TSTP Solution File: SEU154+2 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU154+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:07:15 EDT 2022
% Result : Theorem 1.28s 1.51s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 104
% Syntax : Number of formulae : 986 ( 540 unt; 27 typ; 0 def)
% Number of atoms : 5910 (2363 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 12020 (2193 ~;1960 |; 134 &;7636 @)
% ( 46 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 7 con; 0-3 aty)
% Number of variables : 2655 ( 0 ^2647 !; 8 ?;2655 :)
% Comments :
%------------------------------------------------------------------------------
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_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_sK10_D,type,
sK10_D: $i > $i > $i > $i ).
thf(tp_sK11_C,type,
sK11_C: $i > $i > $i ).
thf(tp_sK12_B,type,
sK12_B: $i > $i ).
thf(tp_sK13_C,type,
sK13_C: $i > $i > $i ).
thf(tp_sK14_C,type,
sK14_C: $i > $i > $i ).
thf(tp_sK15_C,type,
sK15_C: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY152,type,
sK2_SY152: $i ).
thf(tp_sK3_C,type,
sK3_C: $i > $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_D,type,
sK6_D: $i > $i > $i > $i ).
thf(tp_sK7_D,type,
sK7_D: $i > $i > $i > $i ).
thf(tp_sK8_C,type,
sK8_C: $i > $i > $i ).
thf(tp_sK9_D,type,
sK9_D: $i > $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(5,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(7,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(8,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(11,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(12,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(18,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(19,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(34,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(46,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(48,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(50,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(55,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(59,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(61,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(64,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(67,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(74,axiom,
! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(76,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(77,conjecture,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(78,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[77]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[78]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(82,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(83,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(84,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(86,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(87,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(88,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(89,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(90,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(91,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(95,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(97,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(98,plain,
$true = $true,
inference(unfold_def,[status(thm)],[19]) ).
thf(99,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(100,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(101,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(102,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(103,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(104,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(106,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(107,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)],[28]) ).
thf(108,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)],[29]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(110,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)],[31]) ).
thf(111,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)],[32]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(113,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(115,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(120,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(121,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(122,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(123,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(125,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(126,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(127,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(128,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(131,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(132,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(133,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(134,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(135,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)],[56]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(137,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(138,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(139,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(140,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(141,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(142,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(143,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(144,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(145,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(146,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(147,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(148,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(149,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(150,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(151,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(152,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(153,plain,
( ( ! [A: $i,B: $i] :
~ ( ( disjoint @ ( singleton @ A ) @ B )
& ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(154,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(155,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(156,plain,
( ( ! [SY152: $i] :
( ~ ( in @ sK1_A @ SY152 )
=> ( disjoint @ ( singleton @ sK1_A ) @ SY152 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[79]) ).
thf(157,plain,
( ( ~ ( in @ sK1_A @ sK2_SY152 )
=> ( disjoint @ ( singleton @ sK1_A ) @ sK2_SY152 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[156]) ).
thf(158,plain,
( ( ~ ( in @ sK1_A @ sK2_SY152 ) )
= $true ),
inference(standard_cnf,[status(thm)],[157]) ).
thf(159,plain,
( ( disjoint @ ( singleton @ sK1_A ) @ sK2_SY152 )
= $false ),
inference(standard_cnf,[status(thm)],[157]) ).
thf(160,plain,
( ( ~ ( disjoint @ ( singleton @ sK1_A ) @ sK2_SY152 ) )
= $true ),
inference(polarity_switch,[status(thm)],[159]) ).
thf(161,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(162,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(163,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(164,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_C @ B @ A ) @ A )
| ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
& ( ( in @ ( sK3_C @ B @ A ) @ A )
| ( in @ ( sK3_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(165,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(166,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(167,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(168,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(169,plain,
( ( ! [A: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(170,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(171,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(172,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(173,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(174,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(175,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(176,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(177,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK7_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK7_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ A )
| ( in @ ( sK7_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ B )
| ( in @ ( sK7_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(178,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK8_C @ B @ A ) @ A )
& ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(179,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK9_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK9_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK9_D @ C @ B @ A ) @ C )
| ( in @ ( sK9_D @ C @ B @ A ) @ A )
| ( in @ ( sK9_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(180,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK10_D @ C @ B @ A ) @ C )
| ( ( sK10_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK10_D @ C @ B @ A ) @ C )
| ( ( sK10_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK10_D @ C @ B @ A ) @ C )
| ( ( sK10_D @ C @ B @ A )
= A )
| ( ( sK10_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(181,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK11_C @ B @ A ) @ B )
| ~ ( subset @ ( sK11_C @ B @ A ) @ A ) )
& ( ( in @ ( sK11_C @ B @ A ) @ B )
| ( subset @ ( sK11_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[112]) ).
thf(182,plain,
( ( ! [A: $i] :
( ( in @ ( sK12_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(183,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK13_C @ B @ A )
!= A )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( ( sK13_C @ B @ A )
= A )
| ( in @ ( sK13_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(184,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(185,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(186,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[120]) ).
thf(187,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(188,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[122]) ).
thf(189,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[123]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(191,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(192,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(193,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[129]) ).
thf(194,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK14_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(195,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(196,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[134]) ).
thf(197,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK15_C @ B @ A ) @ A )
& ( in @ ( sK15_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[135]) ).
thf(198,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[137]) ).
thf(199,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(200,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(201,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(202,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(203,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(204,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[147]) ).
thf(205,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(206,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(207,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(208,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(209,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(210,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(211,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[154]) ).
thf(212,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(extcnf_combined,[status(esa)],[155]) ).
thf(213,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(214,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( ( set_union2 @ ( singleton @ A ) @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(215,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ ( singleton @ A ) @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(216,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( subset @ ( singleton @ A ) @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(217,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(218,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(219,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] : ( subset @ A @ ( singleton @ B ) ) )
& ! [A: $i,B: $i] :
( ( A
!= ( singleton @ B ) )
| ( subset @ A @ ( singleton @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(220,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(221,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(223,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ A @ C )
| ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(224,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(225,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(226,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(227,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(228,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] : ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(230,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(231,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= empty_set )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( set_difference @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(232,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(233,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( ( in @ ( sK15_C @ B @ A ) @ A )
& ( in @ ( sK15_C @ B @ A ) @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(234,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ empty_set )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(235,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(237,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(238,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
| ( in @ ( sK14_C @ B @ A ) @ ( set_intersection2 @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) )
| ~ ( disjoint @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(239,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ B @ A )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(240,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( disjoint @ B @ C )
| ~ ( subset @ A @ B )
| ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(241,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(242,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(243,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
!= A )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_difference @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(245,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ C @ B )
| ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(246,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(247,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(248,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(249,plain,
( ( ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ~ ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(250,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(251,plain,
( ( ! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(252,plain,
( ( ! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(253,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(254,plain,
( ( ! [A: $i,B: $i] :
( ( ( ( ( sK13_C @ B @ A )
!= A )
| ~ ( in @ ( sK13_C @ B @ A ) @ B ) )
& ( ( ( sK13_C @ B @ A )
= A )
| ( in @ ( sK13_C @ B @ A ) @ B ) ) )
| ( B
= ( singleton @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( singleton @ A ) )
| ( ! [C: $i] :
( ( C != A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( C = A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(255,plain,
( ( ! [A: $i] :
( ( in @ ( sK12_B @ A ) @ A )
| ( A = empty_set ) )
& ! [A: $i] :
( ( A != empty_set )
| ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(256,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK11_C @ B @ A ) @ B )
| ~ ( subset @ ( sK11_C @ B @ A ) @ A ) )
& ( ( in @ ( sK11_C @ B @ A ) @ B )
| ( subset @ ( sK11_C @ B @ A ) @ A ) ) )
| ( B
= ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ( B
!= ( powerset @ A ) )
| ( ! [C: $i] :
( ~ ( in @ C @ B )
| ( subset @ C @ A ) )
& ! [C: $i] :
( ~ ( subset @ C @ A )
| ( in @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(257,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK10_D @ C @ B @ A ) @ C )
| ( ( sK10_D @ C @ B @ A )
!= A ) )
& ( ~ ( in @ ( sK10_D @ C @ B @ A ) @ C )
| ( ( sK10_D @ C @ B @ A )
!= B ) )
& ( ( in @ ( sK10_D @ C @ B @ A ) @ C )
| ( ( sK10_D @ C @ B @ A )
= A )
| ( ( sK10_D @ C @ B @ A )
= B ) ) )
| ( C
= ( unordered_pair @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( unordered_pair @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( D = A )
| ( D = B ) )
& ! [D: $i] :
( ( D != A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ( D != B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(258,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK9_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ A ) )
& ( ~ ( in @ ( sK9_D @ C @ B @ A ) @ C )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ B ) )
& ( ( in @ ( sK9_D @ C @ B @ A ) @ C )
| ( in @ ( sK9_D @ C @ B @ A ) @ A )
| ( in @ ( sK9_D @ C @ B @ A ) @ B ) ) )
| ( C
= ( set_union2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_union2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A )
| ( in @ D @ B ) )
& ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ B )
| ( in @ D @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK8_C @ B @ A ) @ A )
& ~ ( in @ ( sK8_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(260,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK7_D @ C @ B @ A ) @ A )
| ~ ( in @ ( sK7_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK7_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ A )
| ( in @ ( sK7_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK7_D @ C @ B @ A ) @ B )
| ( in @ ( sK7_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_intersection2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_intersection2 @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(261,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ~ ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ( in @ ( sK6_D @ C @ B @ A ) @ A )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) )
& ( ~ ( in @ ( sK6_D @ C @ B @ A ) @ B )
| ( in @ ( sK6_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( set_difference @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( set_difference @ A @ B ) )
| ( ! [D: $i] :
( ~ ( in @ D @ A )
| ( in @ D @ B )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( in @ D @ A ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ~ ( in @ D @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_intersection2 @ A @ B )
!= empty_set )
| ( disjoint @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(263,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ( proper_subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) )
& ! [A: $i,B: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(264,plain,
$true = $true,
inference(copy,[status(thm)],[104]) ).
thf(265,plain,
$true = $true,
inference(copy,[status(thm)],[103]) ).
thf(266,plain,
$true = $true,
inference(copy,[status(thm)],[102]) ).
thf(267,plain,
$true = $true,
inference(copy,[status(thm)],[101]) ).
thf(268,plain,
$true = $true,
inference(copy,[status(thm)],[100]) ).
thf(269,plain,
$true = $true,
inference(copy,[status(thm)],[99]) ).
thf(270,plain,
$true = $true,
inference(copy,[status(thm)],[98]) ).
thf(271,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(272,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(273,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ! [B: $i] :
~ ( empty @ ( set_union2 @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(274,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(275,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(276,plain,
( ( ! [A: $i] :
~ ( proper_subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(277,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(278,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(279,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(280,plain,
( ( ! [A: $i,B: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(281,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(282,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(283,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_C @ B @ A ) @ A )
| ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
& ( ( in @ ( sK3_C @ B @ A ) @ A )
| ( in @ ( sK3_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(284,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(285,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(286,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(287,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(288,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(289,plain,
( ( ~ ( in @ sK1_A @ sK2_SY152 ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(290,plain,
( ( ~ ( disjoint @ ( singleton @ sK1_A ) @ sK2_SY152 ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(291,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK14_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(292,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(293,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK7_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(294,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( in @ ( sK12_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(295,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK13_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK13_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(296,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(297,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ( in @ ( sK6_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(298,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(299,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(300,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(301,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ( ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX2
= ( set_union2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( set_union2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(302,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(303,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(304,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK11_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK11_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(305,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK10_D @ SX2 @ SX1 @ SX0 )
!= SX0 ) )
| ~ ( ~ ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK10_D @ SX2 @ SX1 @ SX0 )
!= SX1 ) ) )
| ~ ( ( in @ ( sK10_D @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ( ( sK10_D @ SX2 @ SX1 @ SX0 )
= SX0 )
| ( ( sK10_D @ SX2 @ SX1 @ SX0 )
= SX1 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ~ ( ~ ! [SX3: $i] :
( ( SX3 != SX0 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(306,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(307,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(308,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(309,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(310,plain,
! [SV1: $i] :
( ( ( ( singleton @ SV1 )
!= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(311,plain,
! [SV2: $i] :
( ( ! [SY153: $i] :
( ~ ( in @ SV2 @ SY153 )
| ( ( set_union2 @ ( singleton @ SV2 ) @ SY153 )
= SY153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(312,plain,
! [SV3: $i] :
( ( ! [SY154: $i] :
( ~ ( disjoint @ ( singleton @ SV3 ) @ SY154 )
| ~ ( in @ SV3 @ SY154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(313,plain,
! [SV4: $i] :
( ( ! [SY155: $i] :
( ~ ( subset @ SV4 @ SY155 )
| ! [SY156: $i] :
( ( in @ SY156 @ SV4 )
| ( subset @ SV4 @ ( set_difference @ SY155 @ ( singleton @ SY156 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(314,plain,
