309 @ SV90 ) ) ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(942,plain,
! [SV63: $i,SV79: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 ) ) )
= $true )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(943,plain,
! [SV64: $i,SV80: $i] :
( ( ( empty @ SV80 )
= $false )
| ( ( in @ SV64 @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(944,plain,
! [SV82: $i,SV66: $i,SV91: $i] :
( ( ( SV91
!= ( set_difference @ SV66 @ SV82 ) )
= $true )
| ( ( ! [SY310: $i] :
~ ( ~ ( ~ ( in @ SY310 @ SV91 )
| ~ ( ~ ( in @ SY310 @ SV66 )
| ~ ~ ( in @ SY310 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY310 @ SV66 )
| ~ ~ ( in @ SY310 @ SV82 ) )
| ( in @ SY310 @ SV91 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(945,plain,
! [SV82: $i,SV66: $i,SV91: $i] :
( ( ( ~ ! [SY311: $i] :
~ ( ~ ( ~ ( in @ SY311 @ SV91 )
| ~ ( ~ ( in @ SY311 @ SV66 )
| ~ ~ ( in @ SY311 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY311 @ SV66 )
| ~ ~ ( in @ SY311 @ SV82 ) )
| ( in @ SY311 @ SV91 ) ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(946,plain,
! [SV95: $i,SV92: $i,SV83: $i,SV67: $i] :
( ( ~ ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
| ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[919]) ).
thf(947,plain,
! [SV95: $i,SV83: $i,SV92: $i,SV67: $i] :
( ( ~ ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) )
| ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[920]) ).
thf(948,plain,
! [SV68: $i,SV84: $i] :
( ( ( SV84
= ( union @ SV68 ) )
= $false )
| ( ( ! [SY283: $i] :
~ ( ~ ( ~ ( in @ SY283 @ SV84 )
| ~ ! [SY239: $i] :
~ ~ ( ~ ( in @ SY283 @ SY239 )
| ~ ( in @ SY239 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY240: $i] :
~ ~ ( ~ ( in @ SY283 @ SY240 )
| ~ ( in @ SY240 @ SV68 ) )
| ( in @ SY283 @ SV84 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(949,plain,
! [SV68: $i,SV84: $i] :
( ( ( ! [SY286: $i] :
~ ( ~ ( ~ ( in @ SY286 @ SV84 )
| ~ ! [SY242: $i] :
~ ~ ( ~ ( in @ SY286 @ SY242 )
| ~ ( in @ SY242 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY243: $i] :
~ ~ ( ~ ( in @ SY286 @ SY243 )
| ~ ( in @ SY243 @ SV68 ) )
| ( in @ SY286 @ SV84 ) ) ) )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(950,plain,
! [SV69: $i,SV97: $i] :
( ( ( ~ ( in @ SV97 @ SV69 ) )
= $true )
| ( ( SV69 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(951,plain,
! [SV69: $i] :
( ( ( ~ ( in @ ( sK26_SY245 @ SV69 ) @ SV69 ) )
= $false )
| ( ( SV69 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[924]) ).
thf(952,plain,
! [SV70: $i,SV85: $i] :
( ( ( SV85
= ( singleton @ SV70 ) )
= $false )
| ( ( ! [SY289: $i] :
~ ( ~ ( ~ ( in @ SY289 @ SV85 )
| ( SY289 = SV70 ) )
| ~ ( ( SY289 != SV70 )
| ( in @ SY289 @ SV85 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(953,plain,
! [SV70: $i,SV85: $i] :
( ( ( ! [SY290: $i] :
~ ( ~ ( ~ ( in @ SY290 @ SV85 )
| ( SY290 = SV70 ) )
| ~ ( ( SY290 != SV70 )
| ( in @ SY290 @ SV85 ) ) ) )
= $false )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(954,plain,
! [SV96: $i,SV86: $i,SV93: $i,SV71: $i] :
( ( ( ( SV71 != SV93 )
| ( SV86 != SV96 ) )
= $false )
| ( ( ( ordered_pair @ SV71 @ SV86 )
= ( ordered_pair @ SV93 @ SV96 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(955,plain,
! [SV87: $i,SV72: $i,SV94: $i] :
( ( ( SV94
!= ( unordered_pair @ SV72 @ SV87 ) )
= $true )
| ( ( ! [SY314: $i] :
~ ( ~ ( ~ ( in @ SY314 @ SV94 )
| ( SY314 = SV72 )
| ( SY314 = SV87 ) )
| ~ ( ~ ( ( SY314 = SV72 )
| ( SY314 = SV87 ) )
| ( in @ SY314 @ SV94 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(956,plain,
! [SV87: $i,SV72: $i,SV94: $i] :
( ( ( ~ ! [SY315: $i] :
~ ( ~ ( ~ ( in @ SY315 @ SV94 )
| ( SY315 = SV72 )
| ( SY315 = SV87 ) )
| ~ ( ~ ( ( SY315 = SV72 )
| ( SY315 = SV87 ) )
| ( in @ SY315 @ SV94 ) ) ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(957,plain,
! [SV74: $i,SV58: $i,SV88: $i] :
( ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false )
| ( ( ! [SY296: $i] :
~ ( ~ ( ~ ( in @ SY296 @ SV88 )
| ~ ( ~ ( in @ SY296 @ SV58 )
| ~ ( in @ SY296 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY296 @ SV58 )
| ~ ( in @ SY296 @ SV74 ) )
| ( in @ SY296 @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(958,plain,
! [SV74: $i,SV58: $i,SV88: $i] :
( ( ( ! [SY297: $i] :
~ ( ~ ( ~ ( in @ SY297 @ SV88 )
| ~ ( ~ ( in @ SY297 @ SV58 )
| ~ ( in @ SY297 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY297 @ SV58 )
| ~ ( in @ SY297 @ SV74 ) )
| ( in @ SY297 @ SV88 ) ) ) )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[933]) ).
thf(959,plain,
! [SV75: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV59 )
| ( in @ SV98 @ SV75 ) )
= $true )
| ( ( subset @ SV59 @ SV75 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(960,plain,
! [SV59: $i,SV75: $i] :
( ( ( ~ ( in @ ( sK27_SY260 @ SV75 @ SV59 ) @ SV59 )
| ( in @ ( sK27_SY260 @ SV75 @ SV59 ) @ SV75 ) )
= $false )
| ( ( subset @ SV59 @ SV75 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[935]) ).
thf(961,plain,
! [SV76: $i,SV60: $i,SV89: $i] :
( ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false )
| ( ( ! [SY298: $i] :
~ ( ~ ( ~ ( in @ SY298 @ SV89 )
| ~ ! [SY263: $i] :
~ ~ ! [SY264: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY263 @ SV60 )
| ~ ( in @ SY264 @ SV76 ) )
| ( SY298
!= ( ordered_pair @ SY263 @ SY264 ) ) ) )
| ~ ( ~ ~ ! [SY265: $i] :
~ ~ ! [SY266: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY265 @ SV60 )
| ~ ( in @ SY266 @ SV76 ) )
| ( SY298
!= ( ordered_pair @ SY265 @ SY266 ) ) )
| ( in @ SY298 @ SV89 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[936]) ).
thf(962,plain,
! [SV76: $i,SV60: $i,SV89: $i] :
( ( ( ! [SY303: $i] :
~ ( ~ ( ~ ( in @ SY303 @ SV89 )
| ~ ! [SY268: $i] :
~ ~ ! [SY269: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY268 @ SV60 )
| ~ ( in @ SY269 @ SV76 ) )
| ( SY303
!= ( ordered_pair @ SY268 @ SY269 ) ) ) )
| ~ ( ~ ~ ! [SY270: $i] :
~ ~ ! [SY271: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY270 @ SV60 )
| ~ ( in @ SY271 @ SV76 ) )
| ( SY303
!= ( ordered_pair @ SY270 @ SY271 ) ) )
| ( in @ SY303 @ SV89 ) ) ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(963,plain,
! [SV77: $i,SV61: $i] :
( ( ( ~ ~ ( disjoint @ SV61 @ SV77 ) )
= $true )
| ( ( ~ ! [SY272: $i] :
~ ~ ( ~ ( in @ SY272 @ SV61 )
| ~ ( in @ SY272 @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(964,plain,
! [SV77: $i,SV61: $i] :
( ( ( ~ ~ ! [SY273: $i] :
~ ~ ( ~ ( in @ SY273 @ SV61 )
| ~ ( in @ SY273 @ SV77 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(965,plain,
! [SV78: $i,SV62: $i,SV90: $i] :
( ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false )
| ( ( ! [SY308: $i] :
~ ( ~ ( ~ ( in @ SY308 @ SV90 )
| ( in @ SY308 @ SV62 )
| ( in @ SY308 @ SV78 ) )
| ~ ( ~ ( ( in @ SY308 @ SV62 )
| ( in @ SY308 @ SV78 ) )
| ( in @ SY308 @ SV90 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(966,plain,
! [SV78: $i,SV62: $i,SV90: $i] :
( ( ( ! [SY309: $i] :
~ ( ~ ( ~ ( in @ SY309 @ SV90 )
| ( in @ SY309 @ SV62 )
| ( in @ SY309 @ SV78 ) )
| ~ ( ~ ( ( in @ SY309 @ SV62 )
| ( in @ SY309 @ SV78 ) )
| ( in @ SY309 @ SV90 ) ) ) )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(967,plain,
! [SV63: $i,SV79: $i] :
( ( ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 ) ) )
= $true )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[942]) ).
thf(968,plain,
! [SV82: $i,SV66: $i,SV91: $i] :
( ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false )
| ( ( ! [SY310: $i] :
~ ( ~ ( ~ ( in @ SY310 @ SV91 )
| ~ ( ~ ( in @ SY310 @ SV66 )
| ~ ~ ( in @ SY310 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY310 @ SV66 )
| ~ ~ ( in @ SY310 @ SV82 ) )
| ( in @ SY310 @ SV91 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(969,plain,
! [SV82: $i,SV66: $i,SV91: $i] :
( ( ( ! [SY311: $i] :
~ ( ~ ( ~ ( in @ SY311 @ SV91 )
| ~ ( ~ ( in @ SY311 @ SV66 )
| ~ ~ ( in @ SY311 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY311 @ SV66 )
| ~ ~ ( in @ SY311 @ SV82 ) )
| ( in @ SY311 @ SV91 ) ) ) )
= $false )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(970,plain,
! [SV95: $i,SV92: $i,SV83: $i,SV67: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(971,plain,
! [SV95: $i,SV83: $i,SV92: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(972,plain,
! [SV68: $i,SV84: $i,SV99: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV99 @ SV84 )
| ~ ! [SY316: $i] :
~ ~ ( ~ ( in @ SV99 @ SY316 )
| ~ ( in @ SY316 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY317: $i] :
~ ~ ( ~ ( in @ SV99 @ SY317 )
| ~ ( in @ SY317 @ SV68 ) )
| ( in @ SV99 @ SV84 ) ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(973,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
| ~ ! [SY318: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY318 )
| ~ ( in @ SY318 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) ) )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[949]) ).
