%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU160+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:09 AM UTC 2026
% Result : Theorem 1.96s 0.56s
% Output : CNFRefutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 48
% Syntax : Number of formulae : 795 ( 481 unt; 0 typ; 0 def)
% Number of atoms : 4309 (1849 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 6530 (1496 ~;1149 |; 28 &;3746 @)
% ( 49 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 5 con; 0-2 aty)
% Number of variables : 1635 ( 0 ^;1635 !; 0 ?;1635 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY73,type,
sK2_SY73: $i ).
thf(tp_sK3_SY81,type,
sK3_SY81: $i > $i ).
thf(tp_sK4_SY118,type,
sK4_SY118: $i > $i > $i ).
thf(tp_sK5_SY122,type,
sK5_SY122: $i > $i > $i ).
thf(tp_sK6_SY154,type,
sK6_SY154: $i > $i ).
thf(tp_sK7_SY169,type,
sK7_SY169: $i > $i > $i ).
thf(tp_sK8_SY171,type,
sK8_SY171: $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(5,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(7,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(8,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(19,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(41,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(53,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(55,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(57,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(62,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(68,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(71,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(74,axiom,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(77,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(89,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(90,conjecture,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(91,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[90]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[91]) ).
thf(93,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(94,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(96,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(97,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(99,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(100,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(101,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(102,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(103,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(104,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(105,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(106,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(107,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(108,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(109,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(112,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(115,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(116,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(117,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(120,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(121,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(122,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(123,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(125,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(126,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(127,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(128,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(130,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(131,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(132,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(133,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(134,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(135,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(137,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(138,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(139,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(140,plain,
( ( ! [SY73: $i] :
( ( subset @ sK1_A @ ( singleton @ SY73 ) )
<=> ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ SY73 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(141,plain,
( ( ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) )
<=> ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[140]) ).
thf(142,plain,
( ( ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) )
=> ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[141]) ).
thf(143,plain,
( ( ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) )
=> ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[141]) ).
thf(144,plain,
( ( ~ ( ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) )
=> ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[142]) ).
thf(145,plain,
( ( ~ ( ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) )
=> ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[143]) ).
thf(146,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(147,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(148,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(149,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(150,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(151,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(152,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(153,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(154,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(155,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(156,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(157,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(158,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(159,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(160,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(161,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(162,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(163,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(164,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(165,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(166,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(167,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(168,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(169,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(170,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(171,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(172,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(173,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(174,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(175,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(176,plain,
$true = $true,
inference(copy,[status(thm)],[109]) ).
thf(177,plain,
$true = $true,
inference(copy,[status(thm)],[108]) ).
thf(178,plain,
$true = $true,
inference(copy,[status(thm)],[107]) ).
thf(179,plain,
$true = $true,
inference(copy,[status(thm)],[106]) ).
thf(180,plain,
$true = $true,
inference(copy,[status(thm)],[105]) ).
thf(181,plain,
$true = $true,
inference(copy,[status(thm)],[104]) ).
thf(182,plain,
$true = $true,
inference(copy,[status(thm)],[103]) ).
thf(183,plain,
$true = $true,
inference(copy,[status(thm)],[102]) ).
thf(184,plain,
$true = $true,
inference(copy,[status(thm)],[101]) ).
thf(185,plain,
$true = $true,
inference(copy,[status(thm)],[100]) ).