! [SV5: $i] :
( ( ! [SY157: $i,SY158: $i,SY159: $i] :
( ( SV5 = SY159 )
| ( SV5 = SY158 )
| ( ( unordered_pair @ SV5 @ SY157 )
!= ( unordered_pair @ SY158 @ SY159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(315,plain,
! [SV6: $i] :
( ( ! [SY160: $i] :
( ~ ( subset @ SV6 @ SY160 )
| ( ( set_union2 @ SV6 @ SY160 )
= SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(316,plain,
! [SV7: $i] :
( ( ! [SY161: $i] : ( subset @ ( set_intersection2 @ SV7 @ SY161 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(317,plain,
! [SV8: $i] :
( ( ! [SY162: $i,SY163: $i] :
( ~ ( subset @ SV8 @ SY162 )
| ~ ( subset @ SV8 @ SY163 )
| ( subset @ SV8 @ ( set_intersection2 @ SY162 @ SY163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(318,plain,
! [SV9: $i] :
( ( ! [SY164: $i,SY165: $i] :
( ~ ( subset @ SV9 @ SY164 )
| ~ ( subset @ SY164 @ SY165 )
| ( subset @ SV9 @ SY165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(319,plain,
! [SV10: $i] :
( ( ! [SY166: $i] :
( ~ ( subset @ SV10 @ SY166 )
| ! [SY167: $i] : ( subset @ ( set_intersection2 @ SV10 @ SY167 ) @ ( set_intersection2 @ SY166 @ SY167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(320,plain,
! [SV11: $i] :
( ( ! [SY168: $i] :
( ~ ( subset @ SV11 @ SY168 )
| ( ( set_intersection2 @ SV11 @ SY168 )
= SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(321,plain,
! [SV12: $i] :
( ( subset @ empty_set @ SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(322,plain,
! [SV13: $i] :
( ( ! [SY169: $i] :
( ~ ( subset @ SV13 @ SY169 )
| ! [SY170: $i] : ( subset @ ( set_difference @ SV13 @ SY170 ) @ ( set_difference @ SY169 @ SY170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(323,plain,
! [SV14: $i] :
( ( ! [SY171: $i] : ( subset @ ( set_difference @ SV14 @ SY171 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(324,plain,
! [SV15: $i] :
( ( ! [SY172: $i] :
( ( set_union2 @ SV15 @ ( set_difference @ SY172 @ SV15 ) )
= ( set_union2 @ SV15 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(325,plain,
! [SV16: $i] :
( ( ~ ( subset @ SV16 @ empty_set )
| ( SV16 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(326,plain,
! [SV17: $i] :
( ( ! [SY173: $i] :
( ( set_difference @ ( set_union2 @ SV17 @ SY173 ) @ SY173 )
= ( set_difference @ SV17 @ SY173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(327,plain,
! [SV18: $i] :
( ( ! [SY174: $i] :
( ~ ( subset @ SV18 @ SY174 )
| ( SY174
= ( set_union2 @ SV18 @ ( set_difference @ SY174 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(328,plain,
! [SV19: $i] :
( ( ! [SY175: $i] :
( ( set_difference @ SV19 @ ( set_difference @ SV19 @ SY175 ) )
= ( set_intersection2 @ SV19 @ SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(329,plain,
! [SV20: $i] :
( ( ! [SY176: $i] :
( ~ ( proper_subset @ SY176 @ SV20 )
| ~ ( subset @ SV20 @ SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(330,plain,
! [SV21: $i] :
( ( ! [SY177: $i,SY178: $i] :
( ~ ( disjoint @ SY177 @ SY178 )
| ~ ( subset @ SV21 @ SY177 )
| ( disjoint @ SV21 @ SY178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(331,plain,
! [SV22: $i] :
( ( ( unordered_pair @ SV22 @ SV22 )
= ( singleton @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(332,plain,
! [SV23: $i] :
( ( ! [SY179: $i] :
( ~ ( subset @ ( singleton @ SV23 ) @ ( singleton @ SY179 ) )
| ( SV23 = SY179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(333,plain,
! [SV24: $i] :
( ( ! [SY180: $i] : ( subset @ SV24 @ ( set_union2 @ SV24 @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(334,plain,
! [SV25: $i] :
( ( ! [SY181: $i,SY182: $i] :
( ~ ( subset @ SV25 @ SY181 )
| ~ ( subset @ SY182 @ SY181 )
| ( subset @ ( set_union2 @ SV25 @ SY182 ) @ SY181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(335,plain,
! [SV26: $i] :
( ( ! [SY183: $i] :
( ! [SY184: $i] :
( ( singleton @ SV26 )
!= ( unordered_pair @ SY183 @ SY184 ) )
| ( SV26 = SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(336,plain,
! [SV27: $i] :
( ( ! [SY185: $i,SY186: $i] :
( ( ( singleton @ SV27 )
!= ( unordered_pair @ SY185 @ SY186 ) )
| ( SY185 = SY186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(337,plain,
! [SV28: $i] :
( ( ! [SY187: $i] :
( ~ ( in @ SV28 @ SY187 )
| ~ ( in @ SY187 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(338,plain,
! [SV29: $i] :
( ( ! [SY188: $i] :
( ~ ( proper_subset @ SV29 @ SY188 )
| ~ ( proper_subset @ SY188 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(339,plain,
! [SV30: $i] :
( ( ! [SY189: $i] :
( ( unordered_pair @ SV30 @ SY189 )
= ( unordered_pair @ SY189 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(340,plain,
! [SV31: $i] :
( ( ! [SY190: $i] :
( ( set_union2 @ SV31 @ SY190 )
= ( set_union2 @ SY190 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(341,plain,
! [SV32: $i] :
( ( ! [SY191: $i] :
( ( set_intersection2 @ SV32 @ SY191 )
= ( set_intersection2 @ SY191 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(342,plain,
! [SV33: $i] :
( ( ( empty @ SV33 )
| ! [SY192: $i] :
~ ( empty @ ( set_union2 @ SV33 @ SY192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(343,plain,
! [SV34: $i] :
( ( ( empty @ SV34 )
| ! [SY193: $i] :
~ ( empty @ ( set_union2 @ SY193 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(344,plain,
! [SV35: $i] :
( ( ( set_union2 @ SV35 @ SV35 )
= SV35 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(345,plain,
! [SV36: $i] :
( ( ( set_intersection2 @ SV36 @ SV36 )
= SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(346,plain,
! [SV37: $i] :
( ( ~ ( proper_subset @ SV37 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(347,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(348,plain,
! [SV38: $i] :
( ( subset @ SV38 @ SV38 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(349,plain,
! [SV39: $i] :
( ( ! [SY194: $i] :
( ~ ( disjoint @ SV39 @ SY194 )
| ( disjoint @ SY194 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(350,plain,
! [SV40: $i] :
( ( ( set_union2 @ SV40 @ empty_set )
= SV40 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(351,plain,
! [SV41: $i] :
( ( ( set_intersection2 @ SV41 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(352,plain,
! [SV42: $i] :
( ( ( set_difference @ SV42 @ empty_set )
= SV42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(353,plain,
! [SV43: $i] :
( ( ( set_difference @ empty_set @ SV43 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(354,plain,
! [SV44: $i] :
( ( ~ ( empty @ SV44 )
| ( SV44 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(355,plain,
! [SV45: $i] :
( ( ! [SY195: $i] :
( ~ ( empty @ SY195 )
| ~ ( in @ SV45 @ SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(356,plain,
! [SV46: $i] :
( ( ! [SY196: $i] :
( ( SV46 = SY196 )
| ~ ( empty @ SV46 )
| ~ ( empty @ SY196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(357,plain,
( ( in @ sK1_A @ sK2_SY152 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(358,plain,
( ( disjoint @ ( singleton @ sK1_A ) @ sK2_SY152 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(359,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK14_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(360,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(361,plain,
! [SV47: $i] :
( ( ~ ( ~ ! [SY197: $i,SY198: $i] :
( ~ ( ~ ( ~ ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SV47 )
| ~ ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY197 )
| ~ ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY198 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY198 ) )
| ~ ( ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY197 )
| ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY198 ) ) ) )
| ( SY198
= ( set_intersection2 @ SV47 @ SY197 ) ) )
| ~ ! [SY199: $i,SY200: $i] :
( ( SY200
!= ( set_intersection2 @ SV47 @ SY199 ) )
| ~ ( ~ ! [SY201: $i] :
( ~ ( in @ SY201 @ SV47 )
| ~ ( in @ SY201 @ SY199 )
| ( in @ SY201 @ SY200 ) )
| ~ ~ ( ~ ! [SY202: $i] :
( ~ ( in @ SY202 @ SY200 )
| ( in @ SY202 @ SV47 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY200 )
| ( in @ SX3 @ SY199 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(362,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK12_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) )
| ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(363,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK13_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK13_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(364,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(365,plain,
! [SV48: $i] :
( ( ~ ( ~ ! [SY204: $i,SY205: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY204 )
| ~ ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY205 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY205 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY204 )
| ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY205 ) ) ) )
| ( SY205
= ( set_difference @ SV48 @ SY204 ) ) )
| ~ ! [SY206: $i,SY207: $i] :
( ( SY207
!= ( set_difference @ SV48 @ SY206 ) )
| ~ ( ~ ! [SY208: $i] :
( ~ ( in @ SY208 @ SV48 )
| ( in @ SY208 @ SY206 )
| ( in @ SY208 @ SY207 ) )
| ~ ~ ( ~ ! [SY209: $i] :
( ~ ( in @ SY209 @ SY207 )
| ( in @ SY209 @ SV48 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY207 )
| ~ ( in @ SX3 @ SY206 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(366,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(367,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(368,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(369,plain,
! [SV49: $i] :
( ( ~ ( ~ ! [SY211: $i,SY212: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY212 )
| ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY212 )
| ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY211 ) ) )
| ~ ( ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY212 )
| ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SV49 )
| ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY211 ) ) )
| ( SY212
= ( set_union2 @ SV49 @ SY211 ) ) )
| ~ ! [SY213: $i,SY214: $i] :
( ( SY214
!= ( set_union2 @ SV49 @ SY213 ) )
| ~ ( ~ ! [SY215: $i] :
( ~ ( in @ SY215 @ SY214 )
| ( in @ SY215 @ SV49 )
| ( in @ SY215 @ SY213 ) )
| ~ ~ ( ~ ! [SY216: $i] :
( ~ ( in @ SY216 @ SV49 )
| ( in @ SY216 @ SY214 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY213 )
| ( in @ SX3 @ SY214 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(370,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) )
| ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(371,plain,
! [SV50: $i] :
( ( ! [SY218: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SY218 @ SV50 ) @ SV50 )
| ~ ( in @ ( sK3_C @ SY218 @ SV50 ) @ SY218 ) )
| ~ ( ( in @ ( sK3_C @ SY218 @ SV50 ) @ SV50 )
| ( in @ ( sK3_C @ SY218 @ SV50 ) @ SY218 ) ) )
| ( SV50 = SY218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(372,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK11_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK11_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(373,plain,
! [SV51: $i] :
( ( ~ ( ~ ! [SY219: $i,SY220: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK10_D @ SY220 @ SY219 @ SV51 ) @ SY220 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK10_D @ SY220 @ SY219 @ SV51 ) @ SY220 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
!= SY219 ) ) )
| ~ ( ( in @ ( sK10_D @ SY220 @ SY219 @ SV51 ) @ SY220 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
= SV51 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
= SY219 ) ) )
| ( SY220
= ( unordered_pair @ SV51 @ SY219 ) ) )
| ~ ! [SY221: $i,SY222: $i] :
( ( SY222
!= ( unordered_pair @ SV51 @ SY221 ) )
| ~ ( ~ ! [SY223: $i] :
( ~ ( in @ SY223 @ SY222 )
| ( SY223 = SV51 )
| ( SY223 = SY221 ) )
| ~ ~ ( ~ ! [SY224: $i] :
( ( SY224 != SV51 )
| ( in @ SY224 @ SY222 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY221 )
| ( in @ SX3 @ SY222 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(374,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(375,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(376,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(377,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(378,plain,
! [SV1: $i] :
( ( ( singleton @ SV1 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(379,plain,
! [SV52: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV52 )
| ( ( set_union2 @ ( singleton @ SV2 ) @ SV52 )
= SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(380,plain,
! [SV53: $i,SV3: $i] :
( ( ~ ( disjoint @ ( singleton @ SV3 ) @ SV53 )
| ~ ( in @ SV3 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(381,plain,
! [SV54: $i,SV4: $i] :
( ( ~ ( subset @ SV4 @ SV54 )
| ! [SY226: $i] :
( ( in @ SY226 @ SV4 )
| ( subset @ SV4 @ ( set_difference @ SV54 @ ( singleton @ SY226 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(382,plain,
! [SV55: $i,SV5: $i] :
( ( ! [SY227: $i,SY228: $i] :
( ( SV5 = SY228 )
| ( SV5 = SY227 )
| ( ( unordered_pair @ SV5 @ SV55 )
!= ( unordered_pair @ SY227 @ SY228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(383,plain,
! [SV56: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV56 )
| ( ( set_union2 @ SV6 @ SV56 )
= SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(384,plain,
! [SV57: $i,SV7: $i] :
( ( subset @ ( set_intersection2 @ SV7 @ SV57 ) @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(385,plain,
! [SV58: $i,SV8: $i] :
( ( ! [SY229: $i] :
( ~ ( subset @ SV8 @ SV58 )
| ~ ( subset @ SV8 @ SY229 )
| ( subset @ SV8 @ ( set_intersection2 @ SV58 @ SY229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(386,plain,
! [SV59: $i,SV9: $i] :
( ( ! [SY230: $i] :
( ~ ( subset @ SV9 @ SV59 )
| ~ ( subset @ SV59 @ SY230 )
| ( subset @ SV9 @ SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(387,plain,
! [SV60: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV60 )
| ! [SY231: $i] : ( subset @ ( set_intersection2 @ SV10 @ SY231 ) @ ( set_intersection2 @ SV60 @ SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(388,plain,
! [SV61: $i,SV11: $i] :
( ( ~ ( subset @ SV11 @ SV61 )
| ( ( set_intersection2 @ SV11 @ SV61 )
= SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(389,plain,
! [SV62: $i,SV13: $i] :
( ( ~ ( subset @ SV13 @ SV62 )
| ! [SY232: $i] : ( subset @ ( set_difference @ SV13 @ SY232 ) @ ( set_difference @ SV62 @ SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(390,plain,
! [SV63: $i,SV14: $i] :
( ( subset @ ( set_difference @ SV14 @ SV63 ) @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(391,plain,
! [SV64: $i,SV15: $i] :
( ( ( set_union2 @ SV15 @ ( set_difference @ SV64 @ SV15 ) )
= ( set_union2 @ SV15 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(392,plain,
! [SV16: $i] :
( ( ( ~ ( subset @ SV16 @ empty_set ) )
= $true )
| ( ( SV16 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(393,plain,
! [SV65: $i,SV17: $i] :
( ( ( set_difference @ ( set_union2 @ SV17 @ SV65 ) @ SV65 )
= ( set_difference @ SV17 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(394,plain,
! [SV66: $i,SV18: $i] :
( ( ~ ( subset @ SV18 @ SV66 )
| ( SV66
= ( set_union2 @ SV18 @ ( set_difference @ SV66 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(395,plain,
! [SV67: $i,SV19: $i] :
( ( ( set_difference @ SV19 @ ( set_difference @ SV19 @ SV67 ) )
= ( set_intersection2 @ SV19 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(396,plain,
! [SV20: $i,SV68: $i] :
( ( ~ ( proper_subset @ SV68 @ SV20 )
| ~ ( subset @ SV20 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(397,plain,
! [SV21: $i,SV69: $i] :
( ( ! [SY233: $i] :
( ~ ( disjoint @ SV69 @ SY233 )
| ~ ( subset @ SV21 @ SV69 )
| ( disjoint @ SV21 @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(398,plain,
! [SV70: $i,SV23: $i] :
( ( ~ ( subset @ ( singleton @ SV23 ) @ ( singleton @ SV70 ) )
| ( SV23 = SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(399,plain,
! [SV71: $i,SV24: $i] :
( ( subset @ SV24 @ ( set_union2 @ SV24 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(400,plain,
! [SV72: $i,SV25: $i] :
( ( ! [SY234: $i] :
( ~ ( subset @ SV25 @ SV72 )
| ~ ( subset @ SY234 @ SV72 )
| ( subset @ ( set_union2 @ SV25 @ SY234 ) @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(401,plain,
! [SV73: $i,SV26: $i] :
( ( ! [SY235: $i] :
( ( singleton @ SV26 )
!= ( unordered_pair @ SV73 @ SY235 ) )
| ( SV26 = SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(402,plain,
! [SV74: $i,SV27: $i] :
( ( ! [SY236: $i] :
( ( ( singleton @ SV27 )
!= ( unordered_pair @ SV74 @ SY236 ) )
| ( SV74 = SY236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(403,plain,
! [SV75: $i,SV28: $i] :
( ( ~ ( in @ SV28 @ SV75 )
| ~ ( in @ SV75 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(404,plain,
! [SV76: $i,SV29: $i] :
( ( ~ ( proper_subset @ SV29 @ SV76 )
| ~ ( proper_subset @ SV76 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(405,plain,
! [SV77: $i,SV30: $i] :
( ( ( unordered_pair @ SV30 @ SV77 )
= ( unordered_pair @ SV77 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(406,plain,
! [SV78: $i,SV31: $i] :
( ( ( set_union2 @ SV31 @ SV78 )
= ( set_union2 @ SV78 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(407,plain,
! [SV79: $i,SV32: $i] :
( ( ( set_intersection2 @ SV32 @ SV79 )
= ( set_intersection2 @ SV79 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(408,plain,
! [SV33: $i] :
( ( ( empty @ SV33 )
= $true )
| ( ( ! [SY192: $i] :
~ ( empty @ ( set_union2 @ SV33 @ SY192 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(409,plain,
! [SV34: $i] :
( ( ( empty @ SV34 )
= $true )
| ( ( ! [SY193: $i] :
~ ( empty @ ( set_union2 @ SY193 @ SV34 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(410,plain,
! [SV37: $i] :
( ( proper_subset @ SV37 @ SV37 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(411,plain,
! [SV80: $i,SV39: $i] :
( ( ~ ( disjoint @ SV39 @ SV80 )
| ( disjoint @ SV80 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(412,plain,
! [SV44: $i] :
( ( ( ~ ( empty @ SV44 ) )
= $true )
| ( ( SV44 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(413,plain,
! [SV45: $i,SV81: $i] :
( ( ~ ( empty @ SV81 )
| ~ ( in @ SV45 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(414,plain,
! [SV82: $i,SV46: $i] :
( ( ( SV46 = SV82 )
| ~ ( empty @ SV46 )
| ~ ( empty @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(415,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK14_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(416,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(417,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[360]) ).
thf(418,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[360]) ).
thf(419,plain,
! [SV47: $i] :
( ( ~ ! [SY197: $i,SY198: $i] :
( ~ ( ~ ( ~ ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SV47 )
| ~ ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY197 )
| ~ ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY198 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY198 ) )
| ~ ( ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY197 )
| ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY198 ) ) ) )
| ( SY198
= ( set_intersection2 @ SV47 @ SY197 ) ) )
| ~ ! [SY199: $i,SY200: $i] :
( ( SY200
!= ( set_intersection2 @ SV47 @ SY199 ) )
| ~ ( ~ ! [SY201: $i] :
( ~ ( in @ SY201 @ SV47 )
| ~ ( in @ SY201 @ SY199 )
| ( in @ SY201 @ SY200 ) )
| ~ ~ ( ~ ! [SY202: $i] :
( ~ ( in @ SY202 @ SY200 )
| ( in @ SY202 @ SV47 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY200 )
| ( in @ SX3 @ SY199 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(420,plain,
( ( ~ ! [SX0: $i] :
( ( in @ ( sK12_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(421,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[362]) ).
thf(422,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK13_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK13_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(423,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[363]) ).
thf(424,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(425,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(426,plain,
! [SV48: $i] :
( ( ~ ! [SY204: $i,SY205: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY204 )
| ~ ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY205 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY205 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY204 )
| ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY205 ) ) ) )
| ( SY205
= ( set_difference @ SV48 @ SY204 ) ) )
| ~ ! [SY206: $i,SY207: $i] :
( ( SY207
!= ( set_difference @ SV48 @ SY206 ) )
| ~ ( ~ ! [SY208: $i] :
( ~ ( in @ SY208 @ SV48 )
| ( in @ SY208 @ SY206 )
| ( in @ SY208 @ SY207 ) )
| ~ ~ ( ~ ! [SY209: $i] :
( ~ ( in @ SY209 @ SY207 )
| ( in @ SY209 @ SV48 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY207 )
| ~ ( in @ SX3 @ SY206 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(427,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(428,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(429,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[367]) ).
thf(430,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[367]) ).
thf(431,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(432,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(433,plain,
! [SV49: $i] :
( ( ~ ! [SY211: $i,SY212: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY212 )
| ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY212 )
| ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY211 ) ) )
| ~ ( ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY212 )
| ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SV49 )
| ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY211 ) ) )
| ( SY212
= ( set_union2 @ SV49 @ SY211 ) ) )
| ~ ! [SY213: $i,SY214: $i] :
( ( SY214
!= ( set_union2 @ SV49 @ SY213 ) )
| ~ ( ~ ! [SY215: $i] :
( ~ ( in @ SY215 @ SY214 )
| ( in @ SY215 @ SV49 )
| ( in @ SY215 @ SY213 ) )
| ~ ~ ( ~ ! [SY216: $i] :
( ~ ( in @ SY216 @ SV49 )
| ( in @ SY216 @ SY214 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY213 )
| ( in @ SX3 @ SY214 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(434,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(435,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(436,plain,
! [SV50: $i,SV83: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
| ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 ) )
| ~ ( ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
| ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 ) ) )
| ( SV50 = SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(437,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK11_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK11_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(438,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(439,plain,
! [SV51: $i] :
( ( ~ ! [SY219: $i,SY220: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK10_D @ SY220 @ SY219 @ SV51 ) @ SY220 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK10_D @ SY220 @ SY219 @ SV51 ) @ SY220 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
!= SY219 ) ) )
| ~ ( ( in @ ( sK10_D @ SY220 @ SY219 @ SV51 ) @ SY220 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
= SV51 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
= SY219 ) ) )
| ( SY220
= ( unordered_pair @ SV51 @ SY219 ) ) )
| ~ ! [SY221: $i,SY222: $i] :
( ( SY222
!= ( unordered_pair @ SV51 @ SY221 ) )
| ~ ( ~ ! [SY223: $i] :
( ~ ( in @ SY223 @ SY222 )
| ( SY223 = SV51 )
| ( SY223 = SY221 ) )
| ~ ~ ( ~ ! [SY224: $i] :
( ( SY224 != SV51 )
| ( in @ SY224 @ SY222 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY221 )
| ( in @ SX3 @ SY222 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(440,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(441,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[374]) ).
thf(442,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(443,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(444,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(445,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(446,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[377]) ).
thf(447,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[377]) ).