thf(974,plain,
! [SV69: $i,SV97: $i] :
( ( ( in @ SV97 @ SV69 )
= $false )
| ( ( SV69 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(975,plain,
! [SV69: $i] :
( ( ( in @ ( sK26_SY245 @ SV69 ) @ SV69 )
= $true )
| ( ( SV69 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(976,plain,
! [SV70: $i,SV85: $i,SV100: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV100 @ SV85 )
| ( SV100 = SV70 ) )
| ~ ( ( SV100 != SV70 )
| ( in @ SV100 @ SV85 ) ) ) )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(977,plain,
! [SV85: $i,SV70: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 )
| ( ( sK29_SY290 @ SV70 @ SV85 )
= SV70 ) )
| ~ ( ( ( sK29_SY290 @ SV70 @ SV85 )
!= SV70 )
| ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 ) ) ) )
= $false )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[953]) ).
thf(978,plain,
! [SV96: $i,SV86: $i,SV93: $i,SV71: $i] :
( ( ( SV71 != SV93 )
= $false )
| ( ( ( ordered_pair @ SV71 @ SV86 )
= ( ordered_pair @ SV93 @ SV96 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(979,plain,
! [SV93: $i,SV71: $i,SV96: $i,SV86: $i] :
( ( ( SV86 != SV96 )
= $false )
| ( ( ( ordered_pair @ SV71 @ SV86 )
= ( ordered_pair @ SV93 @ SV96 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[954]) ).
thf(980,plain,
! [SV87: $i,SV72: $i,SV94: $i] :
( ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false )
| ( ( ! [SY314: $i] :
~ ( ~ ( ~ ( in @ SY314 @ SV94 )
| ( SY314 = SV72 )
| ( SY314 = SV87 ) )
| ~ ( ~ ( ( SY314 = SV72 )
| ( SY314 = SV87 ) )
| ( in @ SY314 @ SV94 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(981,plain,
! [SV87: $i,SV72: $i,SV94: $i] :
( ( ( ! [SY315: $i] :
~ ( ~ ( ~ ( in @ SY315 @ SV94 )
| ( SY315 = SV72 )
| ( SY315 = SV87 ) )
| ~ ( ~ ( ( SY315 = SV72 )
| ( SY315 = SV87 ) )
| ( in @ SY315 @ SV94 ) ) ) )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(982,plain,
! [SV74: $i,SV58: $i,SV88: $i,SV101: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV101 @ SV88 )
| ~ ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) )
| ( in @ SV101 @ SV88 ) ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(983,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
| ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) ) ) )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[958]) ).
thf(984,plain,
! [SV75: $i,SV59: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV59 ) )
= $true )
| ( ( in @ SV98 @ SV75 )
= $true )
| ( ( subset @ SV59 @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[959]) ).
thf(985,plain,
! [SV59: $i,SV75: $i] :
( ( ( ~ ( in @ ( sK27_SY260 @ SV75 @ SV59 ) @ SV59 ) )
= $false )
| ( ( subset @ SV59 @ SV75 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[960]) ).
thf(986,plain,
! [SV59: $i,SV75: $i] :
( ( ( in @ ( sK27_SY260 @ SV75 @ SV59 ) @ SV75 )
= $false )
| ( ( subset @ SV59 @ SV75 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[960]) ).
thf(987,plain,
! [SV76: $i,SV60: $i,SV89: $i,SV102: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV102 @ SV89 )
| ~ ! [SY320: $i] :
~ ~ ! [SY321: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY320 @ SV60 )
| ~ ( in @ SY321 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY320 @ SY321 ) ) ) )
| ~ ( ~ ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV60 )
| ~ ( in @ SY323 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY322 @ SY323 ) ) )
| ( in @ SV102 @ SV89 ) ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(988,plain,
! [SV89: $i,SV60: $i,SV76: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
| ~ ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV60 )
| ~ ( in @ SY325 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY324 @ SY325 ) ) ) )
| ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[962]) ).
thf(989,plain,
! [SV77: $i,SV61: $i] :
( ( ( ~ ( disjoint @ SV61 @ SV77 ) )
= $false )
| ( ( ~ ! [SY272: $i] :
~ ~ ( ~ ( in @ SY272 @ SV61 )
| ~ ( in @ SY272 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(990,plain,
! [SV77: $i,SV61: $i] :
( ( ( ~ ! [SY273: $i] :
~ ~ ( ~ ( in @ SY273 @ SV61 )
| ~ ( in @ SY273 @ SV77 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(991,plain,
! [SV78: $i,SV62: $i,SV90: $i,SV103: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV103 @ SV90 )
| ( in @ SV103 @ SV62 )
| ( in @ SV103 @ SV78 ) )
| ~ ( ~ ( ( in @ SV103 @ SV62 )
| ( in @ SV103 @ SV78 ) )
| ( in @ SV103 @ SV90 ) ) ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(992,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ~ ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) ) ) )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[966]) ).
thf(993,plain,
! [SV63: $i,SV79: $i] :
( ( ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 ) ) )
= $true )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[967]) ).
thf(994,plain,
! [SV63: $i,SV79: $i] :
( ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 ) ) )
= $true )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[967]) ).
thf(995,plain,
! [SV82: $i,SV66: $i,SV91: $i,SV104: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV104 @ SV91 )
| ~ ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) )
| ( in @ SV104 @ SV91 ) ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(996,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
| ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) ) ) )
= $false )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[969]) ).
thf(997,plain,
! [SV95: $i,SV92: $i,SV83: $i,SV67: $i] :
( ( ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(998,plain,
! [SV95: $i,SV83: $i,SV92: $i,SV67: $i] :
( ( ( ~ ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) ) )
= $false )
| ( ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(999,plain,
! [SV68: $i,SV84: $i,SV99: $i] :
( ( ( ~ ( ~ ( in @ SV99 @ SV84 )
| ~ ! [SY316: $i] :
~ ~ ( ~ ( in @ SV99 @ SY316 )
| ~ ( in @ SY316 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY317: $i] :
~ ~ ( ~ ( in @ SV99 @ SY317 )
| ~ ( in @ SY317 @ SV68 ) )
| ( in @ SV99 @ SV84 ) ) )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1000,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
| ~ ! [SY318: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY318 )
| ~ ( in @ SY318 @ SV68 ) ) )
| ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(1001,plain,
! [SV70: $i,SV85: $i,SV100: $i] :
( ( ( ~ ( ~ ( in @ SV100 @ SV85 )
| ( SV100 = SV70 ) )
| ~ ( ( SV100 != SV70 )
| ( in @ SV100 @ SV85 ) ) )
= $false )
| ( ( SV85
= ( singleton @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1002,plain,
! [SV85: $i,SV70: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 )
| ( ( sK29_SY290 @ SV70 @ SV85 )
= SV70 ) )
| ~ ( ( ( sK29_SY290 @ SV70 @ SV85 )
!= SV70 )
| ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[977]) ).
thf(1003,plain,
! [SV96: $i,SV86: $i,SV93: $i,SV71: $i] :
( ( ( SV71 = SV93 )
= $true )
| ( ( ( ordered_pair @ SV71 @ SV86 )
= ( ordered_pair @ SV93 @ SV96 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[978]) ).
thf(1004,plain,
! [SV93: $i,SV71: $i,SV96: $i,SV86: $i] :
( ( ( SV86 = SV96 )
= $true )
| ( ( ( ordered_pair @ SV71 @ SV86 )
= ( ordered_pair @ SV93 @ SV96 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[979]) ).
thf(1005,plain,
! [SV87: $i,SV72: $i,SV94: $i,SV105: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV105 @ SV94 )
| ( SV105 = SV72 )
| ( SV105 = SV87 ) )
| ~ ( ~ ( ( SV105 = SV72 )
| ( SV105 = SV87 ) )
| ( in @ SV105 @ SV94 ) ) ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1006,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ~ ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) ) ) )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[981]) ).
thf(1007,plain,
! [SV74: $i,SV58: $i,SV88: $i,SV101: $i] :
( ( ( ~ ( ~ ( in @ SV101 @ SV88 )
| ~ ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) )
| ( in @ SV101 @ SV88 ) ) )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1008,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
| ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[983]) ).
thf(1009,plain,
! [SV75: $i,SV59: $i,SV98: $i] :
( ( ( in @ SV98 @ SV59 )
= $false )
| ( ( in @ SV98 @ SV75 )
= $true )
| ( ( subset @ SV59 @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1010,plain,
! [SV59: $i,SV75: $i] :
( ( ( in @ ( sK27_SY260 @ SV75 @ SV59 ) @ SV59 )
= $true )
| ( ( subset @ SV59 @ SV75 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[985]) ).
thf(1011,plain,
! [SV76: $i,SV60: $i,SV89: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ SV102 @ SV89 )
| ~ ! [SY320: $i] :
~ ~ ! [SY321: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY320 @ SV60 )
| ~ ( in @ SY321 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY320 @ SY321 ) ) ) )
| ~ ( ~ ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV60 )
| ~ ( in @ SY323 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY322 @ SY323 ) ) )
| ( in @ SV102 @ SV89 ) ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1012,plain,
! [SV89: $i,SV60: $i,SV76: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
| ~ ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV60 )
| ~ ( in @ SY325 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY324 @ SY325 ) ) ) )
| ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(1013,plain,
! [SV77: $i,SV61: $i] :
( ( ( disjoint @ SV61 @ SV77 )
= $true )
| ( ( ~ ! [SY272: $i] :
~ ~ ( ~ ( in @ SY272 @ SV61 )
| ~ ( in @ SY272 @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(1014,plain,
! [SV77: $i,SV61: $i] :
( ( ( ! [SY273: $i] :
~ ~ ( ~ ( in @ SY273 @ SV61 )
| ~ ( in @ SY273 @ SV77 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[990]) ).