thf(186,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(187,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(188,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(189,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(190,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(191,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(192,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(193,plain,
( ( ~ ( ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) )
=> ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(194,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(195,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( proper_subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(196,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(197,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(198,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(199,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_difference @ SX0 @ SX2 ) @ ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(200,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_intersection2 @ SX0 @ SX2 ) @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(201,plain,
( ( ~ ( ~ ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) )
| ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(202,plain,
( ( ! [SX0: $i] :
( ( singleton @ SX0 )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(203,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(204,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( disjoint @ SX1 @ SX2 ) )
| ( disjoint @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(205,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(206,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(207,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(208,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( proper_subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( proper_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(209,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(210,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(211,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(212,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(213,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(214,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(215,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(216,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(217,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(218,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX0 @ SX2 ) )
| ( subset @ SX0 @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(219,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX1 ) )
| ( subset @ ( set_union2 @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(220,plain,
! [SV1: $i] :
( ( ! [SY74: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY74 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(221,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(222,plain,
! [SV3: $i] :
( ( ! [SY75: $i] : ( subset @ ( set_difference @ SV3 @ SY75 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(223,plain,
! [SV4: $i] :
( ( ( unordered_pair @ SV4 @ SV4 )
= ( singleton @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(224,plain,
! [SV5: $i] :
( ( ! [SY76: $i] : ( subset @ SV5 @ ( set_union2 @ SV5 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(225,plain,
! [SV6: $i] :
( ( ! [SY77: $i] : ( subset @ SV6 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(226,plain,
! [SV7: $i] :
( ( ( set_union2 @ SV7 @ empty_set )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(227,plain,
! [SV8: $i] :
( ( ( set_intersection2 @ SV8 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(228,plain,
! [SV9: $i] :
( ( ( set_difference @ SV9 @ empty_set )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(229,plain,
! [SV10: $i] :
( ( ( set_difference @ empty_set @ SV10 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(230,plain,
! [SV11: $i] :
( ( ! [SY78: $i] :
~ ( ~ ( ~ ( subset @ SV11 @ ( singleton @ SY78 ) )
| ( SV11 = empty_set )
| ( SV11
= ( singleton @ SY78 ) ) )
| ~ ( ~ ( ( SV11 = empty_set )
| ( SV11
= ( singleton @ SY78 ) ) )
| ( subset @ SV11 @ ( singleton @ SY78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(231,plain,
! [SV12: $i] :
( ( ! [SY79: $i] :
~ ~ ( ~ ( subset @ SV12 @ SY79 )