thf(448,plain,
! [SV52: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV52 ) )
= $true )
| ( ( ( set_union2 @ ( singleton @ SV2 ) @ SV52 )
= SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(449,plain,
! [SV53: $i,SV3: $i] :
( ( ( ~ ( disjoint @ ( singleton @ SV3 ) @ SV53 ) )
= $true )
| ( ( ~ ( in @ SV3 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(450,plain,
! [SV54: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV54 ) )
= $true )
| ( ( ! [SY226: $i] :
( ( in @ SY226 @ SV4 )
| ( subset @ SV4 @ ( set_difference @ SV54 @ ( singleton @ SY226 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(451,plain,
! [SV55: $i,SV84: $i,SV5: $i] :
( ( ! [SY237: $i] :
( ( SV5 = SY237 )
| ( SV5 = SV84 )
| ( ( unordered_pair @ SV5 @ SV55 )
!= ( unordered_pair @ SV84 @ SY237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(452,plain,
! [SV56: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV56 ) )
= $true )
| ( ( ( set_union2 @ SV6 @ SV56 )
= SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(453,plain,
! [SV85: $i,SV58: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ SV58 )
| ~ ( subset @ SV8 @ SV85 )
| ( subset @ SV8 @ ( set_intersection2 @ SV58 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(454,plain,
! [SV86: $i,SV59: $i,SV9: $i] :
( ( ~ ( subset @ SV9 @ SV59 )
| ~ ( subset @ SV59 @ SV86 )
| ( subset @ SV9 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(455,plain,
! [SV60: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV60 ) )
= $true )
| ( ( ! [SY231: $i] : ( subset @ ( set_intersection2 @ SV10 @ SY231 ) @ ( set_intersection2 @ SV60 @ SY231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(456,plain,
! [SV61: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV61 ) )
= $true )
| ( ( ( set_intersection2 @ SV11 @ SV61 )
= SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(457,plain,
! [SV62: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV62 ) )
= $true )
| ( ( ! [SY232: $i] : ( subset @ ( set_difference @ SV13 @ SY232 ) @ ( set_difference @ SV62 @ SY232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(458,plain,
! [SV16: $i] :
( ( ( subset @ SV16 @ empty_set )
= $false )
| ( ( SV16 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(459,plain,
! [SV66: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV66 ) )
= $true )
| ( ( SV66
= ( set_union2 @ SV18 @ ( set_difference @ SV66 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(460,plain,
! [SV20: $i,SV68: $i] :
( ( ( ~ ( proper_subset @ SV68 @ SV20 ) )
= $true )
| ( ( ~ ( subset @ SV20 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(461,plain,
! [SV21: $i,SV87: $i,SV69: $i] :
( ( ~ ( disjoint @ SV69 @ SV87 )
| ~ ( subset @ SV21 @ SV69 )
| ( disjoint @ SV21 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(462,plain,
! [SV70: $i,SV23: $i] :
( ( ( ~ ( subset @ ( singleton @ SV23 ) @ ( singleton @ SV70 ) ) )
= $true )
| ( ( SV23 = SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(463,plain,
! [SV88: $i,SV72: $i,SV25: $i] :
( ( ~ ( subset @ SV25 @ SV72 )
| ~ ( subset @ SV88 @ SV72 )
| ( subset @ ( set_union2 @ SV25 @ SV88 ) @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(464,plain,
! [SV73: $i,SV26: $i] :
( ( ( ! [SY235: $i] :
( ( singleton @ SV26 )
!= ( unordered_pair @ SV73 @ SY235 ) ) )
= $true )
| ( ( SV26 = SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(465,plain,
! [SV89: $i,SV74: $i,SV27: $i] :
( ( ( ( singleton @ SV27 )
!= ( unordered_pair @ SV74 @ SV89 ) )
| ( SV74 = SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(466,plain,
! [SV75: $i,SV28: $i] :
( ( ( ~ ( in @ SV28 @ SV75 ) )
= $true )
| ( ( ~ ( in @ SV75 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(467,plain,
! [SV76: $i,SV29: $i] :
( ( ( ~ ( proper_subset @ SV29 @ SV76 ) )
= $true )
| ( ( ~ ( proper_subset @ SV76 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(468,plain,
! [SV90: $i,SV33: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV33 @ SV90 ) ) )
= $true )
| ( ( empty @ SV33 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(469,plain,
! [SV34: $i,SV91: $i] :
( ( ( ~ ( empty @ ( set_union2 @ SV91 @ SV34 ) ) )
= $true )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(470,plain,
! [SV80: $i,SV39: $i] :
( ( ( ~ ( disjoint @ SV39 @ SV80 ) )
= $true )
| ( ( disjoint @ SV80 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(471,plain,
! [SV44: $i] :
( ( ( empty @ SV44 )
= $false )
| ( ( SV44 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(472,plain,
! [SV45: $i,SV81: $i] :
( ( ( ~ ( empty @ SV81 ) )
= $true )
| ( ( ~ ( in @ SV45 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(473,plain,
! [SV82: $i,SV46: $i] :
( ( ( ( SV46 = SV82 )
| ~ ( empty @ SV46 ) )
= $true )
| ( ( ~ ( empty @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(474,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ( in @ ( sK14_C @ SX1 @ SX0 ) @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(475,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
~ ( in @ SX2 @ ( set_intersection2 @ SX0 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(476,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 = SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ( proper_subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(477,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(478,plain,
! [SV47: $i] :
( ( ~ ! [SY197: $i,SY198: $i] :
( ~ ( ~ ( ~ ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SV47 )
| ~ ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY197 )
| ~ ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY198 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY198 ) )
| ~ ( ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY197 )
| ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY198 ) ) ) )
| ( SY198
= ( set_intersection2 @ SV47 @ SY197 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[419]) ).
thf(479,plain,
! [SV47: $i] :
( ( ~ ! [SY199: $i,SY200: $i] :
( ( SY200
!= ( set_intersection2 @ SV47 @ SY199 ) )
| ~ ( ~ ! [SY201: $i] :
( ~ ( in @ SY201 @ SV47 )
| ~ ( in @ SY201 @ SY199 )
| ( in @ SY201 @ SY200 ) )
| ~ ~ ( ~ ! [SY202: $i] :
( ~ ( in @ SY202 @ SY200 )
| ( in @ SY202 @ SV47 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY200 )
| ( in @ SX3 @ SY199 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[419]) ).
thf(480,plain,
( ( ! [SX0: $i] :
( ( in @ ( sK12_B @ SX0 ) @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(481,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(482,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ( ( sK13_C @ SX1 @ SX0 )
!= SX0 )
| ~ ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( ( sK13_C @ SX1 @ SX0 )
= SX0 )
| ( in @ ( sK13_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(483,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( singleton @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(484,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( disjoint @ SX0 @ SX1 )
| ~ ( ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK15_C @ SX1 @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(485,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ~ ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(486,plain,
! [SV48: $i] :
( ( ~ ! [SY204: $i,SY205: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY204 )
| ~ ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY205 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY205 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY204 )
| ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY205 ) ) ) )
| ( SY205
= ( set_difference @ SV48 @ SY204 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(487,plain,
! [SV48: $i] :
( ( ~ ! [SY206: $i,SY207: $i] :
( ( SY207
!= ( set_difference @ SV48 @ SY206 ) )
| ~ ( ~ ! [SY208: $i] :
( ~ ( in @ SY208 @ SV48 )
| ( in @ SY208 @ SY206 )
| ( in @ SY208 @ SY207 ) )
| ~ ~ ( ~ ! [SY209: $i] :
( ~ ( in @ SY209 @ SY207 )
| ( in @ SY209 @ SV48 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY207 )
| ~ ( in @ SX3 @ SY206 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(488,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= SX0 )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(489,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(490,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK8_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(491,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(492,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(493,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(494,plain,
! [SV49: $i] :
( ( ~ ! [SY211: $i,SY212: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY212 )
| ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY212 )
| ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY211 ) ) )
| ~ ( ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY212 )
| ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SV49 )
| ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY211 ) ) )
| ( SY212
= ( set_union2 @ SV49 @ SY211 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(495,plain,
! [SV49: $i] :
( ( ~ ! [SY213: $i,SY214: $i] :
( ( SY214
!= ( set_union2 @ SV49 @ SY213 ) )
| ~ ( ~ ! [SY215: $i] :
( ~ ( in @ SY215 @ SY214 )
| ( in @ SY215 @ SV49 )
| ( in @ SY215 @ SY213 ) )
| ~ ~ ( ~ ! [SY216: $i] :
( ~ ( in @ SY216 @ SV49 )
| ( in @ SY216 @ SY214 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY213 )
| ( in @ SX3 @ SY214 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(496,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(497,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(498,plain,
! [SV50: $i,SV83: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
| ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 ) )
| ~ ( ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
| ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 ) ) ) )
= $true )
| ( ( SV50 = SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(499,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( subset @ ( sK11_C @ SX1 @ SX0 ) @ SX0 ) )
| ~ ( ( in @ ( sK11_C @ SX1 @ SX0 ) @ SX1 )
| ( subset @ ( sK11_C @ SX1 @ SX0 ) @ SX0 ) ) )
| ( SX1
= ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(500,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX1
!= ( powerset @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX0 ) )
| ~ ! [SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(501,plain,
! [SV51: $i] :
( ( ~ ! [SY219: $i,SY220: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK10_D @ SY220 @ SY219 @ SV51 ) @ SY220 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK10_D @ SY220 @ SY219 @ SV51 ) @ SY220 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
!= SY219 ) ) )
| ~ ( ( in @ ( sK10_D @ SY220 @ SY219 @ SV51 ) @ SY220 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
= SV51 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
= SY219 ) ) )
| ( SY220
= ( unordered_pair @ SV51 @ SY219 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(502,plain,
! [SV51: $i] :
( ( ~ ! [SY221: $i,SY222: $i] :
( ( SY222
!= ( unordered_pair @ SV51 @ SY221 ) )
| ~ ( ~ ! [SY223: $i] :
( ~ ( in @ SY223 @ SY222 )
| ( SY223 = SV51 )
| ( SY223 = SY221 ) )
| ~ ~ ( ~ ! [SY224: $i] :
( ( SY224 != SV51 )
| ( in @ SY224 @ SY222 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY221 )
| ( in @ SX3 @ SY222 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(503,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(504,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(505,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(506,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(507,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(508,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(509,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(510,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(511,plain,
! [SV52: $i,SV2: $i] :
( ( ( in @ SV2 @ SV52 )
= $false )
| ( ( ( set_union2 @ ( singleton @ SV2 ) @ SV52 )
= SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(512,plain,
! [SV53: $i,SV3: $i] :
( ( ( disjoint @ ( singleton @ SV3 ) @ SV53 )
= $false )
| ( ( ~ ( in @ SV3 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(513,plain,
! [SV54: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV54 )
= $false )
| ( ( ! [SY226: $i] :
( ( in @ SY226 @ SV4 )
| ( subset @ SV4 @ ( set_difference @ SV54 @ ( singleton @ SY226 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(514,plain,
! [SV55: $i,SV84: $i,SV92: $i,SV5: $i] :
( ( ( SV5 = SV92 )
| ( SV5 = SV84 )
| ( ( unordered_pair @ SV5 @ SV55 )
!= ( unordered_pair @ SV84 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(515,plain,
! [SV56: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV56 )
= $false )
| ( ( ( set_union2 @ SV6 @ SV56 )
= SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(516,plain,
! [SV85: $i,SV58: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV58 )
| ~ ( subset @ SV8 @ SV85 ) )
= $true )
| ( ( subset @ SV8 @ ( set_intersection2 @ SV58 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(517,plain,
! [SV86: $i,SV59: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV59 )
| ~ ( subset @ SV59 @ SV86 ) )
= $true )
| ( ( subset @ SV9 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(518,plain,
! [SV60: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV60 )
= $false )
| ( ( ! [SY231: $i] : ( subset @ ( set_intersection2 @ SV10 @ SY231 ) @ ( set_intersection2 @ SV60 @ SY231 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(519,plain,
! [SV61: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV61 )
= $false )
| ( ( ( set_intersection2 @ SV11 @ SV61 )
= SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(520,plain,
! [SV62: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV62 )
= $false )
| ( ( ! [SY232: $i] : ( subset @ ( set_difference @ SV13 @ SY232 ) @ ( set_difference @ SV62 @ SY232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(521,plain,
! [SV66: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV66 )
= $false )
| ( ( SV66
= ( set_union2 @ SV18 @ ( set_difference @ SV66 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(522,plain,
! [SV20: $i,SV68: $i] :
( ( ( proper_subset @ SV68 @ SV20 )
= $false )
| ( ( ~ ( subset @ SV20 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(523,plain,
! [SV21: $i,SV87: $i,SV69: $i] :
( ( ( ~ ( disjoint @ SV69 @ SV87 )
| ~ ( subset @ SV21 @ SV69 ) )
= $true )
| ( ( disjoint @ SV21 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(524,plain,
! [SV70: $i,SV23: $i] :
( ( ( subset @ ( singleton @ SV23 ) @ ( singleton @ SV70 ) )
= $false )
| ( ( SV23 = SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(525,plain,
! [SV88: $i,SV72: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV72 )
| ~ ( subset @ SV88 @ SV72 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV25 @ SV88 ) @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(526,plain,
! [SV93: $i,SV73: $i,SV26: $i] :
( ( ( ( ( singleton @ SV26 )
!= ( unordered_pair @ SV73 @ SV93 ) ) )
= $true )
| ( ( SV26 = SV73 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(527,plain,
! [SV89: $i,SV74: $i,SV27: $i] :
( ( ( ( ( singleton @ SV27 )
!= ( unordered_pair @ SV74 @ SV89 ) ) )
= $true )
| ( ( SV74 = SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(528,plain,
! [SV75: $i,SV28: $i] :
( ( ( in @ SV28 @ SV75 )
= $false )
| ( ( ~ ( in @ SV75 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(529,plain,
! [SV76: $i,SV29: $i] :
( ( ( proper_subset @ SV29 @ SV76 )
= $false )
| ( ( ~ ( proper_subset @ SV76 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(530,plain,
! [SV90: $i,SV33: $i] :
( ( ( empty @ ( set_union2 @ SV33 @ SV90 ) )
= $false )
| ( ( empty @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(531,plain,
! [SV34: $i,SV91: $i] :
( ( ( empty @ ( set_union2 @ SV91 @ SV34 ) )
= $false )
| ( ( empty @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(532,plain,
! [SV80: $i,SV39: $i] :
( ( ( disjoint @ SV39 @ SV80 )
= $false )
| ( ( disjoint @ SV80 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(533,plain,
! [SV45: $i,SV81: $i] :
( ( ( empty @ SV81 )
= $false )
| ( ( ~ ( in @ SV45 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(534,plain,
! [SV82: $i,SV46: $i] :
( ( ( SV46 = SV82 )
= $true )
| ( ( ~ ( empty @ SV46 ) )
= $true )
| ( ( ~ ( empty @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(535,plain,
! [SV94: $i] :
( ( ! [SY238: $i] :
( ( disjoint @ SV94 @ SY238 )
| ( in @ ( sK14_C @ SY238 @ SV94 ) @ ( set_intersection2 @ SV94 @ SY238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(536,plain,
! [SV95: $i] :
( ( ! [SY239: $i] :
( ! [SY240: $i] :
~ ( in @ SY240 @ ( set_intersection2 @ SV95 @ SY239 ) )
| ~ ( disjoint @ SV95 @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(537,plain,
! [SV96: $i] :
( ( ! [SY241: $i] :
( ( SV96 = SY241 )
| ~ ( subset @ SV96 @ SY241 )
| ( proper_subset @ SV96 @ SY241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(538,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(539,plain,
! [SV47: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ~ ( ~ ( ~ ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SV47 )
| ~ ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY197 )
| ~ ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY198 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY198 ) )
| ~ ( ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY197 )
| ( in @ ( sK7_D @ SY198 @ SY197 @ SV47 ) @ SY198 ) ) ) )
| ( SY198
= ( set_intersection2 @ SV47 @ SY197 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(540,plain,
! [SV47: $i] :
( ( ! [SY199: $i,SY200: $i] :
( ( SY200
!= ( set_intersection2 @ SV47 @ SY199 ) )
| ~ ( ~ ! [SY201: $i] :