thf(1015,plain,
! [SV78: $i,SV62: $i,SV90: $i,SV103: $i] :
( ( ( ~ ( ~ ( in @ SV103 @ SV90 )
| ( in @ SV103 @ SV62 )
| ( in @ SV103 @ SV78 ) )
| ~ ( ~ ( ( in @ SV103 @ SV62 )
| ( in @ SV103 @ SV78 ) )
| ( in @ SV103 @ SV90 ) ) )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1016,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ~ ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[992]) ).
thf(1017,plain,
! [SV63: $i,SV79: $i] :
( ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 ) ) )
= $true )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[993]) ).
thf(1018,plain,
! [SV63: $i,SV79: $i] :
( ( ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 ) )
= $false )
| ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
= $false )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1019,plain,
! [SV82: $i,SV66: $i,SV91: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ SV104 @ SV91 )
| ~ ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) )
| ( in @ SV104 @ SV91 ) ) )
= $false )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[995]) ).
thf(1020,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
| ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(1021,plain,
! [SV95: $i,SV83: $i,SV92: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1022,plain,
! [SV95: $i,SV83: $i,SV92: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV92 )
| ~ ( in @ SV83 @ SV95 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[998]) ).
thf(1023,plain,
! [SV68: $i,SV84: $i,SV99: $i] :
( ( ( ~ ( ~ ( in @ SV99 @ SV84 )
| ~ ! [SY316: $i] :
~ ~ ( ~ ( in @ SV99 @ SY316 )
| ~ ( in @ SY316 @ SV68 ) ) ) )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1024,plain,
! [SV84: $i,SV68: $i,SV99: $i] :
( ( ( ~ ( ~ ~ ! [SY317: $i] :
~ ~ ( ~ ( in @ SV99 @ SY317 )
| ~ ( in @ SY317 @ SV68 ) )
| ( in @ SV99 @ SV84 ) ) )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1025,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
| ~ ! [SY318: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY318 )
| ~ ( in @ SY318 @ SV68 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1026,plain,
! [SV70: $i,SV85: $i,SV100: $i] :
( ( ( ~ ( ~ ( in @ SV100 @ SV85 )
| ( SV100 = SV70 ) ) )
= $false )
| ( ( SV85
= ( singleton @ SV70 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1027,plain,
! [SV85: $i,SV70: $i,SV100: $i] :
( ( ( ~ ( ( SV100 != SV70 )
| ( in @ SV100 @ SV85 ) ) )
= $false )
| ( ( SV85
= ( singleton @ SV70 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1028,plain,
! [SV85: $i,SV70: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 )
| ( ( sK29_SY290 @ SV70 @ SV85 )
= SV70 ) ) )
= $true )
| ( ( ~ ( ( ( sK29_SY290 @ SV70 @ SV85 )
!= SV70 )
| ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1029,plain,
! [SV87: $i,SV72: $i,SV94: $i,SV105: $i] :
( ( ( ~ ( ~ ( in @ SV105 @ SV94 )
| ( SV105 = SV72 )
| ( SV105 = SV87 ) )
| ~ ( ~ ( ( SV105 = SV72 )
| ( SV105 = SV87 ) )
| ( in @ SV105 @ SV94 ) ) )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1005]) ).
thf(1030,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ~ ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1031,plain,
! [SV74: $i,SV58: $i,SV88: $i,SV101: $i] :
( ( ( ~ ( ~ ( in @ SV101 @ SV88 )
| ~ ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) ) ) )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1007]) ).
thf(1032,plain,
! [SV88: $i,SV74: $i,SV58: $i,SV101: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) )
| ( in @ SV101 @ SV88 ) ) )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1007]) ).
thf(1033,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
| ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1034,plain,
! [SV76: $i,SV60: $i,SV89: $i,SV102: $i] :
( ( ( ~ ( ~ ( in @ SV102 @ SV89 )
| ~ ! [SY320: $i] :
~ ~ ! [SY321: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY320 @ SV60 )
| ~ ( in @ SY321 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY320 @ SY321 ) ) ) ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1011]) ).
thf(1035,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV60: $i] :
( ( ( ~ ( ~ ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV60 )
| ~ ( in @ SY323 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY322 @ SY323 ) ) )
| ( in @ SV102 @ SV89 ) ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1011]) ).
thf(1036,plain,
! [SV89: $i,SV60: $i,SV76: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
| ~ ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV60 )
| ~ ( in @ SY325 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY324 @ SY325 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1012]) ).
thf(1037,plain,
! [SV77: $i,SV61: $i] :
( ( ( ! [SY272: $i] :
~ ~ ( ~ ( in @ SY272 @ SV61 )
| ~ ( in @ SY272 @ SV77 ) ) )
= $false )
| ( ( disjoint @ SV61 @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1013]) ).
thf(1038,plain,
! [SV77: $i,SV61: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( in @ SV106 @ SV61 )
| ~ ( in @ SV106 @ SV77 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1039,plain,
! [SV78: $i,SV62: $i,SV90: $i,SV103: $i] :
( ( ( ~ ( ~ ( in @ SV103 @ SV90 )
| ( in @ SV103 @ SV62 )
| ( in @ SV103 @ SV78 ) ) )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1040,plain,
! [SV90: $i,SV78: $i,SV62: $i,SV103: $i] :
( ( ( ~ ( ~ ( ( in @ SV103 @ SV62 )
| ( in @ SV103 @ SV78 ) )
| ( in @ SV103 @ SV90 ) ) )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1015]) ).
thf(1041,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ~ ( ~ ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) ) )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1042,plain,
! [SV63: $i,SV79: $i] :
( ( ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
| ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 ) )
= $false )
| ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 )
= $true )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1043,plain,
! [SV63: $i,SV79: $i] :
( ( ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 ) )
= $false )
| ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
= $false )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1044,plain,
! [SV63: $i,SV79: $i] :
( ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 )
= $false )
| ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
= $false )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1018]) ).
thf(1045,plain,
! [SV82: $i,SV66: $i,SV91: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ SV104 @ SV91 )
| ~ ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) ) ) )
= $false )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1046,plain,
! [SV91: $i,SV82: $i,SV66: $i,SV104: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) )
| ( in @ SV104 @ SV91 ) ) )
= $false )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1019]) ).
thf(1047,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
| ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1048,plain,
! [SV95: $i,SV83: $i,SV92: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV92 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1021]) ).
thf(1049,plain,
! [SV92: $i,SV67: $i,SV95: $i,SV83: $i] :
( ( ( ~ ( in @ SV83 @ SV95 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1021]) ).
thf(1050,plain,
! [SV95: $i,SV83: $i,SV92: $i,SV67: $i] :
( ( ( ~ ( in @ SV67 @ SV92 ) )
= $true )
| ( ( ~ ( in @ SV83 @ SV95 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1051,plain,
! [SV68: $i,SV84: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ SV84 )
| ~ ! [SY316: $i] :
~ ~ ( ~ ( in @ SV99 @ SY316 )
| ~ ( in @ SY316 @ SV68 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1023]) ).
thf(1052,plain,
! [SV84: $i,SV68: $i,SV99: $i] :
( ( ( ~ ~ ! [SY317: $i] :
~ ~ ( ~ ( in @ SV99 @ SY317 )
| ~ ( in @ SY317 @ SV68 ) )
| ( in @ SV99 @ SV84 ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1024]) ).
thf(1053,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
| ~ ! [SY318: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY318 )
| ~ ( in @ SY318 @ SV68 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1054,plain,
! [SV70: $i,SV85: $i,SV100: $i] :
( ( ( ~ ( in @ SV100 @ SV85 )
| ( SV100 = SV70 ) )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1026]) ).
thf(1055,plain,
! [SV85: $i,SV70: $i,SV100: $i] :
( ( ( ( SV100 != SV70 )
| ( in @ SV100 @ SV85 ) )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1027]) ).
thf(1056,plain,
! [SV85: $i,SV70: $i] :
( ( ( ~ ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 )
| ( ( sK29_SY290 @ SV70 @ SV85 )
= SV70 ) )
= $false )
| ( ( ~ ( ( ( sK29_SY290 @ SV70 @ SV85 )
!= SV70 )
| ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1057,plain,
! [SV87: $i,SV72: $i,SV94: $i,SV105: $i] :
( ( ( ~ ( ~ ( in @ SV105 @ SV94 )
| ( SV105 = SV72 )
| ( SV105 = SV87 ) ) )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1058,plain,
! [SV94: $i,SV87: $i,SV72: $i,SV105: $i] :
( ( ( ~ ( ~ ( ( SV105 = SV72 )
| ( SV105 = SV87 ) )
| ( in @ SV105 @ SV94 ) ) )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1029]) ).
thf(1059,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1060,plain,
! [SV74: $i,SV58: $i,SV88: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ SV88 )
| ~ ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1031]) ).
thf(1061,plain,
! [SV88: $i,SV74: $i,SV58: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) )
| ( in @ SV101 @ SV88 ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1032]) ).
thf(1062,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
| ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1063,plain,
! [SV76: $i,SV60: $i,SV89: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ SV89 )
| ~ ! [SY320: $i] :
~ ~ ! [SY321: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY320 @ SV60 )
| ~ ( in @ SY321 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY320 @ SY321 ) ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1034]) ).
thf(1064,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV60: $i] :
( ( ( ~ ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV60 )
| ~ ( in @ SY323 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY322 @ SY323 ) ) )
| ( in @ SV102 @ SV89 ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1035]) ).
thf(1065,plain,
! [SV89: $i,SV60: $i,SV76: $i] :
( ( ( ~ ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
| ~ ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV60 )
| ~ ( in @ SY325 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY324 @ SY325 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1066,plain,
! [SV61: $i,SV77: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK35_SY272 @ SV77 @ SV61 ) @ SV61 )
| ~ ( in @ ( sK35_SY272 @ SV77 @ SV61 ) @ SV77 ) ) )
= $false )
| ( ( disjoint @ SV61 @ SV77 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1037]) ).
thf(1067,plain,
! [SV77: $i,SV61: $i,SV106: $i] :
( ( ( ~ ( ~ ( in @ SV106 @ SV61 )
| ~ ( in @ SV106 @ SV77 ) ) )
= $false )
| ( ( ~ ( disjoint @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1068,plain,
! [SV78: $i,SV62: $i,SV90: $i,SV103: $i] :
( ( ( ~ ( in @ SV103 @ SV90 )
| ( in @ SV103 @ SV62 )
| ( in @ SV103 @ SV78 ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1039]) ).