| ~ ( proper_subset @ SY79 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(232,plain,
! [SV13: $i] :
( ( ~ ( ~ ( ( SV13 != empty_set )
| ! [SY80: $i] :
~ ( in @ SY80 @ SV13 ) )
| ~ ( ~ ! [SY81: $i] :
~ ( in @ SY81 @ SV13 )
| ( SV13 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(233,plain,
! [SV14: $i] :
( ( ! [SY82: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV14 ) @ SY82 )
| ( in @ SV14 @ SY82 ) )
| ~ ( ~ ( in @ SV14 @ SY82 )
| ( subset @ ( singleton @ SV14 ) @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(234,plain,
! [SV15: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ( ( singleton @ SV15 )
!= ( unordered_pair @ SY83 @ SY84 ) )
| ( SY83 = SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(235,plain,
! [SV16: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ~ ( subset @ SV16 @ SY85 )
| ( subset @ ( set_difference @ SV16 @ SY86 ) @ ( set_difference @ SY85 @ SY86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(236,plain,
! [SV17: $i] :
( ( ! [SY87: $i,SY88: $i] :
( ~ ( subset @ SV17 @ SY87 )
| ( subset @ ( set_intersection2 @ SV17 @ SY88 ) @ ( set_intersection2 @ SY87 @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(237,plain,
( ( ~ ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) )
| ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(238,plain,
! [SV18: $i] :
( ( ( singleton @ SV18 )
!= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(239,plain,
! [SV19: $i] :
( ( ! [SY89: $i] :
( ~ ( subset @ SV19 @ SY89 )
| ( ( set_intersection2 @ SV19 @ SY89 )
= SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(240,plain,
! [SV20: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ~ ( ~ ( subset @ SV20 @ SY90 )
| ~ ( disjoint @ SY90 @ SY91 ) )
| ( disjoint @ SV20 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(241,plain,
! [SV21: $i] :
( ( ! [SY92: $i] :
( ~ ( subset @ ( singleton @ SV21 ) @ ( singleton @ SY92 ) )
| ( SV21 = SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(242,plain,
! [SV22: $i] :
( ( ! [SY93: $i] :
~ ( ~ ( ~ ( subset @ SV22 @ SY93 )
| ! [SY94: $i] :
( ~ ( in @ SY94 @ SV22 )
| ( in @ SY94 @ SY93 ) ) )
| ~ ( ~ ! [SY95: $i] :
( ~ ( in @ SY95 @ SV22 )
| ( in @ SY95 @ SY93 ) )
| ( subset @ SV22 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(243,plain,
! [SV23: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ~ ( ~ ( subset @ SV23 @ SY96 )
| ~ ( subset @ SY96 @ SY97 ) )
| ( subset @ SV23 @ SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(244,plain,
! [SV24: $i] :
( ( ! [SY98: $i] :
~ ( ~ ( ~ ( proper_subset @ SV24 @ SY98 )
| ~ ( ~ ( subset @ SV24 @ SY98 )
| ~ ( ( SV24 != SY98 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SY98 )
| ~ ( ( SV24 != SY98 ) ) )
| ( proper_subset @ SV24 @ SY98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(245,plain,
! [SV25: $i] :
( ( ~ ( subset @ SV25 @ empty_set )
| ( SV25 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(246,plain,
! [SV26: $i] :
( ( ! [SY99: $i] :
~ ( ~ ( ( ( set_difference @ SV26 @ SY99 )
!= empty_set )
| ( subset @ SV26 @ SY99 ) )
| ~ ( ~ ( subset @ SV26 @ SY99 )
| ( ( set_difference @ SV26 @ SY99 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(247,plain,
! [SV27: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ( ( singleton @ SV27 )
!= ( unordered_pair @ SY100 @ SY101 ) )
| ( SV27 = SY100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(248,plain,
! [SV28: $i] :
( ( ! [SY102: $i] :
~ ( ~ ( ( SV28 != SY102 )
| ~ ( ~ ( subset @ SV28 @ SY102 )
| ~ ( subset @ SY102 @ SV28 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV28 @ SY102 )
| ~ ( subset @ SY102 @ SV28 ) )
| ( SV28 = SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(249,plain,
! [SV29: $i] :
( ( ! [SY103: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV29 ) @ SY103 )
| ( in @ SV29 @ SY103 ) )
| ~ ( ~ ( in @ SV29 @ SY103 )
| ( subset @ ( singleton @ SV29 ) @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(250,plain,
! [SV30: $i] :
( ( ! [SY104: $i] :
( ~ ( subset @ SV30 @ SY104 )
| ( ( set_union2 @ SV30 @ SY104 )
= SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(251,plain,
! [SV31: $i] :
( ( ! [SY105: $i] :
~ ( ~ ( ( SY105
!= ( singleton @ SV31 ) )
| ! [SY106: $i] :
~ ( ~ ( ~ ( in @ SY106 @ SY105 )
| ( SY106 = SV31 ) )
| ~ ( ( SY106 != SV31 )
| ( in @ SY106 @ SY105 ) ) ) )
| ~ ( ~ ! [SY107: $i] :
~ ( ~ ( ~ ( in @ SY107 @ SY105 )