( ~ ( in @ SY201 @ SV47 )
| ~ ( in @ SY201 @ SY199 )
| ( in @ SY201 @ SY200 ) )
| ~ ~ ( ~ ! [SY202: $i] :
( ~ ( in @ SY202 @ SY200 )
| ( in @ SY202 @ SV47 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY200 )
| ( in @ SX3 @ SY199 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(541,plain,
! [SV97: $i] :
( ( ( in @ ( sK12_B @ SV97 ) @ SV97 )
| ( SV97 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(542,plain,
! [SV98: $i] :
( ( ( SV98 != empty_set )
| ! [SY242: $i] :
~ ( in @ SY242 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(543,plain,
! [SV99: $i] :
( ( ! [SY243: $i] :
( ~ ( ~ ( ( ( sK13_C @ SY243 @ SV99 )
!= SV99 )
| ~ ( in @ ( sK13_C @ SY243 @ SV99 ) @ SY243 ) )
| ~ ( ( ( sK13_C @ SY243 @ SV99 )
= SV99 )
| ( in @ ( sK13_C @ SY243 @ SV99 ) @ SY243 ) ) )
| ( SY243
= ( singleton @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(544,plain,
! [SV100: $i] :
( ( ! [SY244: $i] :
( ( SY244
!= ( singleton @ SV100 ) )
| ~ ( ~ ! [SY245: $i] :
( ( SY245 != SV100 )
| ( in @ SY245 @ SY244 ) )
| ~ ! [SY246: $i] :
( ~ ( in @ SY246 @ SY244 )
| ( SY246 = SV100 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(545,plain,
! [SV101: $i] :
( ( ! [SY247: $i] :
( ( disjoint @ SV101 @ SY247 )
| ~ ( ~ ( in @ ( sK15_C @ SY247 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK15_C @ SY247 @ SV101 ) @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(546,plain,
! [SV102: $i] :
( ( ! [SY248: $i] :
( ! [SY249: $i] :
( ~ ( in @ SY249 @ SV102 )
| ~ ( in @ SY249 @ SY248 ) )
| ~ ( disjoint @ SV102 @ SY248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(547,plain,
! [SV48: $i] :
( ( ! [SY204: $i,SY205: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY204 )
| ~ ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY205 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY205 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY204 )
| ( in @ ( sK6_D @ SY205 @ SY204 @ SV48 ) @ SY205 ) ) ) )
| ( SY205
= ( set_difference @ SV48 @ SY204 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(548,plain,
! [SV48: $i] :
( ( ! [SY206: $i,SY207: $i] :
( ( SY207
!= ( set_difference @ SV48 @ SY206 ) )
| ~ ( ~ ! [SY208: $i] :
( ~ ( in @ SY208 @ SV48 )
| ( in @ SY208 @ SY206 )
| ( in @ SY208 @ SY207 ) )
| ~ ~ ( ~ ! [SY209: $i] :
( ~ ( in @ SY209 @ SY207 )
| ( in @ SY209 @ SV48 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY207 )
| ~ ( in @ SX3 @ SY206 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(549,plain,
! [SV103: $i] :
( ( ! [SY250: $i] :
( ( ( set_difference @ SV103 @ SY250 )
!= SV103 )
| ( disjoint @ SV103 @ SY250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(550,plain,
! [SV104: $i] :
( ( ! [SY251: $i] :
( ~ ( disjoint @ SV104 @ SY251 )
| ( ( set_difference @ SV104 @ SY251 )
= SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(551,plain,
! [SV105: $i] :
( ( ! [SY252: $i] :
( ~ ( ~ ( in @ ( sK8_C @ SY252 @ SV105 ) @ SV105 )
| ~ ~ ( in @ ( sK8_C @ SY252 @ SV105 ) @ SY252 ) )
| ( subset @ SV105 @ SY252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(552,plain,
! [SV106: $i] :
( ( ! [SY253: $i] :
( ~ ( subset @ SV106 @ SY253 )
| ! [SY254: $i] :
( ~ ( in @ SY254 @ SV106 )
| ( in @ SY254 @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(553,plain,
! [SV107: $i] :
( ( ! [SY255: $i] :
( ~ ( in @ SV107 @ SY255 )
| ( subset @ ( singleton @ SV107 ) @ SY255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(554,plain,
! [SV108: $i] :
( ( ! [SY256: $i] :
( ~ ( subset @ ( singleton @ SV108 ) @ SY256 )
| ( in @ SV108 @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(555,plain,
! [SV49: $i] :
( ( ! [SY211: $i,SY212: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY212 )
| ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY212 )
| ~ ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY211 ) ) )
| ~ ( ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY212 )
| ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SV49 )
| ( in @ ( sK9_D @ SY212 @ SY211 @ SV49 ) @ SY211 ) ) )
| ( SY212
= ( set_union2 @ SV49 @ SY211 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(556,plain,
! [SV49: $i] :
( ( ! [SY213: $i,SY214: $i] :
( ( SY214
!= ( set_union2 @ SV49 @ SY213 ) )
| ~ ( ~ ! [SY215: $i] :
( ~ ( in @ SY215 @ SY214 )
| ( in @ SY215 @ SV49 )
| ( in @ SY215 @ SY213 ) )
| ~ ~ ( ~ ! [SY216: $i] :
( ~ ( in @ SY216 @ SV49 )
| ( in @ SY216 @ SY214 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SY213 )
| ( in @ SX3 @ SY214 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(557,plain,
! [SV109: $i] :
( ( ! [SY257: $i] :
( ~ ( subset @ SV109 @ SY257 )
| ~ ( subset @ SY257 @ SV109 )
| ( SV109 = SY257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(558,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(559,plain,
! [SV50: $i,SV83: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
| ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 ) )
| ~ ( ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
| ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 ) ) )
= $false )
| ( ( SV50 = SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(560,plain,
! [SV110: $i] :
( ( ! [SY258: $i] :
( ~ ( ~ ( ~ ( in @ ( sK11_C @ SY258 @ SV110 ) @ SY258 )
| ~ ( subset @ ( sK11_C @ SY258 @ SV110 ) @ SV110 ) )
| ~ ( ( in @ ( sK11_C @ SY258 @ SV110 ) @ SY258 )
| ( subset @ ( sK11_C @ SY258 @ SV110 ) @ SV110 ) ) )
| ( SY258
= ( powerset @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(561,plain,
! [SV111: $i] :
( ( ! [SY259: $i] :
( ( SY259
!= ( powerset @ SV111 ) )
| ~ ( ~ ! [SY260: $i] :
( ~ ( in @ SY260 @ SY259 )
| ( subset @ SY260 @ SV111 ) )
| ~ ! [SY261: $i] :
( ~ ( subset @ SY261 @ SV111 )
| ( in @ SY261 @ SY259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(562,plain,
! [SV51: $i] :
( ( ! [SY219: $i,SY220: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK10_D @ SY220 @ SY219 @ SV51 ) @ SY220 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK10_D @ SY220 @ SY219 @ SV51 ) @ SY220 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
!= SY219 ) ) )
| ~ ( ( in @ ( sK10_D @ SY220 @ SY219 @ SV51 ) @ SY220 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
= SV51 )
| ( ( sK10_D @ SY220 @ SY219 @ SV51 )
= SY219 ) ) )
| ( SY220
= ( unordered_pair @ SV51 @ SY219 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(563,plain,
! [SV51: $i] :
( ( ! [SY221: $i,SY222: $i] :
( ( SY222
!= ( unordered_pair @ SV51 @ SY221 ) )
| ~ ( ~ ! [SY223: $i] :
( ~ ( in @ SY223 @ SY222 )
| ( SY223 = SV51 )
| ( SY223 = SY221 ) )
| ~ ~ ( ~ ! [SY224: $i] :
( ( SY224 != SV51 )
| ( in @ SY224 @ SY222 ) )
| ~ ! [SX3: $i] :
( ( SX3 != SY221 )
| ( in @ SX3 @ SY222 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(564,plain,
! [SV112: $i] :
( ( ! [SY262: $i] :
( ( ( set_difference @ SV112 @ SY262 )
!= empty_set )
| ( subset @ SV112 @ SY262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(565,plain,
! [SV113: $i] :
( ( ! [SY263: $i] :
( ~ ( subset @ SV113 @ SY263 )
| ( ( set_difference @ SV113 @ SY263 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(566,plain,
! [SV114: $i] :
( ( ! [SY264: $i] :
( ( ( set_intersection2 @ SV114 @ SY264 )
!= empty_set )
| ( disjoint @ SV114 @ SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(567,plain,
! [SV115: $i] :
( ( ! [SY265: $i] :
( ~ ( disjoint @ SV115 @ SY265 )
| ( ( set_intersection2 @ SV115 @ SY265 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(568,plain,
! [SV116: $i] :
( ( ! [SY266: $i] :
( ( ( set_difference @ SV116 @ SY266 )
!= empty_set )
| ( subset @ SV116 @ SY266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(569,plain,
! [SV117: $i] :
( ( ! [SY267: $i] :
( ~ ( subset @ SV117 @ SY267 )
| ( ( set_difference @ SV117 @ SY267 )
= empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(570,plain,
! [SV118: $i] :
( ( ! [SY268: $i] :
( ~ ( subset @ SV118 @ ( singleton @ SY268 ) )
| ( SV118 = empty_set )
| ( SV118
= ( singleton @ SY268 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(571,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(572,plain,
! [SV53: $i,SV3: $i] :
( ( ( in @ SV3 @ SV53 )
= $false )
| ( ( disjoint @ ( singleton @ SV3 ) @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(573,plain,
! [SV54: $i,SV4: $i,SV119: $i] :
( ( ( ( in @ SV119 @ SV4 )
| ( subset @ SV4 @ ( set_difference @ SV54 @ ( singleton @ SV119 ) ) ) )
= $true )
| ( ( subset @ SV4 @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(574,plain,
! [SV55: $i,SV84: $i,SV92: $i,SV5: $i] :
( ( ( SV5 = SV92 )
= $true )
| ( ( ( SV5 = SV84 )
| ( ( unordered_pair @ SV5 @ SV55 )
!= ( unordered_pair @ SV84 @ SV92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(575,plain,
! [SV85: $i,SV58: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV58 ) )
= $true )
| ( ( ~ ( subset @ SV8 @ SV85 ) )
= $true )
| ( ( subset @ SV8 @ ( set_intersection2 @ SV58 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(576,plain,
! [SV86: $i,SV59: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV59 ) )
= $true )
| ( ( ~ ( subset @ SV59 @ SV86 ) )
= $true )
| ( ( subset @ SV9 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(577,plain,
! [SV60: $i,SV120: $i,SV10: $i] :
( ( ( subset @ ( set_intersection2 @ SV10 @ SV120 ) @ ( set_intersection2 @ SV60 @ SV120 ) )
= $true )
| ( ( subset @ SV10 @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(578,plain,
! [SV62: $i,SV121: $i,SV13: $i] :
( ( ( subset @ ( set_difference @ SV13 @ SV121 ) @ ( set_difference @ SV62 @ SV121 ) )
= $true )
| ( ( subset @ SV13 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(579,plain,
! [SV68: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV68 )
= $false )
| ( ( proper_subset @ SV68 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(580,plain,
! [SV21: $i,SV87: $i,SV69: $i] :
( ( ( ~ ( disjoint @ SV69 @ SV87 ) )
= $true )
| ( ( ~ ( subset @ SV21 @ SV69 ) )
= $true )
| ( ( disjoint @ SV21 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(581,plain,
! [SV88: $i,SV72: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV72 ) )
= $true )
| ( ( ~ ( subset @ SV88 @ SV72 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV25 @ SV88 ) @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(582,plain,
! [SV93: $i,SV73: $i,SV26: $i] :
( ( ( ( singleton @ SV26 )
= ( unordered_pair @ SV73 @ SV93 ) )
= $false )
| ( ( SV26 = SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(583,plain,
! [SV89: $i,SV74: $i,SV27: $i] :
( ( ( ( singleton @ SV27 )
= ( unordered_pair @ SV74 @ SV89 ) )
= $false )
| ( ( SV74 = SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(584,plain,
! [SV28: $i,SV75: $i] :
( ( ( in @ SV75 @ SV28 )
= $false )
| ( ( in @ SV28 @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(585,plain,
! [SV29: $i,SV76: $i] :
( ( ( proper_subset @ SV76 @ SV29 )
= $false )
| ( ( proper_subset @ SV29 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(586,plain,
! [SV81: $i,SV45: $i] :
( ( ( in @ SV45 @ SV81 )
= $false )
| ( ( empty @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(587,plain,
! [SV82: $i,SV46: $i] :
( ( ( empty @ SV46 )
= $false )
| ( ( SV46 = SV82 )
= $true )
| ( ( ~ ( empty @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(588,plain,
! [SV122: $i,SV94: $i] :
( ( ( disjoint @ SV94 @ SV122 )
| ( in @ ( sK14_C @ SV122 @ SV94 ) @ ( set_intersection2 @ SV94 @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(589,plain,
! [SV123: $i,SV95: $i] :
( ( ! [SY269: $i] :
~ ( in @ SY269 @ ( set_intersection2 @ SV95 @ SV123 ) )
| ~ ( disjoint @ SV95 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(590,plain,
! [SV124: $i,SV96: $i] :
( ( ( SV96 = SV124 )
| ~ ( subset @ SV96 @ SV124 )
| ( proper_subset @ SV96 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(591,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(592,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(593,plain,
! [SV47: $i,SV125: $i] :
( ( ! [SY270: $i] :
( ~ ( ~ ( ~ ( in @ ( sK7_D @ SY270 @ SV125 @ SV47 ) @ SV47 )
| ~ ( in @ ( sK7_D @ SY270 @ SV125 @ SV47 ) @ SV125 )
| ~ ( in @ ( sK7_D @ SY270 @ SV125 @ SV47 ) @ SY270 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SY270 @ SV125 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SY270 @ SV125 @ SV47 ) @ SY270 ) )
| ~ ( ( in @ ( sK7_D @ SY270 @ SV125 @ SV47 ) @ SV125 )
| ( in @ ( sK7_D @ SY270 @ SV125 @ SV47 ) @ SY270 ) ) ) )
| ( SY270
= ( set_intersection2 @ SV47 @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(594,plain,
! [SV126: $i,SV47: $i] :
( ( ! [SY271: $i] :
( ( SY271
!= ( set_intersection2 @ SV47 @ SV126 ) )
| ~ ( ~ ! [SY272: $i] :
( ~ ( in @ SY272 @ SV47 )
| ~ ( in @ SY272 @ SV126 )
| ( in @ SY272 @ SY271 ) )
| ~ ~ ( ~ ! [SY202: $i] :
( ~ ( in @ SY202 @ SY271 )
| ( in @ SY202 @ SV47 ) )
| ~ ! [SY274: $i] :
( ~ ( in @ SY274 @ SY271 )
| ( in @ SY274 @ SV126 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(595,plain,
! [SV97: $i] :
( ( ( in @ ( sK12_B @ SV97 ) @ SV97 )
= $true )
| ( ( SV97 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(596,plain,
! [SV98: $i] :
( ( ( ( SV98 != empty_set ) )
= $true )
| ( ( ! [SY242: $i] :
~ ( in @ SY242 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(597,plain,
! [SV99: $i,SV127: $i] :
( ( ~ ( ~ ( ( ( sK13_C @ SV127 @ SV99 )
!= SV99 )
| ~ ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 ) )
| ~ ( ( ( sK13_C @ SV127 @ SV99 )
= SV99 )
| ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 ) ) )
| ( SV127
= ( singleton @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(598,plain,
! [SV100: $i,SV128: $i] :
( ( ( SV128
!= ( singleton @ SV100 ) )
| ~ ( ~ ! [SY275: $i] :
( ( SY275 != SV100 )
| ( in @ SY275 @ SV128 ) )
| ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SV128 )
| ( SY276 = SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(599,plain,
! [SV129: $i,SV101: $i] :
( ( ( disjoint @ SV101 @ SV129 )
| ~ ( ~ ( in @ ( sK15_C @ SV129 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK15_C @ SV129 @ SV101 ) @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(600,plain,
! [SV130: $i,SV102: $i] :
( ( ! [SY277: $i] :
( ~ ( in @ SY277 @ SV102 )
| ~ ( in @ SY277 @ SV130 ) )
| ~ ( disjoint @ SV102 @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(601,plain,
! [SV48: $i,SV131: $i] :
( ( ! [SY278: $i] :
( ~ ( ~ ( ~ ( in @ ( sK6_D @ SY278 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SY278 @ SV131 @ SV48 ) @ SV131 )
| ~ ( in @ ( sK6_D @ SY278 @ SV131 @ SV48 ) @ SY278 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SY278 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SY278 @ SV131 @ SV48 ) @ SY278 ) )
| ~ ( ~ ( in @ ( sK6_D @ SY278 @ SV131 @ SV48 ) @ SV131 )
| ( in @ ( sK6_D @ SY278 @ SV131 @ SV48 ) @ SY278 ) ) ) )
| ( SY278
= ( set_difference @ SV48 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(602,plain,
! [SV132: $i,SV48: $i] :
( ( ! [SY279: $i] :
( ( SY279
!= ( set_difference @ SV48 @ SV132 ) )
| ~ ( ~ ! [SY280: $i] :
( ~ ( in @ SY280 @ SV48 )
| ( in @ SY280 @ SV132 )
| ( in @ SY280 @ SY279 ) )
| ~ ~ ( ~ ! [SY209: $i] :
( ~ ( in @ SY209 @ SY279 )
| ( in @ SY209 @ SV48 ) )
| ~ ! [SY282: $i] :
( ~ ( in @ SY282 @ SY279 )
| ~ ( in @ SY282 @ SV132 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(603,plain,
! [SV133: $i,SV103: $i] :
( ( ( ( set_difference @ SV103 @ SV133 )
!= SV103 )
| ( disjoint @ SV103 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(604,plain,
! [SV134: $i,SV104: $i] :
( ( ~ ( disjoint @ SV104 @ SV134 )
| ( ( set_difference @ SV104 @ SV134 )
= SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(605,plain,
! [SV105: $i,SV135: $i] :
( ( ~ ( ~ ( in @ ( sK8_C @ SV135 @ SV105 ) @ SV105 )
| ~ ~ ( in @ ( sK8_C @ SV135 @ SV105 ) @ SV135 ) )
| ( subset @ SV105 @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(606,plain,
! [SV136: $i,SV106: $i] :
( ( ~ ( subset @ SV106 @ SV136 )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ SV106 )
| ( in @ SY283 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(607,plain,
! [SV137: $i,SV107: $i] :
( ( ~ ( in @ SV107 @ SV137 )
| ( subset @ ( singleton @ SV107 ) @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(608,plain,
! [SV138: $i,SV108: $i] :
( ( ~ ( subset @ ( singleton @ SV108 ) @ SV138 )
| ( in @ SV108 @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(609,plain,
! [SV49: $i,SV139: $i] :
( ( ! [SY284: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SY284 @ SV139 @ SV49 ) @ SY284 )
| ~ ( in @ ( sK9_D @ SY284 @ SV139 @ SV49 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK9_D @ SY284 @ SV139 @ SV49 ) @ SY284 )
| ~ ( in @ ( sK9_D @ SY284 @ SV139 @ SV49 ) @ SV139 ) ) )
| ~ ( ( in @ ( sK9_D @ SY284 @ SV139 @ SV49 ) @ SY284 )
| ( in @ ( sK9_D @ SY284 @ SV139 @ SV49 ) @ SV49 )
| ( in @ ( sK9_D @ SY284 @ SV139 @ SV49 ) @ SV139 ) ) )
| ( SY284
= ( set_union2 @ SV49 @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(610,plain,
! [SV140: $i,SV49: $i] :
( ( ! [SY285: $i] :
( ( SY285
!= ( set_union2 @ SV49 @ SV140 ) )
| ~ ( ~ ! [SY286: $i] :
( ~ ( in @ SY286 @ SY285 )
| ( in @ SY286 @ SV49 )
| ( in @ SY286 @ SV140 ) )
| ~ ~ ( ~ ! [SY216: $i] :
( ~ ( in @ SY216 @ SV49 )
| ( in @ SY216 @ SY285 ) )
| ~ ! [SY288: $i] :
( ~ ( in @ SY288 @ SV140 )
| ( in @ SY288 @ SY285 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(611,plain,
! [SV141: $i,SV109: $i] :
( ( ~ ( subset @ SV109 @ SV141 )
| ~ ( subset @ SV141 @ SV109 )
| ( SV109 = SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(612,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[558]) ).
thf(613,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[558]) ).
thf(614,plain,
! [SV50: $i,SV83: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
| ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 ) ) )
= $false )
| ( ( SV50 = SV83 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[559]) ).