thf(1069,plain,
! [SV90: $i,SV78: $i,SV62: $i,SV103: $i] :
( ( ( ~ ( ( in @ SV103 @ SV62 )
| ( in @ SV103 @ SV78 ) )
| ( in @ SV103 @ SV90 ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1070,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ~ ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1071,plain,
! [SV63: $i,SV79: $i] :
( ( ( ~ ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 ) )
= $false )
| ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 )
= $true )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1072,plain,
! [SV63: $i,SV79: $i] :
( ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 )
= $false )
| ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 )
= $true )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1042]) ).
thf(1073,plain,
! [SV63: $i,SV79: $i] :
( ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
= $true )
| ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
= $false )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1074,plain,
! [SV82: $i,SV66: $i,SV91: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV91 )
| ~ ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1075,plain,
! [SV91: $i,SV82: $i,SV66: $i,SV104: $i] :
( ( ( ~ ~ ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) )
| ( in @ SV104 @ SV91 ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1046]) ).
thf(1076,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
| ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1077,plain,
! [SV95: $i,SV83: $i,SV92: $i,SV67: $i] :
( ( ( in @ SV67 @ SV92 )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1048]) ).
thf(1078,plain,
! [SV92: $i,SV67: $i,SV95: $i,SV83: $i] :
( ( ( in @ SV83 @ SV95 )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1049]) ).
thf(1079,plain,
! [SV95: $i,SV83: $i,SV92: $i,SV67: $i] :
( ( ( in @ SV67 @ SV92 )
= $false )
| ( ( ~ ( in @ SV83 @ SV95 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1080,plain,
! [SV68: $i,SV84: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ SV84 ) )
= $true )
| ( ( ~ ! [SY316: $i] :
~ ~ ( ~ ( in @ SV99 @ SY316 )
| ~ ( in @ SY316 @ SV68 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1081,plain,
! [SV84: $i,SV68: $i,SV99: $i] :
( ( ( ~ ~ ! [SY317: $i] :
~ ~ ( ~ ( in @ SV99 @ SY317 )
| ~ ( in @ SY317 @ SV68 ) ) )
= $true )
| ( ( in @ SV99 @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1052]) ).
thf(1082,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1083,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ! [SY318: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY318 )
| ~ ( in @ SY318 @ SV68 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1053]) ).
thf(1084,plain,
! [SV70: $i,SV85: $i,SV100: $i] :
( ( ( ~ ( in @ SV100 @ SV85 ) )
= $true )
| ( ( SV100 = SV70 )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1054]) ).
thf(1085,plain,
! [SV85: $i,SV70: $i,SV100: $i] :
( ( ( SV100 != SV70 )
= $true )
| ( ( in @ SV100 @ SV85 )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1086,plain,
! [SV85: $i,SV70: $i] :
( ( ( ~ ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 ) )
= $false )
| ( ( ~ ( ( ( sK29_SY290 @ SV70 @ SV85 )
!= SV70 )
| ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1087,plain,
! [SV85: $i,SV70: $i] :
( ( ( ( sK29_SY290 @ SV70 @ SV85 )
= SV70 )
= $false )
| ( ( ~ ( ( ( sK29_SY290 @ SV70 @ SV85 )
!= SV70 )
| ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1056]) ).
thf(1088,plain,
! [SV87: $i,SV72: $i,SV94: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV94 )
| ( SV105 = SV72 )
| ( SV105 = SV87 ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1057]) ).
thf(1089,plain,
! [SV94: $i,SV87: $i,SV72: $i,SV105: $i] :
( ( ( ~ ( ( SV105 = SV72 )
| ( SV105 = SV87 ) )
| ( in @ SV105 @ SV94 ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1058]) ).
thf(1090,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ~ ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1091,plain,
! [SV74: $i,SV58: $i,SV88: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ SV88 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1092,plain,
! [SV88: $i,SV74: $i,SV58: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) ) )
= $true )
| ( ( in @ SV101 @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1093,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1094,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1062]) ).
thf(1095,plain,
! [SV76: $i,SV60: $i,SV89: $i,SV102: $i] :
( ( ( ~ ( in @ SV102 @ SV89 ) )
= $true )
| ( ( ~ ! [SY320: $i] :
~ ~ ! [SY321: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY320 @ SV60 )
| ~ ( in @ SY321 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY320 @ SY321 ) ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1063]) ).
thf(1096,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV60: $i] :
( ( ( ~ ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV60 )
| ~ ( in @ SY323 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY322 @ SY323 ) ) ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1097,plain,
! [SV89: $i,SV60: $i,SV76: $i] :
( ( ( ~ ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1098,plain,
! [SV89: $i,SV76: $i,SV60: $i] :
( ( ( ~ ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV60 )
| ~ ( in @ SY325 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY324 @ SY325 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1065]) ).
thf(1099,plain,
! [SV61: $i,SV77: $i] :
( ( ( ~ ( ~ ( in @ ( sK35_SY272 @ SV77 @ SV61 ) @ SV61 )
| ~ ( in @ ( sK35_SY272 @ SV77 @ SV61 ) @ SV77 ) ) )
= $true )
| ( ( disjoint @ SV61 @ SV77 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1066]) ).
thf(1100,plain,
! [SV77: $i,SV61: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ SV61 )
| ~ ( in @ SV106 @ SV77 ) )
= $true )
| ( ( ~ ( disjoint @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1101,plain,
! [SV78: $i,SV62: $i,SV90: $i,SV103: $i] :
( ( ( ~ ( in @ SV103 @ SV90 ) )
= $true )
| ( ( ( in @ SV103 @ SV62 )
| ( in @ SV103 @ SV78 ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1102,plain,
! [SV90: $i,SV78: $i,SV62: $i,SV103: $i] :
( ( ( ~ ( ( in @ SV103 @ SV62 )
| ( in @ SV103 @ SV78 ) ) )
= $true )
| ( ( in @ SV103 @ SV90 )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1103,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ~ ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1104,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1070]) ).
thf(1105,plain,
! [SV63: $i,SV79: $i] :
( ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV79 )
= $true )
| ( ( in @ ( sK25_SY277 @ SV79 @ SV63 ) @ SV63 )
= $true )
| ( ( SV63 = SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1071]) ).
thf(1106,plain,
! [SV82: $i,SV66: $i,SV91: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV91 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1107,plain,
! [SV91: $i,SV82: $i,SV66: $i,SV104: $i] :
( ( ( ~ ~ ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) ) )
= $true )
| ( ( in @ SV104 @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1108,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1109,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1110,plain,
! [SV92: $i,SV67: $i,SV95: $i,SV83: $i] :
( ( ( in @ SV83 @ SV95 )
= $false )
| ( ( in @ SV67 @ SV92 )
= $false )
| ( ( in @ ( ordered_pair @ SV67 @ SV83 ) @ ( cartesian_product2 @ SV92 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1111,plain,
! [SV68: $i,SV84: $i,SV99: $i] :
( ( ( in @ SV99 @ SV84 )
= $false )
| ( ( ~ ! [SY316: $i] :
~ ~ ( ~ ( in @ SV99 @ SY316 )
| ~ ( in @ SY316 @ SV68 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1080]) ).
thf(1112,plain,
! [SV84: $i,SV68: $i,SV99: $i] :
( ( ( ~ ! [SY317: $i] :
~ ~ ( ~ ( in @ SV99 @ SY317 )
| ~ ( in @ SY317 @ SV68 ) ) )
= $false )
| ( ( in @ SV99 @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1113,plain,
! [SV84: $i,SV68: $i] :
( ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1082]) ).
thf(1114,plain,
! [SV84: $i,SV68: $i] :
( ( ( ! [SY318: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY318 )
| ~ ( in @ SY318 @ SV68 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1115,plain,
! [SV70: $i,SV85: $i,SV100: $i] :
( ( ( in @ SV100 @ SV85 )
= $false )
| ( ( SV100 = SV70 )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1116,plain,
! [SV85: $i,SV70: $i,SV100: $i] :
( ( ( SV100 = SV70 )
= $false )
| ( ( in @ SV100 @ SV85 )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1117,plain,
! [SV85: $i,SV70: $i] :
( ( ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 )
= $true )
| ( ( ~ ( ( ( sK29_SY290 @ SV70 @ SV85 )
!= SV70 )
| ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 ) ) )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1086]) ).
thf(1118,plain,
! [SV85: $i,SV70: $i] :
( ( ( ( ( sK29_SY290 @ SV70 @ SV85 )
!= SV70 )
| ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 ) )
= $false )
| ( ( ( sK29_SY290 @ SV70 @ SV85 )
= SV70 )
= $false )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1119,plain,
! [SV87: $i,SV72: $i,SV94: $i,SV105: $i] :
( ( ( ~ ( in @ SV105 @ SV94 ) )
= $true )
| ( ( ( SV105 = SV72 )
| ( SV105 = SV87 ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1120,plain,
! [SV94: $i,SV87: $i,SV72: $i,SV105: $i] :
( ( ( ~ ( ( SV105 = SV72 )
| ( SV105 = SV87 ) ) )
= $true )
| ( ( in @ SV105 @ SV94 )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1121,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ~ ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1122,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1123,plain,
! [SV74: $i,SV58: $i,SV88: $i,SV101: $i] :
( ( ( in @ SV101 @ SV88 )
= $false )
| ( ( ~ ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1124,plain,
! [SV88: $i,SV74: $i,SV58: $i,SV101: $i] :
( ( ( ~ ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) ) )
= $false )
| ( ( in @ SV101 @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1125,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1126,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1127,plain,
! [SV76: $i,SV60: $i,SV89: $i,SV102: $i] :
( ( ( in @ SV102 @ SV89 )
= $false )
| ( ( ~ ! [SY320: $i] :
~ ~ ! [SY321: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY320 @ SV60 )
| ~ ( in @ SY321 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY320 @ SY321 ) ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1095]) ).
thf(1128,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV60: $i] :
( ( ( ~ ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV60 )
| ~ ( in @ SY323 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY322 @ SY323 ) ) ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1096]) ).
thf(1129,plain,
! [SV89: $i,SV60: $i,SV76: $i] :
( ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1097]) ).