| ( SY107 = SV31 ) )
| ~ ( ( SY107 != SV31 )
| ( in @ SY107 @ SY105 ) ) )
| ( SY105
= ( singleton @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(252,plain,
! [SV32: $i] :
( ( ~ ( empty @ SV32 )
| ( SV32 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(253,plain,
! [SV33: $i] :
( ( ! [SY108: $i] :
~ ( ~ ( ( ( set_difference @ SV33 @ SY108 )
!= empty_set )
| ( subset @ SV33 @ SY108 ) )
| ~ ( ~ ( subset @ SV33 @ SY108 )
| ( ( set_difference @ SV33 @ SY108 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(254,plain,
! [SV34: $i] :
( ( ! [SY109: $i,SY110: $i] :
( ~ ~ ( ~ ( subset @ SV34 @ SY109 )
| ~ ( subset @ SV34 @ SY110 ) )
| ( subset @ SV34 @ ( set_intersection2 @ SY109 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(255,plain,
! [SV35: $i] :
( ( ! [SY111: $i,SY112: $i] :
( ~ ~ ( ~ ( subset @ SV35 @ SY111 )
| ~ ( subset @ SY112 @ SY111 ) )
| ( subset @ ( set_union2 @ SV35 @ SY112 ) @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(256,plain,
! [SV36: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV36 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(257,plain,
! [SV37: $i,SV3: $i] :
( ( subset @ ( set_difference @ SV3 @ SV37 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(258,plain,
! [SV38: $i,SV5: $i] :
( ( subset @ SV5 @ ( set_union2 @ SV5 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(259,plain,
! [SV6: $i] :
( ( subset @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(260,plain,
! [SV40: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV11 @ ( singleton @ SV40 ) )
| ( SV11 = empty_set )
| ( SV11
= ( singleton @ SV40 ) ) )
| ~ ( ~ ( ( SV11 = empty_set )
| ( SV11
= ( singleton @ SV40 ) ) )
| ( subset @ SV11 @ ( singleton @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(261,plain,
! [SV41: $i,SV12: $i] :
( ( ~ ~ ( ~ ( subset @ SV12 @ SV41 )
| ~ ( proper_subset @ SV41 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(262,plain,
! [SV13: $i] :
( ( ~ ( ( SV13 != empty_set )
| ! [SY80: $i] :
~ ( in @ SY80 @ SV13 ) )
| ~ ( ~ ! [SY81: $i] :
~ ( in @ SY81 @ SV13 )
| ( SV13 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(263,plain,
! [SV42: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV14 ) @ SV42 )
| ( in @ SV14 @ SV42 ) )
| ~ ( ~ ( in @ SV14 @ SV42 )
| ( subset @ ( singleton @ SV14 ) @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(264,plain,
! [SV43: $i,SV15: $i] :
( ( ! [SY113: $i] :
( ( ( singleton @ SV15 )
!= ( unordered_pair @ SV43 @ SY113 ) )
| ( SV43 = SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(265,plain,
! [SV44: $i,SV16: $i] :
( ( ! [SY114: $i] :
( ~ ( subset @ SV16 @ SV44 )
| ( subset @ ( set_difference @ SV16 @ SY114 ) @ ( set_difference @ SV44 @ SY114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(266,plain,
! [SV45: $i,SV17: $i] :
( ( ! [SY115: $i] :
( ~ ( subset @ SV17 @ SV45 )
| ( subset @ ( set_intersection2 @ SV17 @ SY115 ) @ ( set_intersection2 @ SV45 @ SY115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(267,plain,
( ( ~ ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(268,plain,
( ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(269,plain,
! [SV18: $i] :
( ( ( singleton @ SV18 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(270,plain,
! [SV46: $i,SV19: $i] :
( ( ~ ( subset @ SV19 @ SV46 )
| ( ( set_intersection2 @ SV19 @ SV46 )
= SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(271,plain,
! [SV47: $i,SV20: $i] :
( ( ! [SY116: $i] :
( ~ ~ ( ~ ( subset @ SV20 @ SV47 )
| ~ ( disjoint @ SV47 @ SY116 ) )
| ( disjoint @ SV20 @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(272,plain,
! [SV48: $i,SV21: $i] :
( ( ~ ( subset @ ( singleton @ SV21 ) @ ( singleton @ SV48 ) )
| ( SV21 = SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(273,plain,
! [SV49: $i,SV22: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV22 @ SV49 )
| ! [SY117: $i] :
( ~ ( in @ SY117 @ SV22 )
| ( in @ SY117 @ SV49 ) ) )
| ~ ( ~ ! [SY118: $i] :
( ~ ( in @ SY118 @ SV22 )
| ( in @ SY118 @ SV49 ) )
| ( subset @ SV22 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(274,plain,
! [SV50: $i,SV23: $i] :
( ( ! [SY119: $i] :
( ~ ~ ( ~ ( subset @ SV23 @ SV50 )
| ~ ( subset @ SV50 @ SY119 ) )
| ( subset @ SV23 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(275,plain,
! [SV51: $i,SV24: $i] :
( ( ~ ( ~ ( ~ ( proper_subset @ SV24 @ SV51 )