thf(615,plain,
! [SV50: $i,SV83: $i] :
( ( ( ~ ( ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
| ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 ) ) )
= $false )
| ( ( SV50 = SV83 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[559]) ).
thf(616,plain,
! [SV110: $i,SV142: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
| ~ ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 ) )
| ~ ( ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
| ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 ) ) )
| ( SV142
= ( powerset @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(617,plain,
! [SV111: $i,SV143: $i] :
( ( ( SV143
!= ( powerset @ SV111 ) )
| ~ ( ~ ! [SY289: $i] :
( ~ ( in @ SY289 @ SV143 )
| ( subset @ SY289 @ SV111 ) )
| ~ ! [SY290: $i] :
( ~ ( subset @ SY290 @ SV111 )
| ( in @ SY290 @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(618,plain,
! [SV51: $i,SV144: $i] :
( ( ! [SY291: $i] :
( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK10_D @ SY291 @ SV144 @ SV51 ) @ SY291 )
| ( ( sK10_D @ SY291 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK10_D @ SY291 @ SV144 @ SV51 ) @ SY291 )
| ( ( sK10_D @ SY291 @ SV144 @ SV51 )
!= SV144 ) ) )
| ~ ( ( in @ ( sK10_D @ SY291 @ SV144 @ SV51 ) @ SY291 )
| ( ( sK10_D @ SY291 @ SV144 @ SV51 )
= SV51 )
| ( ( sK10_D @ SY291 @ SV144 @ SV51 )
= SV144 ) ) )
| ( SY291
= ( unordered_pair @ SV51 @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(619,plain,
! [SV145: $i,SV51: $i] :
( ( ! [SY292: $i] :
( ( SY292
!= ( unordered_pair @ SV51 @ SV145 ) )
| ~ ( ~ ! [SY293: $i] :
( ~ ( in @ SY293 @ SY292 )
| ( SY293 = SV51 )
| ( SY293 = SV145 ) )
| ~ ~ ( ~ ! [SY224: $i] :
( ( SY224 != SV51 )
| ( in @ SY224 @ SY292 ) )
| ~ ! [SY295: $i] :
( ( SY295 != SV145 )
| ( in @ SY295 @ SY292 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(620,plain,
! [SV146: $i,SV112: $i] :
( ( ( ( set_difference @ SV112 @ SV146 )
!= empty_set )
| ( subset @ SV112 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(621,plain,
! [SV147: $i,SV113: $i] :
( ( ~ ( subset @ SV113 @ SV147 )
| ( ( set_difference @ SV113 @ SV147 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(622,plain,
! [SV148: $i,SV114: $i] :
( ( ( ( set_intersection2 @ SV114 @ SV148 )
!= empty_set )
| ( disjoint @ SV114 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(623,plain,
! [SV149: $i,SV115: $i] :
( ( ~ ( disjoint @ SV115 @ SV149 )
| ( ( set_intersection2 @ SV115 @ SV149 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(624,plain,
! [SV150: $i,SV116: $i] :
( ( ( ( set_difference @ SV116 @ SV150 )
!= empty_set )
| ( subset @ SV116 @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(625,plain,
! [SV151: $i,SV117: $i] :
( ( ~ ( subset @ SV117 @ SV151 )
| ( ( set_difference @ SV117 @ SV151 )
= empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(626,plain,
! [SV152: $i,SV118: $i] :
( ( ~ ( subset @ SV118 @ ( singleton @ SV152 ) )
| ( SV118 = empty_set )
| ( SV118
= ( singleton @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(627,plain,
( ( ~ ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(628,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(629,plain,
! [SV54: $i,SV4: $i,SV119: $i] :
( ( ( in @ SV119 @ SV4 )
= $true )
| ( ( subset @ SV4 @ ( set_difference @ SV54 @ ( singleton @ SV119 ) ) )
= $true )
| ( ( subset @ SV4 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(630,plain,
! [SV92: $i,SV55: $i,SV84: $i,SV5: $i] :
( ( ( SV5 = SV84 )
= $true )
| ( ( ( ( unordered_pair @ SV5 @ SV55 )
!= ( unordered_pair @ SV84 @ SV92 ) ) )
= $true )
| ( ( SV5 = SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(631,plain,
! [SV85: $i,SV58: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV58 )
= $false )
| ( ( ~ ( subset @ SV8 @ SV85 ) )
= $true )
| ( ( subset @ SV8 @ ( set_intersection2 @ SV58 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(632,plain,
! [SV86: $i,SV59: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV59 )
= $false )
| ( ( ~ ( subset @ SV59 @ SV86 ) )
= $true )
| ( ( subset @ SV9 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(633,plain,
! [SV21: $i,SV87: $i,SV69: $i] :
( ( ( disjoint @ SV69 @ SV87 )
= $false )
| ( ( ~ ( subset @ SV21 @ SV69 ) )
= $true )
| ( ( disjoint @ SV21 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(634,plain,
! [SV88: $i,SV72: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV72 )
= $false )
| ( ( ~ ( subset @ SV88 @ SV72 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV25 @ SV88 ) @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(635,plain,
! [SV46: $i,SV82: $i] :
( ( ( empty @ SV82 )
= $false )
| ( ( SV46 = SV82 )
= $true )
| ( ( empty @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(636,plain,
! [SV122: $i,SV94: $i] :
( ( ( disjoint @ SV94 @ SV122 )
= $true )
| ( ( in @ ( sK14_C @ SV122 @ SV94 ) @ ( set_intersection2 @ SV94 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(637,plain,
! [SV123: $i,SV95: $i] :
( ( ( ! [SY269: $i] :
~ ( in @ SY269 @ ( set_intersection2 @ SV95 @ SV123 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV95 @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(638,plain,
! [SV124: $i,SV96: $i] :
( ( ( ( SV96 = SV124 )
| ~ ( subset @ SV96 @ SV124 ) )
= $true )
| ( ( proper_subset @ SV96 @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(639,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(640,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( proper_subset @ SX0 @ SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[592]) ).
thf(641,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
| ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) ) ) )
| ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(642,plain,
! [SV126: $i,SV47: $i,SV154: $i] :
( ( ( SV154
!= ( set_intersection2 @ SV47 @ SV126 ) )
| ~ ( ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ SV47 )
| ~ ( in @ SY296 @ SV126 )
| ( in @ SY296 @ SV154 ) )
| ~ ~ ( ~ ! [SY297: $i] :
( ~ ( in @ SY297 @ SV154 )
| ( in @ SY297 @ SV47 ) )
| ~ ! [SY298: $i] :
( ~ ( in @ SY298 @ SV154 )
| ( in @ SY298 @ SV126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(643,plain,
! [SV98: $i] :
( ( ( SV98 = empty_set )
= $false )
| ( ( ! [SY242: $i] :
~ ( in @ SY242 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(644,plain,
! [SV99: $i,SV127: $i] :
( ( ( ~ ( ~ ( ( ( sK13_C @ SV127 @ SV99 )
!= SV99 )
| ~ ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 ) )
| ~ ( ( ( sK13_C @ SV127 @ SV99 )
= SV99 )
| ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 ) ) ) )
= $true )
| ( ( SV127
= ( singleton @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(645,plain,
! [SV100: $i,SV128: $i] :
( ( ( ( SV128
!= ( singleton @ SV100 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY275: $i] :
( ( SY275 != SV100 )
| ( in @ SY275 @ SV128 ) )
| ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SV128 )
| ( SY276 = SV100 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(646,plain,
! [SV129: $i,SV101: $i] :
( ( ( disjoint @ SV101 @ SV129 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK15_C @ SV129 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK15_C @ SV129 @ SV101 ) @ SV129 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(647,plain,
! [SV130: $i,SV102: $i] :
( ( ( ! [SY277: $i] :
( ~ ( in @ SY277 @ SV102 )
| ~ ( in @ SY277 @ SV130 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV102 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(648,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) ) ) )
| ( SV155
= ( set_difference @ SV48 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(649,plain,
! [SV132: $i,SV48: $i,SV156: $i] :
( ( ( SV156
!= ( set_difference @ SV48 @ SV132 ) )
| ~ ( ~ ! [SY299: $i] :
( ~ ( in @ SY299 @ SV48 )
| ( in @ SY299 @ SV132 )
| ( in @ SY299 @ SV156 ) )
| ~ ~ ( ~ ! [SY300: $i] :
( ~ ( in @ SY300 @ SV156 )
| ( in @ SY300 @ SV48 ) )
| ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV156 )
| ~ ( in @ SY301 @ SV132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(650,plain,
! [SV133: $i,SV103: $i] :
( ( ( ( ( set_difference @ SV103 @ SV133 )
!= SV103 ) )
= $true )
| ( ( disjoint @ SV103 @ SV133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(651,plain,
! [SV134: $i,SV104: $i] :
( ( ( ~ ( disjoint @ SV104 @ SV134 ) )
= $true )
| ( ( ( set_difference @ SV104 @ SV134 )
= SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(652,plain,
! [SV105: $i,SV135: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_C @ SV135 @ SV105 ) @ SV105 )
| ~ ~ ( in @ ( sK8_C @ SV135 @ SV105 ) @ SV135 ) ) )
= $true )
| ( ( subset @ SV105 @ SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(653,plain,
! [SV136: $i,SV106: $i] :
( ( ( ~ ( subset @ SV106 @ SV136 ) )
= $true )
| ( ( ! [SY283: $i] :
( ~ ( in @ SY283 @ SV106 )
| ( in @ SY283 @ SV136 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(654,plain,
! [SV137: $i,SV107: $i] :
( ( ( ~ ( in @ SV107 @ SV137 ) )
= $true )
| ( ( subset @ ( singleton @ SV107 ) @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(655,plain,
! [SV138: $i,SV108: $i] :
( ( ( ~ ( subset @ ( singleton @ SV108 ) @ SV138 ) )
= $true )
| ( ( in @ SV108 @ SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(656,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) ) )
| ~ ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 )
| ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) ) )
| ( SV157
= ( set_union2 @ SV49 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(657,plain,
! [SV140: $i,SV49: $i,SV158: $i] :
( ( ( SV158
!= ( set_union2 @ SV49 @ SV140 ) )
| ~ ( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SV158 )
| ( in @ SY302 @ SV49 )
| ( in @ SY302 @ SV140 ) )
| ~ ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV49 )
| ( in @ SY303 @ SV158 ) )
| ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV140 )
| ( in @ SY304 @ SV158 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(658,plain,
! [SV141: $i,SV109: $i] :
( ( ( ~ ( subset @ SV109 @ SV141 )
| ~ ( subset @ SV141 @ SV109 ) )
= $true )
| ( ( SV109 = SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(659,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[612]) ).
thf(660,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[613]) ).
thf(661,plain,
! [SV50: $i,SV83: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
| ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 ) )
= $true )
| ( ( SV50 = SV83 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(662,plain,
! [SV50: $i,SV83: $i] :
( ( ( ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
| ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 ) )
= $true )
| ( ( SV50 = SV83 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[615]) ).
thf(663,plain,
! [SV110: $i,SV142: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
| ~ ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 ) )
| ~ ( ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
| ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 ) ) ) )
= $true )
| ( ( SV142
= ( powerset @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(664,plain,
! [SV111: $i,SV143: $i] :
( ( ( ( SV143
!= ( powerset @ SV111 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY289: $i] :
( ~ ( in @ SY289 @ SV143 )
| ( subset @ SY289 @ SV111 ) )
| ~ ! [SY290: $i] :
( ~ ( subset @ SY290 @ SV111 )
| ( in @ SY290 @ SV143 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(665,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV144 ) ) )
| ~ ( ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV51 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV144 ) ) )
| ( SV159
= ( unordered_pair @ SV51 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(666,plain,
! [SV145: $i,SV51: $i,SV160: $i] :
( ( ( SV160
!= ( unordered_pair @ SV51 @ SV145 ) )
| ~ ( ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ SV160 )
| ( SY305 = SV51 )
| ( SY305 = SV145 ) )
| ~ ~ ( ~ ! [SY306: $i] :
( ( SY306 != SV51 )
| ( in @ SY306 @ SV160 ) )
| ~ ! [SY307: $i] :
( ( SY307 != SV145 )
| ( in @ SY307 @ SV160 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(667,plain,
! [SV146: $i,SV112: $i] :
( ( ( ( ( set_difference @ SV112 @ SV146 )
!= empty_set ) )
= $true )
| ( ( subset @ SV112 @ SV146 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(668,plain,
! [SV147: $i,SV113: $i] :
( ( ( ~ ( subset @ SV113 @ SV147 ) )
= $true )
| ( ( ( set_difference @ SV113 @ SV147 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(669,plain,
! [SV148: $i,SV114: $i] :
( ( ( ( ( set_intersection2 @ SV114 @ SV148 )
!= empty_set ) )
= $true )
| ( ( disjoint @ SV114 @ SV148 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(670,plain,
! [SV149: $i,SV115: $i] :
( ( ( ~ ( disjoint @ SV115 @ SV149 ) )
= $true )
| ( ( ( set_intersection2 @ SV115 @ SV149 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(671,plain,
! [SV150: $i,SV116: $i] :
( ( ( ( ( set_difference @ SV116 @ SV150 )
!= empty_set ) )
= $true )
| ( ( subset @ SV116 @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(672,plain,
! [SV151: $i,SV117: $i] :
( ( ( ~ ( subset @ SV117 @ SV151 ) )
= $true )
| ( ( ( set_difference @ SV117 @ SV151 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(673,plain,
! [SV152: $i,SV118: $i] :
( ( ( ~ ( subset @ SV118 @ ( singleton @ SV152 ) ) )
= $true )
| ( ( ( SV118 = empty_set )
| ( SV118
= ( singleton @ SV152 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(674,plain,
( ( ! [SX0: $i] :
( ( SX0 != empty_set )
| ! [SX1: $i] : ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[627]) ).
thf(675,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( singleton @ SX1 ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(676,plain,
! [SV92: $i,SV84: $i,SV55: $i,SV5: $i] :
( ( ( ( unordered_pair @ SV5 @ SV55 )
= ( unordered_pair @ SV84 @ SV92 ) )
= $false )
| ( ( SV5 = SV84 )
= $true )
| ( ( SV5 = SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(677,plain,
! [SV58: $i,SV85: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV85 )
= $false )
| ( ( subset @ SV8 @ SV58 )
= $false )
| ( ( subset @ SV8 @ ( set_intersection2 @ SV58 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(678,plain,
! [SV9: $i,SV86: $i,SV59: $i] :
( ( ( subset @ SV59 @ SV86 )
= $false )
| ( ( subset @ SV9 @ SV59 )
= $false )
| ( ( subset @ SV9 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(679,plain,
! [SV87: $i,SV69: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV69 )
= $false )
| ( ( disjoint @ SV69 @ SV87 )
= $false )
| ( ( disjoint @ SV21 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(680,plain,
! [SV25: $i,SV72: $i,SV88: $i] :
( ( ( subset @ SV88 @ SV72 )
= $false )
| ( ( subset @ SV25 @ SV72 )
= $false )
| ( ( subset @ ( set_union2 @ SV25 @ SV88 ) @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(681,plain,
! [SV123: $i,SV95: $i,SV161: $i] :
( ( ( ~ ( in @ SV161 @ ( set_intersection2 @ SV95 @ SV123 ) ) )
= $true )
| ( ( ~ ( disjoint @ SV95 @ SV123 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(682,plain,
! [SV124: $i,SV96: $i] :
( ( ( SV96 = SV124 )
= $true )
| ( ( ~ ( subset @ SV96 @ SV124 ) )
= $true )
| ( ( proper_subset @ SV96 @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(683,plain,
! [SV162: $i] :
( ( ! [SY308: $i] :
( ~ ( proper_subset @ SV162 @ SY308 )
| ( SV162 != SY308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(684,plain,
! [SV163: $i] :
( ( ! [SY309: $i] :
( ~ ( proper_subset @ SV163 @ SY309 )
| ( subset @ SV163 @ SY309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(685,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
| ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) ) ) ) )
= $true )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(686,plain,
! [SV126: $i,SV47: $i,SV154: $i] :
( ( ( ( SV154
!= ( set_intersection2 @ SV47 @ SV126 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ SV47 )
| ~ ( in @ SY296 @ SV126 )
| ( in @ SY296 @ SV154 ) )
| ~ ~ ( ~ ! [SY297: $i] :
( ~ ( in @ SY297 @ SV154 )
| ( in @ SY297 @ SV47 ) )
| ~ ! [SY298: $i] :
( ~ ( in @ SY298 @ SV154 )
| ( in @ SY298 @ SV126 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(687,plain,
! [SV98: $i,SV164: $i] :
( ( ( ~ ( in @ SV164 @ SV98 ) )
= $true )
| ( ( SV98 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(688,plain,
! [SV99: $i,SV127: $i] :
( ( ( ~ ( ( ( sK13_C @ SV127 @ SV99 )
!= SV99 )
| ~ ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 ) )
| ~ ( ( ( sK13_C @ SV127 @ SV99 )
= SV99 )
| ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 ) ) )
= $false )
| ( ( SV127
= ( singleton @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(689,plain,
! [SV100: $i,SV128: $i] :
( ( ( SV128
= ( singleton @ SV100 ) )
= $false )
| ( ( ~ ( ~ ! [SY275: $i] :
( ( SY275 != SV100 )
| ( in @ SY275 @ SV128 ) )
| ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SV128 )
| ( SY276 = SV100 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(690,plain,
! [SV101: $i,SV129: $i] :
( ( ( ~ ( in @ ( sK15_C @ SV129 @ SV101 ) @ SV101 )
| ~ ( in @ ( sK15_C @ SV129 @ SV101 ) @ SV129 ) )
= $false )
| ( ( disjoint @ SV101 @ SV129 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(691,plain,
! [SV130: $i,SV102: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV102 )
| ~ ( in @ SV165 @ SV130 ) )
= $true )
| ( ( ~ ( disjoint @ SV102 @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(692,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) ) ) ) )
= $true )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(693,plain,
! [SV132: $i,SV48: $i,SV156: $i] :
( ( ( ( SV156
!= ( set_difference @ SV48 @ SV132 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY299: $i] :
( ~ ( in @ SY299 @ SV48 )
| ( in @ SY299 @ SV132 )
| ( in @ SY299 @ SV156 ) )
| ~ ~ ( ~ ! [SY300: $i] :
( ~ ( in @ SY300 @ SV156 )
| ( in @ SY300 @ SV48 ) )
| ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV156 )
| ~ ( in @ SY301 @ SV132 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(694,plain,
! [SV133: $i,SV103: $i] :
( ( ( ( set_difference @ SV103 @ SV133 )
= SV103 )
= $false )
| ( ( disjoint @ SV103 @ SV133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(695,plain,
! [SV134: $i,SV104: $i] :
( ( ( disjoint @ SV104 @ SV134 )
= $false )
| ( ( ( set_difference @ SV104 @ SV134 )
= SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(696,plain,
! [SV105: $i,SV135: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV135 @ SV105 ) @ SV105 )
| ~ ~ ( in @ ( sK8_C @ SV135 @ SV105 ) @ SV135 ) )
= $false )
| ( ( subset @ SV105 @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[652]) ).