thf(1130,plain,
! [SV89: $i,SV76: $i,SV60: $i] :
( ( ( ! [SY324: $i] :
~ ~ ! [SY325: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY324 @ SV60 )
| ~ ( in @ SY325 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY324 @ SY325 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1131,plain,
! [SV61: $i,SV77: $i] :
( ( ( ~ ( in @ ( sK35_SY272 @ SV77 @ SV61 ) @ SV61 )
| ~ ( in @ ( sK35_SY272 @ SV77 @ SV61 ) @ SV77 ) )
= $false )
| ( ( disjoint @ SV61 @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1132,plain,
! [SV77: $i,SV61: $i,SV106: $i] :
( ( ( ~ ( in @ SV106 @ SV61 ) )
= $true )
| ( ( ~ ( in @ SV106 @ SV77 ) )
= $true )
| ( ( ~ ( disjoint @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1133,plain,
! [SV78: $i,SV62: $i,SV90: $i,SV103: $i] :
( ( ( in @ SV103 @ SV90 )
= $false )
| ( ( ( in @ SV103 @ SV62 )
| ( in @ SV103 @ SV78 ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1134,plain,
! [SV90: $i,SV78: $i,SV62: $i,SV103: $i] :
( ( ( ( in @ SV103 @ SV62 )
| ( in @ SV103 @ SV78 ) )
= $false )
| ( ( in @ SV103 @ SV90 )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1135,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
= $true )
| ( ( ~ ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1136,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1137,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 )
= $false )
| ( ( ~ ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) ) )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1104]) ).
thf(1138,plain,
! [SV82: $i,SV66: $i,SV91: $i,SV104: $i] :
( ( ( in @ SV104 @ SV91 )
= $false )
| ( ( ~ ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1106]) ).
thf(1139,plain,
! [SV91: $i,SV82: $i,SV66: $i,SV104: $i] :
( ( ( ~ ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) ) )
= $false )
| ( ( in @ SV104 @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1140,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1108]) ).
thf(1141,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1142,plain,
! [SV84: $i,SV68: $i,SV99: $i] :
( ( ( ! [SY316: $i] :
~ ~ ( ~ ( in @ SV99 @ SY316 )
| ~ ( in @ SY316 @ SV68 ) ) )
= $false )
| ( ( in @ SV99 @ SV84 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1143,plain,
! [SV84: $i,SV68: $i,SV99: $i] :
( ( ( ! [SY317: $i] :
~ ~ ( ~ ( in @ SV99 @ SY317 )
| ~ ( in @ SY317 @ SV68 ) ) )
= $true )
| ( ( in @ SV99 @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1112]) ).
thf(1144,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1145,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
| ~ ( in @ SV107 @ SV68 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1146,plain,
! [SV85: $i,SV70: $i] :
( ( ( ( ( sK29_SY290 @ SV70 @ SV85 )
!= SV70 )
| ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 ) )
= $false )
| ( ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1147,plain,
! [SV85: $i,SV70: $i] :
( ( ( ( sK29_SY290 @ SV70 @ SV85 )
!= SV70 )
= $false )
| ( ( ( sK29_SY290 @ SV70 @ SV85 )
= SV70 )
= $false )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1148,plain,
! [SV85: $i,SV70: $i] :
( ( ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 )
= $false )
| ( ( ( sK29_SY290 @ SV70 @ SV85 )
= SV70 )
= $false )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1149,plain,
! [SV87: $i,SV72: $i,SV94: $i,SV105: $i] :
( ( ( in @ SV105 @ SV94 )
= $false )
| ( ( ( SV105 = SV72 )
| ( SV105 = SV87 ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1150,plain,
! [SV94: $i,SV87: $i,SV72: $i,SV105: $i] :
( ( ( ( SV105 = SV72 )
| ( SV105 = SV87 ) )
= $false )
| ( ( in @ SV105 @ SV94 )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1151,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
= $true )
| ( ( ~ ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1121]) ).
thf(1152,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
= $false )
| ( ( ~ ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1153,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 )
= $false )
| ( ( ~ ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1154,plain,
! [SV88: $i,SV74: $i,SV58: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) )
= $false )
| ( ( in @ SV101 @ SV88 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1123]) ).
thf(1155,plain,
! [SV88: $i,SV74: $i,SV58: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ SV58 )
| ~ ( in @ SV101 @ SV74 ) )
= $true )
| ( ( in @ SV101 @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1124]) ).
thf(1156,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1157,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 ) )
= $true )
| ( ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1158,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV60: $i] :
( ( ( ! [SY320: $i] :
~ ~ ! [SY321: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY320 @ SV60 )
| ~ ( in @ SY321 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY320 @ SY321 ) ) ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1159,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV60: $i] :
( ( ( ! [SY322: $i] :
~ ~ ! [SY323: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY322 @ SV60 )
| ~ ( in @ SY323 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SY322 @ SY323 ) ) ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1128]) ).
thf(1160,plain,
! [SV89: $i,SV76: $i,SV60: $i] :
( ( ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1161,plain,
! [SV89: $i,SV76: $i,SV60: $i,SV108: $i] :
( ( ( ~ ~ ! [SY328: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV108 @ SV60 )
| ~ ( in @ SY328 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SV108 @ SY328 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1162,plain,
! [SV61: $i,SV77: $i] :
( ( ( ~ ( in @ ( sK35_SY272 @ SV77 @ SV61 ) @ SV61 ) )
= $false )
| ( ( disjoint @ SV61 @ SV77 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1163,plain,
! [SV61: $i,SV77: $i] :
( ( ( ~ ( in @ ( sK35_SY272 @ SV77 @ SV61 ) @ SV77 ) )
= $false )
| ( ( disjoint @ SV61 @ SV77 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1131]) ).
thf(1164,plain,
! [SV77: $i,SV61: $i,SV106: $i] :
( ( ( in @ SV106 @ SV61 )
= $false )
| ( ( ~ ( in @ SV106 @ SV77 ) )
= $true )
| ( ( ~ ( disjoint @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1165,plain,
! [SV90: $i,SV78: $i,SV62: $i,SV103: $i] :
( ( ( in @ SV103 @ SV62 )
= $true )
| ( ( in @ SV103 @ SV78 )
= $true )
| ( ( in @ SV103 @ SV90 )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1166,plain,
! [SV78: $i,SV90: $i,SV62: $i,SV103: $i] :
( ( ( in @ SV103 @ SV62 )
= $false )
| ( ( in @ SV103 @ SV90 )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1134]) ).
thf(1167,plain,
! [SV62: $i,SV90: $i,SV78: $i,SV103: $i] :
( ( ( in @ SV103 @ SV78 )
= $false )
| ( ( in @ SV103 @ SV90 )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1134]) ).
thf(1168,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) )
= $false )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1169,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) )
= $false )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1170,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 ) )
= $false )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1171,plain,
! [SV91: $i,SV82: $i,SV66: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) )
= $false )
| ( ( in @ SV104 @ SV91 )
= $false )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1172,plain,
! [SV91: $i,SV82: $i,SV66: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV66 )
| ~ ~ ( in @ SV104 @ SV82 ) )
= $true )
| ( ( in @ SV104 @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1173,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1140]) ).
thf(1174,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1175,plain,
! [SV68: $i,SV84: $i,SV99: $i] :
( ( ( ~ ~ ( ~ ( in @ SV99 @ ( sK36_SY316 @ SV84 @ SV68 @ SV99 ) )
| ~ ( in @ ( sK36_SY316 @ SV84 @ SV68 @ SV99 ) @ SV68 ) ) )
= $false )
| ( ( in @ SV99 @ SV84 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1142]) ).
thf(1176,plain,
! [SV84: $i,SV68: $i,SV109: $i,SV99: $i] :
( ( ( ~ ~ ( ~ ( in @ SV99 @ SV109 )
| ~ ( in @ SV109 @ SV68 ) ) )
= $true )
| ( ( in @ SV99 @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1177,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1144]) ).
thf(1178,plain,
! [SV84: $i,SV68: $i] :
( ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1144]) ).
thf(1179,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
| ~ ( in @ SV107 @ SV68 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1180,plain,
! [SV85: $i,SV70: $i] :
( ( ( ( sK29_SY290 @ SV70 @ SV85 )
!= SV70 )
= $false )
| ( ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1146]) ).
thf(1181,plain,
! [SV85: $i,SV70: $i] :
( ( ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 )
= $false )
| ( ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1146]) ).
thf(1182,plain,
! [SV85: $i,SV70: $i] :
( ( ( ( sK29_SY290 @ SV70 @ SV85 )
= SV70 )
= $true )
| ( ( ( sK29_SY290 @ SV70 @ SV85 )
= SV70 )
= $false )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1147]) ).
thf(1183,plain,
! [SV94: $i,SV87: $i,SV72: $i,SV105: $i] :
( ( ( SV105 = SV72 )
= $true )
| ( ( SV105 = SV87 )
= $true )
| ( ( in @ SV105 @ SV94 )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1149]) ).
thf(1184,plain,
! [SV87: $i,SV94: $i,SV72: $i,SV105: $i] :
( ( ( SV105 = SV72 )
= $false )
| ( ( in @ SV105 @ SV94 )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1150]) ).
thf(1185,plain,
! [SV72: $i,SV94: $i,SV87: $i,SV105: $i] :
( ( ( SV105 = SV87 )
= $false )
| ( ( in @ SV105 @ SV94 )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1150]) ).
thf(1186,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) )
= $false )
| ( ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1187,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) )
= $false )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1152]) ).
thf(1188,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
| ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 ) )
= $false )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1153]) ).
thf(1189,plain,
! [SV74: $i,SV88: $i,SV58: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ SV58 ) )
= $false )
| ( ( in @ SV101 @ SV88 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1154]) ).
thf(1190,plain,
! [SV58: $i,SV88: $i,SV74: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ SV74 ) )
= $false )
| ( ( in @ SV101 @ SV88 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1154]) ).
thf(1191,plain,
! [SV88: $i,SV74: $i,SV58: $i,SV101: $i] :
( ( ( ~ ( in @ SV101 @ SV58 ) )
= $true )
| ( ( ~ ( in @ SV101 @ SV74 ) )
= $true )
| ( ( in @ SV101 @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1192,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) ) )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1156]) ).
thf(1193,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1156]) ).
thf(1194,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $false )
| ( ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1195,plain,
! [SV60: $i,SV76: $i,SV102: $i,SV89: $i] :
( ( ( ~ ~ ! [SY329: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ SY329 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SY329 ) ) ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1158]) ).
thf(1196,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV60: $i,SV110: $i] :
( ( ( ~ ~ ! [SY330: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV110 @ SV60 )
| ~ ( in @ SY330 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SV110 @ SY330 ) ) ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1197,plain,
! [SV89: $i,SV76: $i,SV60: $i] :
( ( ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1160]) ).
thf(1198,plain,
! [SV89: $i,SV60: $i,SV76: $i] :
( ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1160]) ).