| ~ ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) )
| ( proper_subset @ SV24 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(276,plain,
! [SV25: $i] :
( ( ( ~ ( subset @ SV25 @ empty_set ) )
= $true )
| ( ( SV25 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(277,plain,
! [SV52: $i,SV26: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV26 @ SV52 )
!= empty_set )
| ( subset @ SV26 @ SV52 ) )
| ~ ( ~ ( subset @ SV26 @ SV52 )
| ( ( set_difference @ SV26 @ SV52 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(278,plain,
! [SV53: $i,SV27: $i] :
( ( ! [SY120: $i] :
( ( ( singleton @ SV27 )
!= ( unordered_pair @ SV53 @ SY120 ) )
| ( SV27 = SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(279,plain,
! [SV54: $i,SV28: $i] :
( ( ~ ( ~ ( ( SV28 != SV54 )
| ~ ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) )
| ( SV28 = SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(280,plain,
! [SV55: $i,SV29: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV29 ) @ SV55 )
| ( in @ SV29 @ SV55 ) )
| ~ ( ~ ( in @ SV29 @ SV55 )
| ( subset @ ( singleton @ SV29 ) @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(281,plain,
! [SV56: $i,SV30: $i] :
( ( ~ ( subset @ SV30 @ SV56 )
| ( ( set_union2 @ SV30 @ SV56 )
= SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(282,plain,
! [SV31: $i,SV57: $i] :
( ( ~ ( ~ ( ( SV57
!= ( singleton @ SV31 ) )
| ! [SY121: $i] :
~ ( ~ ( ~ ( in @ SY121 @ SV57 )
| ( SY121 = SV31 ) )
| ~ ( ( SY121 != SV31 )
| ( in @ SY121 @ SV57 ) ) ) )
| ~ ( ~ ! [SY122: $i] :
~ ( ~ ( ~ ( in @ SY122 @ SV57 )
| ( SY122 = SV31 ) )
| ~ ( ( SY122 != SV31 )
| ( in @ SY122 @ SV57 ) ) )
| ( SV57
= ( singleton @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(283,plain,
! [SV32: $i] :
( ( ( ~ ( empty @ SV32 ) )
= $true )
| ( ( SV32 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(284,plain,
! [SV58: $i,SV33: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV33 @ SV58 )
!= empty_set )
| ( subset @ SV33 @ SV58 ) )
| ~ ( ~ ( subset @ SV33 @ SV58 )
| ( ( set_difference @ SV33 @ SV58 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(285,plain,
! [SV59: $i,SV34: $i] :
( ( ! [SY123: $i] :
( ~ ~ ( ~ ( subset @ SV34 @ SV59 )
| ~ ( subset @ SV34 @ SY123 ) )
| ( subset @ SV34 @ ( set_intersection2 @ SV59 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(286,plain,
! [SV60: $i,SV35: $i] :
( ( ! [SY124: $i] :
( ~ ~ ( ~ ( subset @ SV35 @ SV60 )
| ~ ( subset @ SY124 @ SV60 ) )
| ( subset @ ( set_union2 @ SV35 @ SY124 ) @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(287,plain,
! [SV40: $i,SV11: $i] :
( ( ~ ( ~ ( subset @ SV11 @ ( singleton @ SV40 ) )
| ( SV11 = empty_set )
| ( SV11
= ( singleton @ SV40 ) ) )
| ~ ( ~ ( ( SV11 = empty_set )
| ( SV11
= ( singleton @ SV40 ) ) )
| ( subset @ SV11 @ ( singleton @ SV40 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(288,plain,
! [SV41: $i,SV12: $i] :
( ( ~ ( ~ ( subset @ SV12 @ SV41 )
| ~ ( proper_subset @ SV41 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(289,plain,
! [SV13: $i] :
( ( ~ ( ( SV13 != empty_set )
| ! [SY80: $i] :
~ ( in @ SY80 @ SV13 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(290,plain,
! [SV13: $i] :
( ( ~ ( ~ ! [SY81: $i] :
~ ( in @ SY81 @ SV13 )
| ( SV13 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(291,plain,
! [SV42: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV14 ) @ SV42 )
| ( in @ SV14 @ SV42 ) )
| ~ ( ~ ( in @ SV14 @ SV42 )
| ( subset @ ( singleton @ SV14 ) @ SV42 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(292,plain,
! [SV61: $i,SV43: $i,SV15: $i] :
( ( ( ( singleton @ SV15 )
!= ( unordered_pair @ SV43 @ SV61 ) )
| ( SV43 = SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(293,plain,
! [SV62: $i,SV44: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV44 )
| ( subset @ ( set_difference @ SV16 @ SV62 ) @ ( set_difference @ SV44 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(294,plain,
! [SV63: $i,SV45: $i,SV17: $i] :
( ( ~ ( subset @ SV17 @ SV45 )
| ( subset @ ( set_intersection2 @ SV17 @ SV63 ) @ ( set_intersection2 @ SV45 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(295,plain,
( ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(296,plain,
( ( sK1_A = empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(297,plain,
( ( sK1_A
= ( singleton @ sK2_SY73 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[268]) ).