thf(697,plain,
! [SV136: $i,SV106: $i] :
( ( ( subset @ SV106 @ SV136 )
= $false )
| ( ( ! [SY283: $i] :
( ~ ( in @ SY283 @ SV106 )
| ( in @ SY283 @ SV136 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(698,plain,
! [SV137: $i,SV107: $i] :
( ( ( in @ SV107 @ SV137 )
= $false )
| ( ( subset @ ( singleton @ SV107 ) @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(699,plain,
! [SV138: $i,SV108: $i] :
( ( ( subset @ ( singleton @ SV108 ) @ SV138 )
= $false )
| ( ( in @ SV108 @ SV138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(700,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) ) )
| ~ ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 )
| ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) ) ) )
= $true )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(701,plain,
! [SV140: $i,SV49: $i,SV158: $i] :
( ( ( ( SV158
!= ( set_union2 @ SV49 @ SV140 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SV158 )
| ( in @ SY302 @ SV49 )
| ( in @ SY302 @ SV140 ) )
| ~ ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV49 )
| ( in @ SY303 @ SV158 ) )
| ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV140 )
| ( in @ SY304 @ SV158 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(702,plain,
! [SV141: $i,SV109: $i] :
( ( ( ~ ( subset @ SV109 @ SV141 ) )
= $true )
| ( ( ~ ( subset @ SV141 @ SV109 ) )
= $true )
| ( ( SV109 = SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(703,plain,
! [SV166: $i] :
( ( ! [SY310: $i] :
( ( SV166 != SY310 )
| ( subset @ SV166 @ SY310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(704,plain,
! [SV167: $i] :
( ( ! [SY311: $i] :
( ( SV167 != SY311 )
| ( subset @ SY311 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(705,plain,
! [SV50: $i,SV83: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 ) )
= $true )
| ( ( ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 ) )
= $true )
| ( ( SV50 = SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(706,plain,
! [SV50: $i,SV83: $i] :
( ( ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
= $true )
| ( ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 )
= $true )
| ( ( SV50 = SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[662]) ).
thf(707,plain,
! [SV110: $i,SV142: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
| ~ ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 ) )
| ~ ( ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
| ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 ) ) )
= $false )
| ( ( SV142
= ( powerset @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(708,plain,
! [SV111: $i,SV143: $i] :
( ( ( SV143
= ( powerset @ SV111 ) )
= $false )
| ( ( ~ ( ~ ! [SY289: $i] :
( ~ ( in @ SY289 @ SV143 )
| ( subset @ SY289 @ SV111 ) )
| ~ ! [SY290: $i] :
( ~ ( subset @ SY290 @ SV111 )
| ( in @ SY290 @ SV143 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(709,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV144 ) ) )
| ~ ( ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV51 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV144 ) ) ) )
= $true )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(710,plain,
! [SV145: $i,SV51: $i,SV160: $i] :
( ( ( ( SV160
!= ( unordered_pair @ SV51 @ SV145 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ SV160 )
| ( SY305 = SV51 )
| ( SY305 = SV145 ) )
| ~ ~ ( ~ ! [SY306: $i] :
( ( SY306 != SV51 )
| ( in @ SY306 @ SV160 ) )
| ~ ! [SY307: $i] :
( ( SY307 != SV145 )
| ( in @ SY307 @ SV160 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[666]) ).
thf(711,plain,
! [SV146: $i,SV112: $i] :
( ( ( ( set_difference @ SV112 @ SV146 )
= empty_set )
= $false )
| ( ( subset @ SV112 @ SV146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(712,plain,
! [SV147: $i,SV113: $i] :
( ( ( subset @ SV113 @ SV147 )
= $false )
| ( ( ( set_difference @ SV113 @ SV147 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(713,plain,
! [SV148: $i,SV114: $i] :
( ( ( ( set_intersection2 @ SV114 @ SV148 )
= empty_set )
= $false )
| ( ( disjoint @ SV114 @ SV148 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(714,plain,
! [SV149: $i,SV115: $i] :
( ( ( disjoint @ SV115 @ SV149 )
= $false )
| ( ( ( set_intersection2 @ SV115 @ SV149 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(715,plain,
! [SV150: $i,SV116: $i] :
( ( ( ( set_difference @ SV116 @ SV150 )
= empty_set )
= $false )
| ( ( subset @ SV116 @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(716,plain,
! [SV151: $i,SV117: $i] :
( ( ( subset @ SV117 @ SV151 )
= $false )
| ( ( ( set_difference @ SV117 @ SV151 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(717,plain,
! [SV152: $i,SV118: $i] :
( ( ( subset @ SV118 @ ( singleton @ SV152 ) )
= $false )
| ( ( ( SV118 = empty_set )
| ( SV118
= ( singleton @ SV152 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(718,plain,
! [SV168: $i] :
( ( ( SV168 != empty_set )
| ! [SY312: $i] : ( subset @ SV168 @ ( singleton @ SY312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(719,plain,
! [SV169: $i] :
( ( ! [SY313: $i] :
( ( SV169
!= ( singleton @ SY313 ) )
| ( subset @ SV169 @ ( singleton @ SY313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(720,plain,
! [SV123: $i,SV95: $i,SV161: $i] :
( ( ( in @ SV161 @ ( set_intersection2 @ SV95 @ SV123 ) )
= $false )
| ( ( ~ ( disjoint @ SV95 @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(721,plain,
! [SV124: $i,SV96: $i] :
( ( ( subset @ SV96 @ SV124 )
= $false )
| ( ( SV96 = SV124 )
= $true )
| ( ( proper_subset @ SV96 @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(722,plain,
! [SV170: $i,SV162: $i] :
( ( ~ ( proper_subset @ SV162 @ SV170 )
| ( SV162 != SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(723,plain,
! [SV171: $i,SV163: $i] :
( ( ~ ( proper_subset @ SV163 @ SV171 )
| ( subset @ SV163 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(724,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
| ~ ~ ( ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
| ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) ) ) )
= $false )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(725,plain,
! [SV126: $i,SV47: $i,SV154: $i] :
( ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false )
| ( ( ~ ( ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ SV47 )
| ~ ( in @ SY296 @ SV126 )
| ( in @ SY296 @ SV154 ) )
| ~ ~ ( ~ ! [SY297: $i] :
( ~ ( in @ SY297 @ SV154 )
| ( in @ SY297 @ SV47 ) )
| ~ ! [SY298: $i] :
( ~ ( in @ SY298 @ SV154 )
| ( in @ SY298 @ SV126 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(726,plain,
! [SV98: $i,SV164: $i] :
( ( ( in @ SV164 @ SV98 )
= $false )
| ( ( SV98 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(727,plain,
! [SV99: $i,SV127: $i] :
( ( ( ~ ( ( ( sK13_C @ SV127 @ SV99 )
!= SV99 )
| ~ ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 ) ) )
= $false )
| ( ( SV127
= ( singleton @ SV99 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(728,plain,
! [SV99: $i,SV127: $i] :
( ( ( ~ ( ( ( sK13_C @ SV127 @ SV99 )
= SV99 )
| ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 ) ) )
= $false )
| ( ( SV127
= ( singleton @ SV99 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[688]) ).
thf(729,plain,
! [SV128: $i,SV100: $i] :
( ( ( ~ ! [SY275: $i] :
( ( SY275 != SV100 )
| ( in @ SY275 @ SV128 ) )
| ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SV128 )
| ( SY276 = SV100 ) ) )
= $false )
| ( ( SV128
= ( singleton @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(730,plain,
! [SV101: $i,SV129: $i] :
( ( ( ~ ( in @ ( sK15_C @ SV129 @ SV101 ) @ SV101 ) )
= $false )
| ( ( disjoint @ SV101 @ SV129 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(731,plain,
! [SV101: $i,SV129: $i] :
( ( ( ~ ( in @ ( sK15_C @ SV129 @ SV101 ) @ SV129 ) )
= $false )
| ( ( disjoint @ SV101 @ SV129 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[690]) ).
thf(732,plain,
! [SV130: $i,SV102: $i,SV165: $i] :
( ( ( ~ ( in @ SV165 @ SV102 ) )
= $true )
| ( ( ~ ( in @ SV165 @ SV130 ) )
= $true )
| ( ( ~ ( disjoint @ SV102 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(733,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
| ~ ~ ( ~ ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) ) ) )
= $false )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(734,plain,
! [SV132: $i,SV48: $i,SV156: $i] :
( ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false )
| ( ( ~ ( ~ ! [SY299: $i] :
( ~ ( in @ SY299 @ SV48 )
| ( in @ SY299 @ SV132 )
| ( in @ SY299 @ SV156 ) )
| ~ ~ ( ~ ! [SY300: $i] :
( ~ ( in @ SY300 @ SV156 )
| ( in @ SY300 @ SV48 ) )
| ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV156 )
| ~ ( in @ SY301 @ SV132 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(735,plain,
! [SV105: $i,SV135: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV135 @ SV105 ) @ SV105 ) )
= $false )
| ( ( subset @ SV105 @ SV135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(736,plain,
! [SV105: $i,SV135: $i] :
( ( ( ~ ~ ( in @ ( sK8_C @ SV135 @ SV105 ) @ SV135 ) )
= $false )
| ( ( subset @ SV105 @ SV135 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(737,plain,
! [SV136: $i,SV106: $i,SV172: $i] :
( ( ( ~ ( in @ SV172 @ SV106 )
| ( in @ SV172 @ SV136 ) )
= $true )
| ( ( subset @ SV106 @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(738,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) ) )
| ~ ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 )
| ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) ) )
= $false )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(739,plain,
! [SV140: $i,SV49: $i,SV158: $i] :
( ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false )
| ( ( ~ ( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SV158 )
| ( in @ SY302 @ SV49 )
| ( in @ SY302 @ SV140 ) )
| ~ ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV49 )
| ( in @ SY303 @ SV158 ) )
| ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV140 )
| ( in @ SY304 @ SV158 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(740,plain,
! [SV141: $i,SV109: $i] :
( ( ( subset @ SV109 @ SV141 )
= $false )
| ( ( ~ ( subset @ SV141 @ SV109 ) )
= $true )
| ( ( SV109 = SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(741,plain,
! [SV173: $i,SV166: $i] :
( ( ( SV166 != SV173 )
| ( subset @ SV166 @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(742,plain,
! [SV174: $i,SV167: $i] :
( ( ( SV167 != SV174 )
| ( subset @ SV174 @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(743,plain,
! [SV50: $i,SV83: $i] :
( ( ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
= $false )
| ( ( ~ ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 ) )
= $true )
| ( ( SV50 = SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(744,plain,
! [SV110: $i,SV142: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
| ~ ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 ) ) )
= $false )
| ( ( SV142
= ( powerset @ SV110 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[707]) ).
thf(745,plain,
! [SV110: $i,SV142: $i] :
( ( ( ~ ( ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
| ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 ) ) )
= $false )
| ( ( SV142
= ( powerset @ SV110 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[707]) ).
thf(746,plain,
! [SV111: $i,SV143: $i] :
( ( ( ~ ! [SY289: $i] :
( ~ ( in @ SY289 @ SV143 )
| ( subset @ SY289 @ SV111 ) )
| ~ ! [SY290: $i] :
( ~ ( subset @ SY290 @ SV111 )
| ( in @ SY290 @ SV143 ) ) )
= $false )
| ( ( SV143
= ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(747,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV144 ) ) )
| ~ ( ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV51 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV144 ) ) )
= $false )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(748,plain,
! [SV145: $i,SV51: $i,SV160: $i] :
( ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false )
| ( ( ~ ( ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ SV160 )
| ( SY305 = SV51 )
| ( SY305 = SV145 ) )
| ~ ~ ( ~ ! [SY306: $i] :
( ( SY306 != SV51 )
| ( in @ SY306 @ SV160 ) )
| ~ ! [SY307: $i] :
( ( SY307 != SV145 )
| ( in @ SY307 @ SV160 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(749,plain,
! [SV152: $i,SV118: $i] :
( ( ( SV118 = empty_set )
= $true )
| ( ( SV118
= ( singleton @ SV152 ) )
= $true )
| ( ( subset @ SV118 @ ( singleton @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[717]) ).
thf(750,plain,
! [SV168: $i] :
( ( ( ( SV168 != empty_set ) )
= $true )
| ( ( ! [SY312: $i] : ( subset @ SV168 @ ( singleton @ SY312 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(751,plain,
! [SV175: $i,SV169: $i] :
( ( ( SV169
!= ( singleton @ SV175 ) )
| ( subset @ SV169 @ ( singleton @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(752,plain,
! [SV161: $i,SV123: $i,SV95: $i] :
( ( ( disjoint @ SV95 @ SV123 )
= $false )
| ( ( in @ SV161 @ ( set_intersection2 @ SV95 @ SV123 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(753,plain,
! [SV170: $i,SV162: $i] :
( ( ( ~ ( proper_subset @ SV162 @ SV170 ) )
= $true )
| ( ( ( SV162 != SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(754,plain,
! [SV171: $i,SV163: $i] :
( ( ( ~ ( proper_subset @ SV163 @ SV171 ) )
= $true )
| ( ( subset @ SV163 @ SV171 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[723]) ).
thf(755,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) ) )
= $false )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[724]) ).
thf(756,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
| ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) ) ) )
= $false )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[724]) ).
thf(757,plain,
! [SV154: $i,SV126: $i,SV47: $i] :
( ( ( ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ SV47 )
| ~ ( in @ SY296 @ SV126 )
| ( in @ SY296 @ SV154 ) )
| ~ ~ ( ~ ! [SY297: $i] :
( ~ ( in @ SY297 @ SV154 )
| ( in @ SY297 @ SV47 ) )
| ~ ! [SY298: $i] :
( ~ ( in @ SY298 @ SV154 )
| ( in @ SY298 @ SV126 ) ) ) )
= $false )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(758,plain,
! [SV99: $i,SV127: $i] :
( ( ( ( ( sK13_C @ SV127 @ SV99 )
!= SV99 )
| ~ ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 ) )
= $true )
| ( ( SV127
= ( singleton @ SV99 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[727]) ).
thf(759,plain,
! [SV99: $i,SV127: $i] :
( ( ( ( ( sK13_C @ SV127 @ SV99 )
= SV99 )
| ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 ) )
= $true )
| ( ( SV127
= ( singleton @ SV99 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(760,plain,
! [SV128: $i,SV100: $i] :
( ( ( ~ ! [SY275: $i] :
( ( SY275 != SV100 )
| ( in @ SY275 @ SV128 ) ) )
= $false )
| ( ( SV128
= ( singleton @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(761,plain,
! [SV100: $i,SV128: $i] :
( ( ( ~ ! [SY276: $i] :
( ~ ( in @ SY276 @ SV128 )
| ( SY276 = SV100 ) ) )
= $false )
| ( ( SV128
= ( singleton @ SV100 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[729]) ).
thf(762,plain,
! [SV101: $i,SV129: $i] :
( ( ( in @ ( sK15_C @ SV129 @ SV101 ) @ SV101 )
= $true )
| ( ( disjoint @ SV101 @ SV129 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[730]) ).
thf(763,plain,
! [SV101: $i,SV129: $i] :
( ( ( in @ ( sK15_C @ SV129 @ SV101 ) @ SV129 )
= $true )
| ( ( disjoint @ SV101 @ SV129 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[731]) ).
thf(764,plain,
! [SV130: $i,SV102: $i,SV165: $i] :
( ( ( in @ SV165 @ SV102 )
= $false )
| ( ( ~ ( in @ SV165 @ SV130 ) )
= $true )
| ( ( ~ ( disjoint @ SV102 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(765,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) ) )
= $false )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(766,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ~ ( ~ ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) ) ) )
= $false )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[733]) ).
thf(767,plain,
! [SV156: $i,SV132: $i,SV48: $i] :
( ( ( ~ ! [SY299: $i] :
( ~ ( in @ SY299 @ SV48 )
| ( in @ SY299 @ SV132 )
| ( in @ SY299 @ SV156 ) )
| ~ ~ ( ~ ! [SY300: $i] :
( ~ ( in @ SY300 @ SV156 )
| ( in @ SY300 @ SV48 ) )
| ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV156 )
| ~ ( in @ SY301 @ SV132 ) ) ) )
= $false )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(768,plain,
! [SV105: $i,SV135: $i] :
( ( ( in @ ( sK8_C @ SV135 @ SV105 ) @ SV105 )
= $true )
| ( ( subset @ SV105 @ SV135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[735]) ).
thf(769,plain,
! [SV105: $i,SV135: $i] :
( ( ( ~ ( in @ ( sK8_C @ SV135 @ SV105 ) @ SV135 ) )
= $true )
| ( ( subset @ SV105 @ SV135 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(770,plain,
! [SV136: $i,SV106: $i,SV172: $i] :
( ( ( ~ ( in @ SV172 @ SV106 ) )
= $true )
| ( ( in @ SV172 @ SV136 )
= $true )
| ( ( subset @ SV106 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(771,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) ) ) )
= $false )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[738]) ).
thf(772,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ~ ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 )
| ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) ) )
= $false )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[738]) ).