thf(1199,plain,
! [SV89: $i,SV76: $i,SV60: $i,SV108: $i] :
( ( ( ~ ! [SY328: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV108 @ SV60 )
| ~ ( in @ SY328 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SV108 @ SY328 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1200,plain,
! [SV61: $i,SV77: $i] :
( ( ( in @ ( sK35_SY272 @ SV77 @ SV61 ) @ SV61 )
= $true )
| ( ( disjoint @ SV61 @ SV77 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1162]) ).
thf(1201,plain,
! [SV61: $i,SV77: $i] :
( ( ( in @ ( sK35_SY272 @ SV77 @ SV61 ) @ SV77 )
= $true )
| ( ( disjoint @ SV61 @ SV77 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1163]) ).
thf(1202,plain,
! [SV61: $i,SV77: $i,SV106: $i] :
( ( ( in @ SV106 @ SV77 )
= $false )
| ( ( in @ SV106 @ SV61 )
= $false )
| ( ( ~ ( disjoint @ SV61 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1203,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) ) )
= $false )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1168]) ).
thf(1204,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
= $false )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1168]) ).
thf(1205,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) ) )
= $false )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1206,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
= $false )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1169]) ).
thf(1207,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ~ ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) ) )
= $false )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1208,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
= $false )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1209,plain,
! [SV82: $i,SV91: $i,SV66: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV66 ) )
= $false )
| ( ( in @ SV104 @ SV91 )
= $false )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1210,plain,
! [SV66: $i,SV91: $i,SV82: $i,SV104: $i] :
( ( ( ~ ~ ( in @ SV104 @ SV82 ) )
= $false )
| ( ( in @ SV104 @ SV91 )
= $false )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1171]) ).
thf(1211,plain,
! [SV91: $i,SV82: $i,SV66: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV66 ) )
= $true )
| ( ( ~ ~ ( in @ SV104 @ SV82 ) )
= $true )
| ( ( in @ SV104 @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1212,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) ) )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1173]) ).
thf(1213,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1173]) ).
thf(1214,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1215,plain,
! [SV68: $i,SV84: $i,SV99: $i] :
( ( ( ~ ( ~ ( in @ SV99 @ ( sK36_SY316 @ SV84 @ SV68 @ SV99 ) )
| ~ ( in @ ( sK36_SY316 @ SV84 @ SV68 @ SV99 ) @ SV68 ) ) )
= $true )
| ( ( in @ SV99 @ SV84 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1175]) ).
thf(1216,plain,
! [SV84: $i,SV68: $i,SV109: $i,SV99: $i] :
( ( ( ~ ( ~ ( in @ SV99 @ SV109 )
| ~ ( in @ SV109 @ SV68 ) ) )
= $false )
| ( ( in @ SV99 @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1217,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) ) )
= $true )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1177]) ).
thf(1218,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
| ~ ( in @ SV107 @ SV68 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1219,plain,
! [SV85: $i,SV70: $i] :
( ( ( ( sK29_SY290 @ SV70 @ SV85 )
= SV70 )
= $true )
| ( ( in @ ( sK29_SY290 @ SV70 @ SV85 ) @ SV85 )
= $true )
| ( ( SV85
= ( singleton @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1220,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) ) )
= $false )
| ( ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1221,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
= $false )
| ( ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1222,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) ) )
= $false )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1187]) ).
thf(1223,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
= $false )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1187]) ).
thf(1224,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ~ ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) ) )
= $false )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1225,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
= $false )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1226,plain,
! [SV74: $i,SV88: $i,SV58: $i,SV101: $i] :
( ( ( in @ SV101 @ SV58 )
= $true )
| ( ( in @ SV101 @ SV88 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1189]) ).
thf(1227,plain,
! [SV58: $i,SV88: $i,SV74: $i,SV101: $i] :
( ( ( in @ SV101 @ SV74 )
= $true )
| ( ( in @ SV101 @ SV88 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1190]) ).
thf(1228,plain,
! [SV88: $i,SV74: $i,SV58: $i,SV101: $i] :
( ( ( in @ SV101 @ SV58 )
= $false )
| ( ( ~ ( in @ SV101 @ SV74 ) )
= $true )
| ( ( in @ SV101 @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1229,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) ) )
= $true )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1192]) ).
thf(1230,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) ) )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1231,plain,
! [SV60: $i,SV76: $i,SV102: $i,SV89: $i] :
( ( ( ~ ! [SY329: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ SY329 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SY329 ) ) ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1195]) ).
thf(1232,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV60: $i,SV110: $i] :
( ( ( ~ ! [SY330: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV110 @ SV60 )
| ~ ( in @ SY330 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SV110 @ SY330 ) ) ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1233,plain,
! [SV89: $i,SV76: $i,SV60: $i] :
( ( ( ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) ) )
= $true )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1197]) ).
thf(1234,plain,
! [SV89: $i,SV76: $i,SV60: $i,SV108: $i] :
( ( ( ! [SY328: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV108 @ SV60 )
| ~ ( in @ SY328 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SV108 @ SY328 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1235,plain,
! [SV106: $i,SV77: $i,SV61: $i] :
( ( ( disjoint @ SV61 @ SV77 )
= $false )
| ( ( in @ SV106 @ SV61 )
= $false )
| ( ( in @ SV106 @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1236,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
= $true )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1203]) ).
thf(1237,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
= $true )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1205]) ).
thf(1238,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
| ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 ) )
= $true )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1207]) ).
thf(1239,plain,
! [SV82: $i,SV91: $i,SV66: $i,SV104: $i] :
( ( ( in @ SV104 @ SV66 )
= $true )
| ( ( in @ SV104 @ SV91 )
= $false )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1209]) ).
thf(1240,plain,
! [SV66: $i,SV91: $i,SV82: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV82 ) )
= $true )
| ( ( in @ SV104 @ SV91 )
= $false )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1210]) ).
thf(1241,plain,
! [SV91: $i,SV82: $i,SV66: $i,SV104: $i] :
( ( ( in @ SV104 @ SV66 )
= $false )
| ( ( ~ ~ ( in @ SV104 @ SV82 ) )
= $true )
| ( ( in @ SV104 @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1242,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) ) )
= $true )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1212]) ).
thf(1243,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1244,plain,
! [SV68: $i,SV84: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ ( sK36_SY316 @ SV84 @ SV68 @ SV99 ) )
| ~ ( in @ ( sK36_SY316 @ SV84 @ SV68 @ SV99 ) @ SV68 ) )
= $false )
| ( ( in @ SV99 @ SV84 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1245,plain,
! [SV84: $i,SV68: $i,SV109: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ SV109 )
| ~ ( in @ SV109 @ SV68 ) )
= $true )
| ( ( in @ SV99 @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1216]) ).
thf(1246,plain,
! [SV84: $i,SV68: $i] :
( ( ( ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1247,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 ) )
= $true )
| ( ( ~ ( in @ SV107 @ SV68 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1248,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
= $true )
| ( ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1249,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
= $true )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1222]) ).
thf(1250,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
| ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 ) )
= $true )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1251,plain,
! [SV88: $i,SV58: $i,SV74: $i,SV101: $i] :
( ( ( in @ SV101 @ SV74 )
= $false )
| ( ( in @ SV101 @ SV58 )
= $false )
| ( ( in @ SV101 @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1252,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1253,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
| ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 ) )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1254,plain,
! [SV60: $i,SV76: $i,SV102: $i,SV89: $i] :
( ( ( ! [SY329: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ SY329 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SY329 ) ) ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1255,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV60: $i,SV110: $i] :
( ( ( ! [SY330: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV110 @ SV60 )
| ~ ( in @ SY330 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SV110 @ SY330 ) ) ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1232]) ).
thf(1256,plain,
! [SV89: $i,SV76: $i,SV60: $i] :
( ( ( ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1257,plain,
! [SV89: $i,SV76: $i,SV111: $i,SV60: $i,SV108: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV108 @ SV60 )
| ~ ( in @ SV111 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SV108 @ SV111 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1258,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
= $true )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 )
= $true )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV90 )
= $true )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1236]) ).
thf(1259,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
= $true )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 )
= $true )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1260,plain,
! [SV90: $i,SV62: $i,SV78: $i] :
( ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV62 )
= $true )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 )
= $true )
| ( ( in @ ( sK32_SY309 @ SV78 @ SV62 @ SV90 ) @ SV78 )
= $false )
| ( ( SV90
= ( set_union2 @ SV62 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1261,plain,
! [SV66: $i,SV91: $i,SV82: $i,SV104: $i] :
( ( ( in @ SV104 @ SV82 )
= $false )
| ( ( in @ SV104 @ SV91 )
= $false )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1262,plain,
! [SV91: $i,SV66: $i,SV82: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV82 ) )
= $false )
| ( ( in @ SV104 @ SV66 )
= $false )
| ( ( in @ SV104 @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1241]) ).
thf(1263,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1242]) ).
thf(1264,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $true )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) ) )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1265,plain,
! [SV68: $i,SV84: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ ( sK36_SY316 @ SV84 @ SV68 @ SV99 ) ) )
= $false )
| ( ( in @ SV99 @ SV84 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1244]) ).
thf(1266,plain,
! [SV99: $i,SV68: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK36_SY316 @ SV84 @ SV68 @ SV99 ) @ SV68 ) )
= $false )
| ( ( in @ SV99 @ SV84 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1244]) ).
thf(1267,plain,
! [SV84: $i,SV68: $i,SV109: $i,SV99: $i] :
( ( ( ~ ( in @ SV99 @ SV109 ) )
= $true )
| ( ( ~ ( in @ SV109 @ SV68 ) )
= $true )
| ( ( in @ SV99 @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1268,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ ( sK38_SY319 @ SV84 @ SV68 ) )
| ~ ( in @ ( sK38_SY319 @ SV84 @ SV68 ) @ SV68 ) ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1246]) ).
thf(1269,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( ~ ( in @ SV107 @ SV68 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1270,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
= $true )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 )
= $true )
| ( ( in @ ( sK34_SY315 @ SV87 @ SV72 @ SV94 ) @ SV94 )
= $true )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1271,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
= $true )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 )
= $true )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1272,plain,
! [SV94: $i,SV72: $i,SV87: $i] :
( ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV72 )
= $true )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 )
= $true )
| ( ( ( sK34_SY315 @ SV87 @ SV72 @ SV94 )
= SV87 )
= $false )
| ( ( SV94
= ( unordered_pair @ SV72 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1273,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 ) )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1252]) ).
thf(1274,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1252]) ).
thf(1275,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) ) )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1253]) ).
thf(1276,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1253]) ).
thf(1277,plain,
! [SV60: $i,SV76: $i,SV102: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) @ SV76 ) )
| ( SV102
!= ( ordered_pair @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) ) ) ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1254]) ).
thf(1278,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV112: $i,SV60: $i,SV110: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV110 @ SV60 )
| ~ ( in @ SV112 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SV110 @ SV112 ) ) ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1279,plain,
! [SV60: $i,SV76: $i,SV89: $i] :
( ( ( ~ ~ ! [SY331: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ SY331 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SY331 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1256]) ).
thf(1280,plain,
! [SV89: $i,SV76: $i,SV111: $i,SV60: $i,SV108: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV108 @ SV60 )
| ~ ( in @ SV111 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SV108 @ SV111 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1281,plain,
! [SV91: $i,SV66: $i,SV82: $i,SV104: $i] :
( ( ( in @ SV104 @ SV82 )
= $true )
| ( ( in @ SV104 @ SV66 )
= $false )
| ( ( in @ SV104 @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1262]) ).
thf(1282,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1263]) ).
thf(1283,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1263]) ).
thf(1284,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
| ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 ) )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1285,plain,
! [SV68: $i,SV84: $i,SV99: $i] :
( ( ( in @ SV99 @ ( sK36_SY316 @ SV84 @ SV68 @ SV99 ) )
= $true )
| ( ( in @ SV99 @ SV84 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1265]) ).
thf(1286,plain,
! [SV99: $i,SV68: $i,SV84: $i] :
( ( ( in @ ( sK36_SY316 @ SV84 @ SV68 @ SV99 ) @ SV68 )
= $true )
| ( ( in @ SV99 @ SV84 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1266]) ).
thf(1287,plain,
! [SV84: $i,SV68: $i,SV109: $i,SV99: $i] :
( ( ( in @ SV99 @ SV109 )
= $false )
| ( ( ~ ( in @ SV109 @ SV68 ) )
= $true )
| ( ( in @ SV99 @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1288,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ ( sK38_SY319 @ SV84 @ SV68 ) )
| ~ ( in @ ( sK38_SY319 @ SV84 @ SV68 ) @ SV68 ) ) )
= $true )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1268]) ).
thf(1289,plain,
! [SV84: $i,SV68: $i,SV107: $i] :
( ( ( in @ SV107 @ SV68 )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( ~ ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) ) )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1290,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $true )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1273]) ).
thf(1291,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 )
= $true )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV88 )
= $true )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1274]) ).
thf(1292,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) ) )
= $true )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1275]) ).
thf(1293,plain,
! [SV60: $i,SV76: $i,SV102: $i,SV89: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) @ SV76 ) )
| ( SV102
!= ( ordered_pair @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) ) ) ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1277]) ).
thf(1294,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV112: $i,SV60: $i,SV110: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV110 @ SV60 )
| ~ ( in @ SV112 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SV110 @ SV112 ) ) ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1295,plain,
! [SV60: $i,SV76: $i,SV89: $i] :
( ( ( ~ ! [SY331: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ SY331 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SY331 ) ) ) )
= $true )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1279]) ).
thf(1296,plain,
! [SV89: $i,SV76: $i,SV111: $i,SV60: $i,SV108: $i] :
( ( ( ~ ~ ( ~ ( in @ SV108 @ SV60 )
| ~ ( in @ SV111 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SV108 @ SV111 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1280]) ).
thf(1297,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $true )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1282]) ).
thf(1298,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
= $true )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1283]) ).
thf(1299,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) ) )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1284]) ).
thf(1300,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1284]) ).
thf(1301,plain,
! [SV84: $i,SV99: $i,SV68: $i,SV109: $i] :
( ( ( in @ SV109 @ SV68 )
= $false )
| ( ( in @ SV99 @ SV109 )
= $false )
| ( ( in @ SV99 @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1287]) ).
thf(1302,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ ( sK38_SY319 @ SV84 @ SV68 ) )
| ~ ( in @ ( sK38_SY319 @ SV84 @ SV68 ) @ SV68 ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1288]) ).
thf(1303,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) )
| ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( in @ SV107 @ SV68 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1304,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
| ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1305,plain,
! [SV60: $i,SV76: $i,SV102: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) @ SV76 ) )
| ( SV102
!= ( ordered_pair @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) ) ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1306,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV112: $i,SV60: $i,SV110: $i] :
( ( ( ~ ~ ( ~ ( in @ SV110 @ SV60 )
| ~ ( in @ SV112 @ SV76 ) )
| ( SV102
!= ( ordered_pair @ SV110 @ SV112 ) ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1294]) ).
thf(1307,plain,
! [SV60: $i,SV76: $i,SV89: $i] :
( ( ( ! [SY331: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ SY331 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SY331 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1308,plain,
! [SV89: $i,SV76: $i,SV111: $i,SV60: $i,SV108: $i] :
( ( ( ~ ~ ( ~ ( in @ SV108 @ SV60 )
| ~ ( in @ SV111 @ SV76 ) ) )
= $true )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SV108 @ SV111 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1309,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV91 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1298]) ).
thf(1310,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) ) )
= $true )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1311,plain,
! [SV84: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ ( sK38_SY319 @ SV84 @ SV68 ) ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1302]) ).
thf(1312,plain,
! [SV68: $i,SV84: $i] :
( ( ( ~ ( in @ ( sK38_SY319 @ SV84 @ SV68 ) @ SV68 ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1302]) ).
thf(1313,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( ~ ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( in @ SV107 @ SV68 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1303]) ).
thf(1314,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( in @ SV107 @ SV68 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1303]) ).
thf(1315,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 ) )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1304]) ).
thf(1316,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( ~ ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 ) )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1304]) ).
thf(1317,plain,
! [SV60: $i,SV76: $i,SV102: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) @ SV76 ) ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1305]) ).
thf(1318,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV102: $i] :
( ( ( SV102
!= ( ordered_pair @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1305]) ).
thf(1319,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV112: $i,SV60: $i,SV110: $i] :
( ( ( ~ ~ ( ~ ( in @ SV110 @ SV60 )
| ~ ( in @ SV112 @ SV76 ) ) )
= $true )
| ( ( SV102
!= ( ordered_pair @ SV110 @ SV112 ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1320,plain,
! [SV60: $i,SV76: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) ) ) ) )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1307]) ).
thf(1321,plain,
! [SV89: $i,SV76: $i,SV111: $i,SV60: $i,SV108: $i] :
( ( ( ~ ( ~ ( in @ SV108 @ SV60 )
| ~ ( in @ SV111 @ SV76 ) ) )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SV108 @ SV111 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1322,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
| ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1323,plain,
! [SV84: $i,SV68: $i] :
( ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ ( sK38_SY319 @ SV84 @ SV68 ) )
= $true )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1311]) ).
thf(1324,plain,
! [SV68: $i,SV84: $i] :
( ( ( in @ ( sK38_SY319 @ SV84 @ SV68 ) @ SV68 )
= $true )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV84 )
= $true )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1312]) ).
thf(1325,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( ~ ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) ) )
= $true )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( in @ SV107 @ SV68 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1326,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $true )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1315]) ).
thf(1327,plain,
! [SV88: $i,SV58: $i,SV74: $i] :
( ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 )
= $true )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV58 )
= $false )
| ( ( in @ ( sK30_SY297 @ SV74 @ SV58 @ SV88 ) @ SV74 )
= $false )
| ( ( SV88
= ( set_intersection2 @ SV58 @ SV74 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1316]) ).
thf(1328,plain,
! [SV60: $i,SV76: $i,SV102: $i,SV89: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) @ SV76 ) ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1317]) ).
thf(1329,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV102: $i] :
( ( ( SV102
= ( ordered_pair @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1318]) ).
thf(1330,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV112: $i,SV60: $i,SV110: $i] :
( ( ( ~ ( ~ ( in @ SV110 @ SV60 )
| ~ ( in @ SV112 @ SV76 ) ) )
= $false )
| ( ( SV102
!= ( ordered_pair @ SV110 @ SV112 ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1331,plain,
! [SV60: $i,SV76: $i,SV89: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) ) ) ) )
= $true )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1320]) ).
thf(1332,plain,
! [SV89: $i,SV76: $i,SV111: $i,SV60: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ SV60 )
| ~ ( in @ SV111 @ SV76 ) )
= $true )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SV108 @ SV111 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1321]) ).
thf(1333,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1322]) ).
thf(1334,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1322]) ).
thf(1335,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( ! [SY319: $i] :
~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SY319 )
| ~ ( in @ SY319 @ SV68 ) ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( in @ SV107 @ SV68 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1336,plain,
! [SV60: $i,SV76: $i,SV102: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) @ SV76 ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1337,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV112: $i,SV60: $i,SV110: $i] :
( ( ( ~ ( in @ SV110 @ SV60 )
| ~ ( in @ SV112 @ SV76 ) )
= $true )
| ( ( SV102
!= ( ordered_pair @ SV110 @ SV112 ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1330]) ).
thf(1338,plain,
! [SV60: $i,SV76: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) ) ) )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1339,plain,
! [SV89: $i,SV76: $i,SV111: $i,SV60: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ SV60 ) )
= $true )
| ( ( ~ ( in @ SV111 @ SV76 ) )
= $true )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SV108 @ SV111 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1340,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $true )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1333]) ).
thf(1341,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 ) )
= $true )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1334]) ).
thf(1342,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ ( sK42_SY319 @ SV107 @ SV84 @ SV68 ) )
| ~ ( in @ ( sK42_SY319 @ SV107 @ SV84 @ SV68 ) @ SV68 ) ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( in @ SV107 @ SV68 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1335]) ).
thf(1343,plain,
! [SV60: $i,SV76: $i,SV102: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SV60 ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1344,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) @ SV76 ) )
= $false )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1336]) ).
thf(1345,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV112: $i,SV60: $i,SV110: $i] :
( ( ( ~ ( in @ SV110 @ SV60 ) )
= $true )
| ( ( ~ ( in @ SV112 @ SV76 ) )
= $true )
| ( ( SV102
!= ( ordered_pair @ SV110 @ SV112 ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1346,plain,
! [SV60: $i,SV76: $i,SV89: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) @ SV76 ) ) )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1338]) ).
thf(1347,plain,
! [SV89: $i,SV60: $i,SV76: $i] :
( ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) ) )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1338]) ).