thf(773,plain,
! [SV140: $i,SV49: $i,SV158: $i] :
( ( ( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SV158 )
| ( in @ SY302 @ SV49 )
| ( in @ SY302 @ SV140 ) )
| ~ ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV49 )
| ( in @ SY303 @ SV158 ) )
| ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV140 )
| ( in @ SY304 @ SV158 ) ) ) )
= $false )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(774,plain,
! [SV109: $i,SV141: $i] :
( ( ( subset @ SV141 @ SV109 )
= $false )
| ( ( subset @ SV109 @ SV141 )
= $false )
| ( ( SV109 = SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(775,plain,
! [SV173: $i,SV166: $i] :
( ( ( ( SV166 != SV173 ) )
= $true )
| ( ( subset @ SV166 @ SV173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(776,plain,
! [SV174: $i,SV167: $i] :
( ( ( ( SV167 != SV174 ) )
= $true )
| ( ( subset @ SV174 @ SV167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(777,plain,
! [SV50: $i,SV83: $i] :
( ( ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV83 )
= $false )
| ( ( in @ ( sK3_C @ SV83 @ SV50 ) @ SV50 )
= $false )
| ( ( SV50 = SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(778,plain,
! [SV110: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
| ~ ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 ) )
= $true )
| ( ( SV142
= ( powerset @ SV110 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(779,plain,
! [SV110: $i,SV142: $i] :
( ( ( ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
| ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 ) )
= $true )
| ( ( SV142
= ( powerset @ SV110 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[745]) ).
thf(780,plain,
! [SV111: $i,SV143: $i] :
( ( ( ~ ! [SY289: $i] :
( ~ ( in @ SY289 @ SV143 )
| ( subset @ SY289 @ SV111 ) ) )
= $false )
| ( ( SV143
= ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[746]) ).
thf(781,plain,
! [SV143: $i,SV111: $i] :
( ( ( ~ ! [SY290: $i] :
( ~ ( subset @ SY290 @ SV111 )
| ( in @ SY290 @ SV143 ) ) )
= $false )
| ( ( SV143
= ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[746]) ).
thf(782,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV144 ) ) ) )
= $false )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[747]) ).
thf(783,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ~ ( ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV51 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV144 ) ) )
= $false )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[747]) ).
thf(784,plain,
! [SV145: $i,SV51: $i,SV160: $i] :
( ( ( ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ SV160 )
| ( SY305 = SV51 )
| ( SY305 = SV145 ) )
| ~ ~ ( ~ ! [SY306: $i] :
( ( SY306 != SV51 )
| ( in @ SY306 @ SV160 ) )
| ~ ! [SY307: $i] :
( ( SY307 != SV145 )
| ( in @ SY307 @ SV160 ) ) ) )
= $false )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(785,plain,
! [SV168: $i] :
( ( ( SV168 = empty_set )
= $false )
| ( ( ! [SY312: $i] : ( subset @ SV168 @ ( singleton @ SY312 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(786,plain,
! [SV175: $i,SV169: $i] :
( ( ( ( SV169
!= ( singleton @ SV175 ) ) )
= $true )
| ( ( subset @ SV169 @ ( singleton @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(787,plain,
! [SV170: $i,SV162: $i] :
( ( ( proper_subset @ SV162 @ SV170 )
= $false )
| ( ( ( SV162 != SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(788,plain,
! [SV171: $i,SV163: $i] :
( ( ( proper_subset @ SV163 @ SV171 )
= $false )
| ( ( subset @ SV163 @ SV171 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(789,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
= $true )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[755]) ).
thf(790,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
| ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) ) ) )
= $true )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(791,plain,
! [SV154: $i,SV126: $i,SV47: $i] :
( ( ( ~ ! [SY296: $i] :
( ~ ( in @ SY296 @ SV47 )
| ~ ( in @ SY296 @ SV126 )
| ( in @ SY296 @ SV154 ) ) )
= $false )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(792,plain,
! [SV126: $i,SV47: $i,SV154: $i] :
( ( ( ~ ~ ( ~ ! [SY297: $i] :
( ~ ( in @ SY297 @ SV154 )
| ( in @ SY297 @ SV47 ) )
| ~ ! [SY298: $i] :
( ~ ( in @ SY298 @ SV154 )
| ( in @ SY298 @ SV126 ) ) ) )
= $false )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(793,plain,
! [SV99: $i,SV127: $i] :
( ( ( ( ( sK13_C @ SV127 @ SV99 )
!= SV99 ) )
= $true )
| ( ( ~ ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 ) )
= $true )
| ( ( SV127
= ( singleton @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(794,plain,
! [SV99: $i,SV127: $i] :
( ( ( ( sK13_C @ SV127 @ SV99 )
= SV99 )
= $true )
| ( ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 )
= $true )
| ( ( SV127
= ( singleton @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(795,plain,
! [SV128: $i,SV100: $i] :
( ( ( ! [SY275: $i] :
( ( SY275 != SV100 )
| ( in @ SY275 @ SV128 ) ) )
= $true )
| ( ( SV128
= ( singleton @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[760]) ).
thf(796,plain,
! [SV100: $i,SV128: $i] :
( ( ( ! [SY276: $i] :
( ~ ( in @ SY276 @ SV128 )
| ( SY276 = SV100 ) ) )
= $true )
| ( ( SV128
= ( singleton @ SV100 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[761]) ).
thf(797,plain,
! [SV102: $i,SV130: $i,SV165: $i] :
( ( ( in @ SV165 @ SV130 )
= $false )
| ( ( in @ SV165 @ SV102 )
= $false )
| ( ( ~ ( disjoint @ SV102 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(798,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
= $true )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[765]) ).
thf(799,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ( ~ ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) ) ) )
= $true )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[766]) ).
thf(800,plain,
! [SV156: $i,SV132: $i,SV48: $i] :
( ( ( ~ ! [SY299: $i] :
( ~ ( in @ SY299 @ SV48 )
| ( in @ SY299 @ SV132 )
| ( in @ SY299 @ SV156 ) ) )
= $false )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[767]) ).
thf(801,plain,
! [SV132: $i,SV48: $i,SV156: $i] :
( ( ( ~ ~ ( ~ ! [SY300: $i] :
( ~ ( in @ SY300 @ SV156 )
| ( in @ SY300 @ SV48 ) )
| ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV156 )
| ~ ( in @ SY301 @ SV132 ) ) ) )
= $false )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[767]) ).
thf(802,plain,
! [SV105: $i,SV135: $i] :
( ( ( in @ ( sK8_C @ SV135 @ SV105 ) @ SV135 )
= $false )
| ( ( subset @ SV105 @ SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(803,plain,
! [SV136: $i,SV106: $i,SV172: $i] :
( ( ( in @ SV172 @ SV106 )
= $false )
| ( ( in @ SV172 @ SV136 )
= $true )
| ( ( subset @ SV106 @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(804,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) ) ) )
= $true )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[771]) ).
thf(805,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 )
| ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) )
= $true )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[772]) ).
thf(806,plain,
! [SV140: $i,SV49: $i,SV158: $i] :
( ( ( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SV158 )
| ( in @ SY302 @ SV49 )
| ( in @ SY302 @ SV140 ) ) )
= $false )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(807,plain,
! [SV140: $i,SV158: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV49 )
| ( in @ SY303 @ SV158 ) )
| ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV140 )
| ( in @ SY304 @ SV158 ) ) ) )
= $false )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(808,plain,
! [SV173: $i,SV166: $i] :
( ( ( SV166 = SV173 )
= $false )
| ( ( subset @ SV166 @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(809,plain,
! [SV174: $i,SV167: $i] :
( ( ( SV167 = SV174 )
= $false )
| ( ( subset @ SV174 @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(810,plain,
! [SV110: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 ) )
= $true )
| ( ( ~ ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 ) )
= $true )
| ( ( SV142
= ( powerset @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(811,plain,
! [SV110: $i,SV142: $i] :
( ( ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
= $true )
| ( ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 )
= $true )
| ( ( SV142
= ( powerset @ SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(812,plain,
! [SV111: $i,SV143: $i] :
( ( ( ! [SY289: $i] :
( ~ ( in @ SY289 @ SV143 )
| ( subset @ SY289 @ SV111 ) ) )
= $true )
| ( ( SV143
= ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(813,plain,
! [SV143: $i,SV111: $i] :
( ( ( ! [SY290: $i] :
( ~ ( subset @ SY290 @ SV111 )
| ( in @ SY290 @ SV143 ) ) )
= $true )
| ( ( SV143
= ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(814,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV144 ) ) ) )
= $true )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(815,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV51 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV144 ) )
= $true )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(816,plain,
! [SV145: $i,SV51: $i,SV160: $i] :
( ( ( ~ ! [SY305: $i] :
( ~ ( in @ SY305 @ SV160 )
| ( SY305 = SV51 )
| ( SY305 = SV145 ) ) )
= $false )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(817,plain,
! [SV145: $i,SV160: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ! [SY306: $i] :
( ( SY306 != SV51 )
| ( in @ SY306 @ SV160 ) )
| ~ ! [SY307: $i] :
( ( SY307 != SV145 )
| ( in @ SY307 @ SV160 ) ) ) )
= $false )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(818,plain,
! [SV176: $i,SV168: $i] :
( ( ( subset @ SV168 @ ( singleton @ SV176 ) )
= $true )
| ( ( SV168 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(819,plain,
! [SV175: $i,SV169: $i] :
( ( ( SV169
= ( singleton @ SV175 ) )
= $false )
| ( ( subset @ SV169 @ ( singleton @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(820,plain,
! [SV170: $i,SV162: $i] :
( ( ( SV162 = SV170 )
= $false )
| ( ( proper_subset @ SV162 @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(821,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 ) )
= $true )
| ( ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
= $true )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[789]) ).
thf(822,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
| ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) ) )
= $false )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(823,plain,
! [SV154: $i,SV126: $i,SV47: $i] :
( ( ( ! [SY296: $i] :
( ~ ( in @ SY296 @ SV47 )
| ~ ( in @ SY296 @ SV126 )
| ( in @ SY296 @ SV154 ) ) )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(824,plain,
! [SV126: $i,SV47: $i,SV154: $i] :
( ( ( ~ ( ~ ! [SY297: $i] :
( ~ ( in @ SY297 @ SV154 )
| ( in @ SY297 @ SV47 ) )
| ~ ! [SY298: $i] :
( ~ ( in @ SY298 @ SV154 )
| ( in @ SY298 @ SV126 ) ) ) )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(825,plain,
! [SV99: $i,SV127: $i] :
( ( ( ( sK13_C @ SV127 @ SV99 )
= SV99 )
= $false )
| ( ( ~ ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 ) )
= $true )
| ( ( SV127
= ( singleton @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(826,plain,
! [SV128: $i,SV100: $i,SV177: $i] :
( ( ( ( SV177 != SV100 )
| ( in @ SV177 @ SV128 ) )
= $true )
| ( ( SV128
= ( singleton @ SV100 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(827,plain,
! [SV100: $i,SV128: $i,SV178: $i] :
( ( ( ~ ( in @ SV178 @ SV128 )
| ( SV178 = SV100 ) )
= $true )
| ( ( SV128
= ( singleton @ SV100 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(828,plain,
! [SV165: $i,SV130: $i,SV102: $i] :
( ( ( disjoint @ SV102 @ SV130 )
= $false )
| ( ( in @ SV165 @ SV102 )
= $false )
| ( ( in @ SV165 @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[797]) ).
thf(829,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 ) )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
= $true )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[798]) ).
thf(830,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
| ~ ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) ) )
= $false )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(831,plain,
! [SV156: $i,SV132: $i,SV48: $i] :
( ( ( ! [SY299: $i] :
( ~ ( in @ SY299 @ SV48 )
| ( in @ SY299 @ SV132 )
| ( in @ SY299 @ SV156 ) ) )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(832,plain,
! [SV132: $i,SV48: $i,SV156: $i] :
( ( ( ~ ( ~ ! [SY300: $i] :
( ~ ( in @ SY300 @ SV156 )
| ( in @ SY300 @ SV48 ) )
| ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV156 )
| ~ ( in @ SY301 @ SV132 ) ) ) )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(833,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 ) )
| ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) ) )
= $false )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(834,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
= $true )
| ( ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 )
| ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) )
= $true )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(835,plain,
! [SV140: $i,SV49: $i,SV158: $i] :
( ( ( ! [SY302: $i] :
( ~ ( in @ SY302 @ SV158 )
| ( in @ SY302 @ SV49 )
| ( in @ SY302 @ SV140 ) ) )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(836,plain,
! [SV140: $i,SV158: $i,SV49: $i] :
( ( ( ~ ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV49 )
| ( in @ SY303 @ SV158 ) )
| ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV140 )
| ( in @ SY304 @ SV158 ) ) ) )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(837,plain,
! [SV110: $i,SV142: $i] :
( ( ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
= $false )
| ( ( ~ ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 ) )
= $true )
| ( ( SV142
= ( powerset @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(838,plain,
! [SV111: $i,SV143: $i,SV179: $i] :
( ( ( ~ ( in @ SV179 @ SV143 )
| ( subset @ SV179 @ SV111 ) )
= $true )
| ( ( SV143
= ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(839,plain,
! [SV143: $i,SV111: $i,SV180: $i] :
( ( ( ~ ( subset @ SV180 @ SV111 )
| ( in @ SV180 @ SV143 ) )
= $true )
| ( ( SV143
= ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(840,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV51 ) )
| ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV144 ) ) )
= $false )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(841,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
= $true )
| ( ( ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV51 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV144 ) )
= $true )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(842,plain,
! [SV145: $i,SV51: $i,SV160: $i] :
( ( ( ! [SY305: $i] :
( ~ ( in @ SY305 @ SV160 )
| ( SY305 = SV51 )
| ( SY305 = SV145 ) ) )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[816]) ).
thf(843,plain,
! [SV145: $i,SV160: $i,SV51: $i] :
( ( ( ~ ( ~ ! [SY306: $i] :
( ( SY306 != SV51 )
| ( in @ SY306 @ SV160 ) )
| ~ ! [SY307: $i] :
( ( SY307 != SV145 )
| ( in @ SY307 @ SV160 ) ) ) )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[817]) ).
thf(844,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 ) )
= $true )
| ( ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 ) )
= $true )
| ( ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
= $true )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(845,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) ) )
= $false )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[822]) ).
thf(846,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ~ ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) ) )
= $false )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[822]) ).
thf(847,plain,
! [SV154: $i,SV126: $i,SV47: $i,SV181: $i] :
( ( ( ~ ( in @ SV181 @ SV47 )
| ~ ( in @ SV181 @ SV126 )
| ( in @ SV181 @ SV154 ) )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(848,plain,
! [SV126: $i,SV47: $i,SV154: $i] :
( ( ( ~ ! [SY297: $i] :
( ~ ( in @ SY297 @ SV154 )
| ( in @ SY297 @ SV47 ) )
| ~ ! [SY298: $i] :
( ~ ( in @ SY298 @ SV154 )
| ( in @ SY298 @ SV126 ) ) )
= $false )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[824]) ).
thf(849,plain,
! [SV99: $i,SV127: $i] :
( ( ( in @ ( sK13_C @ SV127 @ SV99 ) @ SV127 )
= $false )
| ( ( ( sK13_C @ SV127 @ SV99 )
= SV99 )
= $false )
| ( ( SV127
= ( singleton @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[825]) ).
thf(850,plain,
! [SV128: $i,SV100: $i,SV177: $i] :
( ( ( ( SV177 != SV100 ) )
= $true )
| ( ( in @ SV177 @ SV128 )
= $true )
| ( ( SV128
= ( singleton @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(851,plain,
! [SV100: $i,SV128: $i,SV178: $i] :
( ( ( ~ ( in @ SV178 @ SV128 ) )
= $true )
| ( ( SV178 = SV100 )
= $true )
| ( ( SV128
= ( singleton @ SV100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(852,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 ) )
= $true )
| ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
= $true )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(853,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) ) )
= $false )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(854,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) ) )
= $false )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(855,plain,
! [SV156: $i,SV132: $i,SV48: $i,SV182: $i] :
( ( ( ~ ( in @ SV182 @ SV48 )
| ( in @ SV182 @ SV132 )
| ( in @ SV182 @ SV156 ) )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(856,plain,
! [SV132: $i,SV48: $i,SV156: $i] :
( ( ( ~ ! [SY300: $i] :
( ~ ( in @ SY300 @ SV156 )
| ( in @ SY300 @ SV48 ) )
| ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV156 )
| ~ ( in @ SY301 @ SV132 ) ) )
= $false )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(857,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 ) ) )
= $false )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(858,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ~ ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) ) )
= $false )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[833]) ).
thf(859,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 )
= $true )
| ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 )
= $true )
| ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
= $true )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(860,plain,
! [SV140: $i,SV49: $i,SV158: $i,SV183: $i] :
( ( ( ~ ( in @ SV183 @ SV158 )
| ( in @ SV183 @ SV49 )
| ( in @ SV183 @ SV140 ) )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(861,plain,
! [SV140: $i,SV158: $i,SV49: $i] :
( ( ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV49 )
| ( in @ SY303 @ SV158 ) )
| ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV140 )
| ( in @ SY304 @ SV158 ) ) )
= $false )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(862,plain,
! [SV110: $i,SV142: $i] :
( ( ( subset @ ( sK11_C @ SV142 @ SV110 ) @ SV110 )
= $false )
| ( ( in @ ( sK11_C @ SV142 @ SV110 ) @ SV142 )
= $false )
| ( ( SV142
= ( powerset @ SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(863,plain,
! [SV111: $i,SV143: $i,SV179: $i] :
( ( ( ~ ( in @ SV179 @ SV143 ) )
= $true )
| ( ( subset @ SV179 @ SV111 )
= $true )
| ( ( SV143
= ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(864,plain,
! [SV143: $i,SV111: $i,SV180: $i] :
( ( ( ~ ( subset @ SV180 @ SV111 ) )
= $true )
| ( ( in @ SV180 @ SV143 )
= $true )
| ( ( SV143
= ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(865,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV51 ) ) )
= $false )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(866,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV144 ) ) )
= $false )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[840]) ).
thf(867,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV51 )
= $true )
| ( ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV144 )
= $true )
| ( ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
= $true )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(868,plain,
! [SV145: $i,SV51: $i,SV160: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ SV160 )
| ( SV184 = SV51 )
| ( SV184 = SV145 ) )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(869,plain,
! [SV145: $i,SV160: $i,SV51: $i] :
( ( ( ~ ! [SY306: $i] :
( ( SY306 != SV51 )
| ( in @ SY306 @ SV160 ) )
| ~ ! [SY307: $i] :
( ( SY307 != SV145 )
| ( in @ SY307 @ SV160 ) ) )
= $false )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(870,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
= $false )
| ( ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 ) )
= $true )
| ( ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
= $true )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(871,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
= $true )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[845]) ).
thf(872,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
| ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
= $true )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[846]) ).
thf(873,plain,
! [SV154: $i,SV126: $i,SV47: $i,SV181: $i] :
( ( ( ~ ( in @ SV181 @ SV47 )
| ~ ( in @ SV181 @ SV126 ) )
= $true )
| ( ( in @ SV181 @ SV154 )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(874,plain,
! [SV126: $i,SV47: $i,SV154: $i] :
( ( ( ~ ! [SY297: $i] :
( ~ ( in @ SY297 @ SV154 )
| ( in @ SY297 @ SV47 ) ) )
= $false )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(875,plain,
! [SV47: $i,SV126: $i,SV154: $i] :
( ( ( ~ ! [SY298: $i] :
( ~ ( in @ SY298 @ SV154 )
| ( in @ SY298 @ SV126 ) ) )
= $false )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[848]) ).
thf(876,plain,
! [SV128: $i,SV100: $i,SV177: $i] :
( ( ( SV177 = SV100 )
= $false )
| ( ( in @ SV177 @ SV128 )
= $true )
| ( ( SV128
= ( singleton @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(877,plain,
! [SV100: $i,SV128: $i,SV178: $i] :
( ( ( in @ SV178 @ SV128 )
= $false )
| ( ( SV178 = SV100 )
= $true )
| ( ( SV128
= ( singleton @ SV100 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(878,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
= $false )
| ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
= $true )
| ( ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
= $true )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[852]) ).
thf(879,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
= $true )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[853]) ).
thf(880,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
| ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 ) )
= $true )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[854]) ).
thf(881,plain,
! [SV156: $i,SV132: $i,SV48: $i,SV182: $i] :
( ( ( ~ ( in @ SV182 @ SV48 )
| ( in @ SV182 @ SV132 ) )
= $true )
| ( ( in @ SV182 @ SV156 )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(882,plain,
! [SV132: $i,SV48: $i,SV156: $i] :
( ( ( ~ ! [SY300: $i] :
( ~ ( in @ SY300 @ SV156 )
| ( in @ SY300 @ SV48 ) ) )
= $false )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(883,plain,
! [SV48: $i,SV132: $i,SV156: $i] :
( ( ( ~ ! [SY301: $i] :
( ~ ( in @ SY301 @ SV156 )
| ~ ( in @ SY301 @ SV132 ) ) )
= $false )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[856]) ).
thf(884,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 ) )
= $true )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[857]) ).
thf(885,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
| ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) )
= $true )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[858]) ).
thf(886,plain,
! [SV140: $i,SV49: $i,SV158: $i,SV183: $i] :
( ( ( ~ ( in @ SV183 @ SV158 ) )
= $true )
| ( ( ( in @ SV183 @ SV49 )
| ( in @ SV183 @ SV140 ) )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(887,plain,
! [SV140: $i,SV158: $i,SV49: $i] :
( ( ( ~ ! [SY303: $i] :
( ~ ( in @ SY303 @ SV49 )
| ( in @ SY303 @ SV158 ) ) )
= $false )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(888,plain,
! [SV49: $i,SV158: $i,SV140: $i] :
( ( ( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SV140 )
| ( in @ SY304 @ SV158 ) ) )
= $false )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[861]) ).
thf(889,plain,
! [SV111: $i,SV143: $i,SV179: $i] :
( ( ( in @ SV179 @ SV143 )
= $false )
| ( ( subset @ SV179 @ SV111 )
= $true )
| ( ( SV143
= ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(890,plain,
! [SV143: $i,SV111: $i,SV180: $i] :
( ( ( subset @ SV180 @ SV111 )
= $false )
| ( ( in @ SV180 @ SV143 )
= $true )
| ( ( SV143
= ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(891,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV51 ) )
= $true )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[865]) ).
thf(892,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
| ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV144 ) )
= $true )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(893,plain,
! [SV145: $i,SV51: $i,SV160: $i,SV184: $i] :
( ( ( ~ ( in @ SV184 @ SV160 ) )
= $true )
| ( ( ( SV184 = SV51 )
| ( SV184 = SV145 ) )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(894,plain,
! [SV145: $i,SV160: $i,SV51: $i] :
( ( ( ~ ! [SY306: $i] :
( ( SY306 != SV51 )
| ( in @ SY306 @ SV160 ) ) )
= $false )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(895,plain,
! [SV51: $i,SV160: $i,SV145: $i] :
( ( ( ~ ! [SY307: $i] :
( ( SY307 != SV145 )
| ( in @ SY307 @ SV160 ) ) )
= $false )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(896,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
= $false )
| ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
= $false )
| ( ( ~ ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 ) )
= $true )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(897,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
= $true )
| ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 )
= $true )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(898,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
= $true )
| ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 )
= $true )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(899,plain,
! [SV154: $i,SV126: $i,SV47: $i,SV181: $i] :
( ( ( ~ ( in @ SV181 @ SV47 ) )
= $true )
| ( ( ~ ( in @ SV181 @ SV126 ) )
= $true )
| ( ( in @ SV181 @ SV154 )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(900,plain,
! [SV126: $i,SV47: $i,SV154: $i] :
( ( ( ! [SY297: $i] :
( ~ ( in @ SY297 @ SV154 )
| ( in @ SY297 @ SV47 ) ) )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[874]) ).
thf(901,plain,
! [SV47: $i,SV126: $i,SV154: $i] :
( ( ( ! [SY298: $i] :
( ~ ( in @ SY298 @ SV154 )
| ( in @ SY298 @ SV126 ) ) )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(902,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 )
= $false )
| ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
= $true )
| ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
= $false )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(903,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV48 )
= $true )
| ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 )
= $true )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(904,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( ~ ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 ) )
= $true )
| ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 )
= $true )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(905,plain,
! [SV156: $i,SV132: $i,SV48: $i,SV182: $i] :
( ( ( ~ ( in @ SV182 @ SV48 ) )
= $true )
| ( ( in @ SV182 @ SV132 )
= $true )
| ( ( in @ SV182 @ SV156 )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(906,plain,
! [SV132: $i,SV48: $i,SV156: $i] :
( ( ( ! [SY300: $i] :
( ~ ( in @ SY300 @ SV156 )
| ( in @ SY300 @ SV48 ) ) )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[882]) ).
thf(907,plain,
! [SV48: $i,SV132: $i,SV156: $i] :
( ( ( ! [SY301: $i] :
( ~ ( in @ SY301 @ SV156 )
| ~ ( in @ SY301 @ SV132 ) ) )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[883]) ).
thf(908,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 ) )
= $true )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(909,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) )
= $true )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(910,plain,
! [SV140: $i,SV49: $i,SV158: $i,SV183: $i] :
( ( ( in @ SV183 @ SV158 )
= $false )
| ( ( ( in @ SV183 @ SV49 )
| ( in @ SV183 @ SV140 ) )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(911,plain,
! [SV140: $i,SV158: $i,SV49: $i] :
( ( ( ! [SY303: $i] :
( ~ ( in @ SY303 @ SV49 )
| ( in @ SY303 @ SV158 ) ) )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[887]) ).
thf(912,plain,
! [SV49: $i,SV158: $i,SV140: $i] :
( ( ( ! [SY304: $i] :
( ~ ( in @ SY304 @ SV140 )
| ( in @ SY304 @ SV158 ) ) )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[888]) ).
thf(913,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 ) )
= $true )
| ( ( ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV51 ) )
= $true )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(914,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ~ ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 ) )
= $true )
| ( ( ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV144 ) )
= $true )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(915,plain,
! [SV145: $i,SV51: $i,SV160: $i,SV184: $i] :
( ( ( in @ SV184 @ SV160 )
= $false )
| ( ( ( SV184 = SV51 )
| ( SV184 = SV145 ) )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(916,plain,
! [SV145: $i,SV160: $i,SV51: $i] :
( ( ( ! [SY306: $i] :
( ( SY306 != SV51 )
| ( in @ SY306 @ SV160 ) ) )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(917,plain,
! [SV51: $i,SV160: $i,SV145: $i] :
( ( ( ! [SY307: $i] :
( ( SY307 != SV145 )
| ( in @ SY307 @ SV160 ) ) )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(918,plain,
! [SV47: $i,SV125: $i,SV153: $i] :
( ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV153 )
= $false )
| ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV47 )
= $false )
| ( ( in @ ( sK7_D @ SV153 @ SV125 @ SV47 ) @ SV125 )
= $false )
| ( ( SV153
= ( set_intersection2 @ SV47 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(919,plain,
! [SV154: $i,SV126: $i,SV47: $i,SV181: $i] :
( ( ( in @ SV181 @ SV47 )
= $false )
| ( ( ~ ( in @ SV181 @ SV126 ) )
= $true )
| ( ( in @ SV181 @ SV154 )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(920,plain,
! [SV126: $i,SV47: $i,SV154: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ SV154 )
| ( in @ SV185 @ SV47 ) )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(921,plain,
! [SV47: $i,SV126: $i,SV154: $i,SV186: $i] :
( ( ( ~ ( in @ SV186 @ SV154 )
| ( in @ SV186 @ SV126 ) )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(922,plain,
! [SV48: $i,SV131: $i,SV155: $i] :
( ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV131 )
= $false )
| ( ( in @ ( sK6_D @ SV155 @ SV131 @ SV48 ) @ SV155 )
= $true )
| ( ( SV155
= ( set_difference @ SV48 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(923,plain,
! [SV156: $i,SV132: $i,SV48: $i,SV182: $i] :
( ( ( in @ SV182 @ SV48 )
= $false )
| ( ( in @ SV182 @ SV132 )
= $true )
| ( ( in @ SV182 @ SV156 )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(924,plain,
! [SV132: $i,SV48: $i,SV156: $i,SV187: $i] :
( ( ( ~ ( in @ SV187 @ SV156 )
| ( in @ SV187 @ SV48 ) )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(925,plain,
! [SV48: $i,SV132: $i,SV156: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ SV156 )
| ~ ( in @ SV188 @ SV132 ) )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(926,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
= $false )
| ( ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 ) )
= $true )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[908]) ).
thf(927,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
= $false )
| ( ( ~ ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 ) )
= $true )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(928,plain,
! [SV158: $i,SV140: $i,SV49: $i,SV183: $i] :
( ( ( in @ SV183 @ SV49 )
= $true )
| ( ( in @ SV183 @ SV140 )
= $true )
| ( ( in @ SV183 @ SV158 )
= $false )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(929,plain,
! [SV140: $i,SV158: $i,SV49: $i,SV189: $i] :
( ( ( ~ ( in @ SV189 @ SV49 )
| ( in @ SV189 @ SV158 ) )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(930,plain,
! [SV49: $i,SV158: $i,SV140: $i,SV190: $i] :
( ( ( ~ ( in @ SV190 @ SV140 )
| ( in @ SV190 @ SV158 ) )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(931,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
= $false )
| ( ( ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV51 ) )
= $true )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(932,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
= $false )
| ( ( ( ( sK10_D @ SV159 @ SV144 @ SV51 )
!= SV144 ) )
= $true )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(933,plain,
! [SV160: $i,SV145: $i,SV51: $i,SV184: $i] :
( ( ( SV184 = SV51 )
= $true )
| ( ( SV184 = SV145 )
= $true )
| ( ( in @ SV184 @ SV160 )
= $false )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(934,plain,
! [SV145: $i,SV160: $i,SV51: $i,SV191: $i] :
( ( ( ( SV191 != SV51 )
| ( in @ SV191 @ SV160 ) )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(935,plain,
! [SV51: $i,SV160: $i,SV145: $i,SV192: $i] :
( ( ( ( SV192 != SV145 )
| ( in @ SV192 @ SV160 ) )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(936,plain,
! [SV154: $i,SV47: $i,SV126: $i,SV181: $i] :
( ( ( in @ SV181 @ SV126 )
= $false )
| ( ( in @ SV181 @ SV47 )
= $false )
| ( ( in @ SV181 @ SV154 )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(937,plain,
! [SV126: $i,SV47: $i,SV154: $i,SV185: $i] :
( ( ( ~ ( in @ SV185 @ SV154 ) )
= $true )
| ( ( in @ SV185 @ SV47 )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(938,plain,
! [SV47: $i,SV126: $i,SV154: $i,SV186: $i] :
( ( ( ~ ( in @ SV186 @ SV154 ) )
= $true )
| ( ( in @ SV186 @ SV126 )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(939,plain,
! [SV132: $i,SV48: $i,SV156: $i,SV187: $i] :
( ( ( ~ ( in @ SV187 @ SV156 ) )
= $true )
| ( ( in @ SV187 @ SV48 )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(940,plain,
! [SV48: $i,SV132: $i,SV156: $i,SV188: $i] :
( ( ( ~ ( in @ SV188 @ SV156 ) )
= $true )
| ( ( ~ ( in @ SV188 @ SV132 ) )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(941,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV49 )
= $false )
| ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
= $false )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(942,plain,
! [SV49: $i,SV139: $i,SV157: $i] :
( ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV139 )
= $false )
| ( ( in @ ( sK9_D @ SV157 @ SV139 @ SV49 ) @ SV157 )
= $false )
| ( ( SV157
= ( set_union2 @ SV49 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(943,plain,
! [SV140: $i,SV158: $i,SV49: $i,SV189: $i] :
( ( ( ~ ( in @ SV189 @ SV49 ) )
= $true )
| ( ( in @ SV189 @ SV158 )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(944,plain,
! [SV49: $i,SV158: $i,SV140: $i,SV190: $i] :
( ( ( ~ ( in @ SV190 @ SV140 ) )
= $true )
| ( ( in @ SV190 @ SV158 )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(945,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV51 )
= $false )
| ( ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
= $false )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(946,plain,
! [SV51: $i,SV144: $i,SV159: $i] :
( ( ( ( sK10_D @ SV159 @ SV144 @ SV51 )
= SV144 )
= $false )
| ( ( in @ ( sK10_D @ SV159 @ SV144 @ SV51 ) @ SV159 )
= $false )
| ( ( SV159
= ( unordered_pair @ SV51 @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(947,plain,
! [SV145: $i,SV160: $i,SV51: $i,SV191: $i] :
( ( ( ( SV191 != SV51 ) )
= $true )
| ( ( in @ SV191 @ SV160 )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(948,plain,
! [SV51: $i,SV160: $i,SV145: $i,SV192: $i] :
( ( ( ( SV192 != SV145 ) )
= $true )
| ( ( in @ SV192 @ SV160 )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(949,plain,
! [SV126: $i,SV47: $i,SV154: $i,SV185: $i] :
( ( ( in @ SV185 @ SV154 )
= $false )
| ( ( in @ SV185 @ SV47 )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(950,plain,
! [SV47: $i,SV126: $i,SV154: $i,SV186: $i] :
( ( ( in @ SV186 @ SV154 )
= $false )
| ( ( in @ SV186 @ SV126 )
= $true )
| ( ( SV154
= ( set_intersection2 @ SV47 @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(951,plain,
! [SV132: $i,SV48: $i,SV156: $i,SV187: $i] :
( ( ( in @ SV187 @ SV156 )
= $false )
| ( ( in @ SV187 @ SV48 )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(952,plain,
! [SV48: $i,SV132: $i,SV156: $i,SV188: $i] :
( ( ( in @ SV188 @ SV156 )
= $false )
| ( ( ~ ( in @ SV188 @ SV132 ) )
= $true )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(953,plain,
! [SV140: $i,SV158: $i,SV49: $i,SV189: $i] :
( ( ( in @ SV189 @ SV49 )
= $false )
| ( ( in @ SV189 @ SV158 )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(954,plain,
! [SV49: $i,SV158: $i,SV140: $i,SV190: $i] :
( ( ( in @ SV190 @ SV140 )
= $false )
| ( ( in @ SV190 @ SV158 )
= $true )
| ( ( SV158
= ( set_union2 @ SV49 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(955,plain,
! [SV145: $i,SV160: $i,SV51: $i,SV191: $i] :
( ( ( SV191 = SV51 )
= $false )
| ( ( in @ SV191 @ SV160 )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(956,plain,
! [SV51: $i,SV160: $i,SV145: $i,SV192: $i] :
( ( ( SV192 = SV145 )
= $false )
| ( ( in @ SV192 @ SV160 )
= $true )
| ( ( SV160
= ( unordered_pair @ SV51 @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[948]) ).
thf(957,plain,
! [SV48: $i,SV156: $i,SV132: $i,SV188: $i] :
( ( ( in @ SV188 @ SV132 )
= $false )
| ( ( in @ SV188 @ SV156 )
= $false )
| ( ( SV156
= ( set_difference @ SV48 @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(958,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[225,957,956,955,954,953,951,950,949,946,945,942,941,936,933,928,923,922,918,903,902,898,897,890,889,877,876,867,862,859,849,828,820,819,818,811,809,808,803,802,794,788,777,774,768,763,762,752,749,726,721,716,715,714,713,712,711,706,699,698,695,694,680,679,678,677,676,636,635,629,595,586,585,584,583,582,579,578,577,572,532,531,530,524,521,519,515,511,471,458,410,407,406,405,399,395,393,391,390,384,378,358,357,353,352,351,350,348,347,345,344,331,321,277,271,270,269,268,267,266,265,264]) ).
thf(959,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[958]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU154+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 03:31:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.36 .
% 0.12/0.37
% 0.12/0.37 No.of.Axioms: 76
% 0.12/0.37
% 0.12/0.37 Length.of.Defs: 0
% 0.12/0.37
% 0.12/0.37 Contains.Choice.Funs: false
% 0.18/0.38 ..
% 0.18/0.41 (rf:0,axioms:76,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:78,loop_count:0,foatp_calls:0,translation:fof_full)...............................................................
% 1.28/1.51
% 1.28/1.51 ********************************
% 1.28/1.51 * All subproblems solved! *
% 1.28/1.51 ********************************
% 1.28/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:77,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:958,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.59/1.79
% 1.59/1.79 %**** Beginning of derivation protocol ****
% 1.59/1.79 % SZS output start CNFRefutation
% See solution above
% 1.59/1.79
% 1.59/1.79 %**** End of derivation protocol ****
% 1.59/1.79 %**** no. of clauses in derivation: 959 ****
% 1.59/1.79 %**** clause counter: 958 ****
% 1.59/1.79
% 1.59/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:77,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:958,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------