thf(1348,plain,
! [SV89: $i,SV76: $i,SV111: $i,SV60: $i,SV108: $i] :
( ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ~ ( in @ SV111 @ SV76 ) )
= $true )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SV108 @ SV111 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1349,plain,
! [SV91: $i,SV66: $i,SV82: $i] :
( ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV66 )
= $false )
| ( ( in @ ( sK33_SY311 @ SV82 @ SV66 @ SV91 ) @ SV82 )
= $true )
| ( ( SV91
= ( set_difference @ SV66 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1350,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ ( sK42_SY319 @ SV107 @ SV84 @ SV68 ) )
| ~ ( in @ ( sK42_SY319 @ SV107 @ SV84 @ SV68 ) @ SV68 ) ) )
= $true )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( in @ SV107 @ SV68 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1342]) ).
thf(1351,plain,
! [SV60: $i,SV76: $i,SV102: $i,SV89: $i] :
( ( ( in @ ( sK37_SY320 @ SV89 @ SV102 @ SV76 @ SV60 ) @ SV60 )
= $true )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1343]) ).
thf(1352,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV60: $i] :
( ( ( in @ ( sK39_SY329 @ SV60 @ SV76 @ SV102 @ SV89 ) @ SV76 )
= $true )
| ( ( in @ SV102 @ SV89 )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1344]) ).
thf(1353,plain,
! [SV89: $i,SV102: $i,SV76: $i,SV112: $i,SV60: $i,SV110: $i] :
( ( ( in @ SV110 @ SV60 )
= $false )
| ( ( ~ ( in @ SV112 @ SV76 ) )
= $true )
| ( ( SV102
!= ( ordered_pair @ SV110 @ SV112 ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1354,plain,
! [SV60: $i,SV76: $i,SV89: $i] :
( ( ( ~ ( ~ ( in @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) @ SV76 ) ) )
= $true )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1346]) ).
thf(1355,plain,
! [SV89: $i,SV60: $i,SV76: $i] :
( ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) ) )
= $true )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1347]) ).
thf(1356,plain,
! [SV89: $i,SV60: $i,SV108: $i,SV76: $i,SV111: $i] :
( ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SV108 @ SV111 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1357,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ ( sK42_SY319 @ SV107 @ SV84 @ SV68 ) )
| ~ ( in @ ( sK42_SY319 @ SV107 @ SV84 @ SV68 ) @ SV68 ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( in @ SV107 @ SV68 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1358,plain,
! [SV89: $i,SV102: $i,SV60: $i,SV110: $i,SV76: $i,SV112: $i] :
( ( ( in @ SV112 @ SV76 )
= $false )
| ( ( in @ SV110 @ SV60 )
= $false )
| ( ( SV102
!= ( ordered_pair @ SV110 @ SV112 ) )
= $true )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1359,plain,
! [SV60: $i,SV76: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) @ SV76 ) )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1360,plain,
! [SV111: $i,SV108: $i,SV89: $i,SV60: $i,SV76: $i] :
( ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( ~ ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1356]) ).
thf(1361,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( ~ ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ ( sK42_SY319 @ SV107 @ SV84 @ SV68 ) ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( in @ SV107 @ SV68 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1362,plain,
! [SV68: $i,SV84: $i,SV107: $i] :
( ( ( ~ ( in @ ( sK42_SY319 @ SV107 @ SV84 @ SV68 ) @ SV68 ) )
= $false )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( in @ SV107 @ SV68 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1357]) ).
thf(1363,plain,
! [SV89: $i,SV76: $i,SV60: $i,SV112: $i,SV110: $i,SV102: $i] :
( ( ( SV102
= ( ordered_pair @ SV110 @ SV112 ) )
= $false )
| ( ( in @ SV110 @ SV60 )
= $false )
| ( ( in @ SV112 @ SV76 )
= $false )
| ( ( in @ SV102 @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1364,plain,
! [SV60: $i,SV76: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SV60 ) )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1365,plain,
! [SV89: $i,SV76: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) @ SV76 ) )
= $false )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1366,plain,
! [SV108: $i,SV111: $i,SV89: $i,SV76: $i,SV60: $i] :
( ( ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) )
| ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 ) )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1367,plain,
! [SV107: $i,SV84: $i,SV68: $i] :
( ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ ( sK42_SY319 @ SV107 @ SV84 @ SV68 ) )
= $true )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( in @ SV107 @ SV68 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1361]) ).
thf(1368,plain,
! [SV68: $i,SV84: $i,SV107: $i] :
( ( ( in @ ( sK42_SY319 @ SV107 @ SV84 @ SV68 ) @ SV68 )
= $true )
| ( ( in @ ( sK28_SY286 @ SV68 @ SV84 ) @ SV107 )
= $false )
| ( ( in @ SV107 @ SV68 )
= $false )
| ( ( SV84
= ( union @ SV68 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1362]) ).
thf(1369,plain,
! [SV60: $i,SV76: $i,SV89: $i] :
( ( ( in @ ( sK40_SY326 @ SV89 @ SV76 @ SV60 ) @ SV60 )
= $true )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1364]) ).
thf(1370,plain,
! [SV89: $i,SV76: $i,SV60: $i] :
( ( ( in @ ( sK41_SY331 @ SV60 @ SV76 @ SV89 ) @ SV76 )
= $true )
| ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $true )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1365]) ).
thf(1371,plain,
! [SV108: $i,SV111: $i,SV89: $i,SV76: $i,SV60: $i] :
( ( ( ~ ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) ) )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1366]) ).
thf(1372,plain,
! [SV108: $i,SV111: $i,SV89: $i,SV60: $i,SV76: $i] :
( ( ( in @ ( sK31_SY303 @ SV76 @ SV60 @ SV89 ) @ SV89 )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1366]) ).
thf(1373,plain,
! [SV108: $i,SV111: $i,SV89: $i,SV76: $i,SV60: $i] :
( ( ( ~ ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) ) )
= $true )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1371]) ).
thf(1374,plain,
! [SV108: $i,SV111: $i,SV89: $i,SV76: $i,SV60: $i] :
( ( ( ! [SY326: $i] :
~ ~ ! [SY327: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY326 @ SV60 )
| ~ ( in @ SY327 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ SY326 @ SY327 ) ) ) )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1375,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV111: $i,SV108: $i] :
( ( ( ~ ~ ! [SY332: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ SY332 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SY332 ) ) ) )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1374]) ).
thf(1376,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV111: $i,SV108: $i] :
( ( ( ~ ! [SY332: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ SY332 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SY332 ) ) ) )
= $true )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1375]) ).
thf(1377,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV111: $i,SV108: $i] :
( ( ( ! [SY332: $i] :
~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ SY332 @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SY332 ) ) ) )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1376]) ).
thf(1378,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV111: $i,SV108: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) ) ) ) )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1377]) ).
thf(1379,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV111: $i,SV108: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) ) ) ) )
= $true )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1380,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV111: $i,SV108: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) @ SV76 ) )
| ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) ) ) )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1381,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV111: $i,SV108: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) @ SV76 ) ) )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1382,plain,
! [SV111: $i,SV108: $i,SV89: $i,SV60: $i,SV76: $i] :
( ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
!= ( ordered_pair @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) ) )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1380]) ).
thf(1383,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV111: $i,SV108: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) @ SV76 ) ) )
= $true )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1381]) ).
thf(1384,plain,
! [SV111: $i,SV108: $i,SV89: $i,SV60: $i,SV76: $i] :
( ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) ) )
= $true )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1382]) ).
thf(1385,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV111: $i,SV108: $i] :
( ( ( ~ ( in @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SV60 )
| ~ ( in @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) @ SV76 ) )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1386,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV111: $i,SV108: $i] :
( ( ( ~ ( in @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SV60 ) )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1385]) ).
thf(1387,plain,
! [SV108: $i,SV111: $i,SV89: $i,SV76: $i,SV60: $i] :
( ( ( ~ ( in @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) @ SV76 ) )
= $false )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1385]) ).
thf(1388,plain,
! [SV60: $i,SV76: $i,SV89: $i,SV111: $i,SV108: $i] :
( ( ( in @ ( sK43_SY326 @ SV108 @ SV111 @ SV89 @ SV76 @ SV60 ) @ SV60 )
= $true )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1386]) ).
thf(1389,plain,
! [SV108: $i,SV111: $i,SV89: $i,SV76: $i,SV60: $i] :
( ( ( in @ ( sK44_SY332 @ SV60 @ SV76 @ SV89 @ SV111 @ SV108 ) @ SV76 )
= $true )
| ( ( in @ SV111 @ SV76 )
= $false )
| ( ( in @ SV108 @ SV60 )
= $false )
| ( ( ( sK31_SY303 @ SV76 @ SV60 @ SV89 )
= ( ordered_pair @ SV108 @ SV111 ) )
= $false )
| ( ( SV89
= ( cartesian_product2 @ SV60 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1387]) ).
thf(1390,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[774,1389,1388,1384,1372,1370,1369,1368,1367,1363,1355,1352,1351,1349,1340,1329,1327,1326,1324,1323,1314,1309,1301,1300,1297,1291,1290,1286,1285,1281,1276,1272,1271,1270,1261,1260,1259,1258,1251,1239,1235,1227,1226,1225,1223,1221,1219,1213,1208,1206,1204,1201,1200,1198,1193,1185,1184,1183,1182,1181,1178,1167,1166,1165,1148,1116,1115,1110,1105,1078,1077,1073,1072,1044,1010,1009,1004,1003,986,975,974,943,929,928,890,839,837,783,782,781,780,779,778,777,776,775]) ).
thf(1391,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1390,760]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.21 % Computer : n001.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Oct 6 15:08:39 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.49/1.41
% 6.49/1.41 No.of.Axioms: 26
% 6.49/1.41
% 6.49/1.41 Length.of.Defs: 0
% 6.49/1.41
% 6.49/1.41 Contains.Choice.Funs: false
% 6.49/1.41 ..................................................
% 6.49/1.41
% 6.49/1.41 ********************************
% 6.49/1.41 * All subproblems solved! *
% 6.49/1.41 ********************************
% 6.49/1.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:26,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1390,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.49/1.41
% 6.49/1.41 %**** Beginning of derivation protocol ****
% 6.49/1.41 % SZS output start CNFRefutation
% See solution above
% 6.49/1.42
% 6.49/1.42 %**** End of derivation protocol ****
% 6.49/1.42 %**** no. of clauses in derivation: 1323 ****
% 6.49/1.42 %**** clause counter: 1390 ****
% 6.49/1.42
% 6.49/1.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:26,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1390,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------