thf(298,plain,
! [SV46: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV46 ) )
= $true )
| ( ( ( set_intersection2 @ SV19 @ SV46 )
= SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(299,plain,
! [SV64: $i,SV47: $i,SV20: $i] :
( ( ~ ~ ( ~ ( subset @ SV20 @ SV47 )
| ~ ( disjoint @ SV47 @ SV64 ) )
| ( disjoint @ SV20 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(300,plain,
! [SV48: $i,SV21: $i] :
( ( ( ~ ( subset @ ( singleton @ SV21 ) @ ( singleton @ SV48 ) ) )
= $true )
| ( ( SV21 = SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(301,plain,
! [SV49: $i,SV22: $i] :
( ( ~ ( ~ ( subset @ SV22 @ SV49 )
| ! [SY117: $i] :
( ~ ( in @ SY117 @ SV22 )
| ( in @ SY117 @ SV49 ) ) )
| ~ ( ~ ! [SY118: $i] :
( ~ ( in @ SY118 @ SV22 )
| ( in @ SY118 @ SV49 ) )
| ( subset @ SV22 @ SV49 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(302,plain,
! [SV65: $i,SV50: $i,SV23: $i] :
( ( ~ ~ ( ~ ( subset @ SV23 @ SV50 )
| ~ ( subset @ SV50 @ SV65 ) )
| ( subset @ SV23 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(303,plain,
! [SV51: $i,SV24: $i] :
( ( ~ ( ~ ( proper_subset @ SV24 @ SV51 )
| ~ ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) )
| ( proper_subset @ SV24 @ SV51 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(304,plain,
! [SV25: $i] :
( ( ( subset @ SV25 @ empty_set )
= $false )
| ( ( SV25 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(305,plain,
! [SV52: $i,SV26: $i] :
( ( ~ ( ( ( set_difference @ SV26 @ SV52 )
!= empty_set )
| ( subset @ SV26 @ SV52 ) )
| ~ ( ~ ( subset @ SV26 @ SV52 )
| ( ( set_difference @ SV26 @ SV52 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(306,plain,
! [SV66: $i,SV53: $i,SV27: $i] :
( ( ( ( singleton @ SV27 )
!= ( unordered_pair @ SV53 @ SV66 ) )
| ( SV27 = SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(307,plain,
! [SV54: $i,SV28: $i] :
( ( ~ ( ( SV28 != SV54 )
| ~ ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) )
| ( SV28 = SV54 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(308,plain,
! [SV55: $i,SV29: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV29 ) @ SV55 )
| ( in @ SV29 @ SV55 ) )
| ~ ( ~ ( in @ SV29 @ SV55 )
| ( subset @ ( singleton @ SV29 ) @ SV55 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(309,plain,
! [SV56: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV56 ) )
= $true )
| ( ( ( set_union2 @ SV30 @ SV56 )
= SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(310,plain,
! [SV31: $i,SV57: $i] :
( ( ~ ( ( SV57
!= ( singleton @ SV31 ) )
| ! [SY121: $i] :
~ ( ~ ( ~ ( in @ SY121 @ SV57 )
| ( SY121 = SV31 ) )
| ~ ( ( SY121 != SV31 )
| ( in @ SY121 @ SV57 ) ) ) )
| ~ ( ~ ! [SY122: $i] :
~ ( ~ ( ~ ( in @ SY122 @ SV57 )
| ( SY122 = SV31 ) )
| ~ ( ( SY122 != SV31 )
| ( in @ SY122 @ SV57 ) ) )
| ( SV57
= ( singleton @ SV31 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(311,plain,
! [SV32: $i] :
( ( ( empty @ SV32 )
= $false )
| ( ( SV32 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(312,plain,
! [SV58: $i,SV33: $i] :
( ( ~ ( ( ( set_difference @ SV33 @ SV58 )
!= empty_set )
| ( subset @ SV33 @ SV58 ) )
| ~ ( ~ ( subset @ SV33 @ SV58 )
| ( ( set_difference @ SV33 @ SV58 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(313,plain,
! [SV67: $i,SV59: $i,SV34: $i] :
( ( ~ ~ ( ~ ( subset @ SV34 @ SV59 )
| ~ ( subset @ SV34 @ SV67 ) )
| ( subset @ SV34 @ ( set_intersection2 @ SV59 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(314,plain,
! [SV68: $i,SV60: $i,SV35: $i] :
( ( ~ ~ ( ~ ( subset @ SV35 @ SV60 )
| ~ ( subset @ SV68 @ SV60 ) )
| ( subset @ ( set_union2 @ SV35 @ SV68 ) @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(315,plain,
! [SV40: $i,SV11: $i] :
( ( ~ ( ~ ( subset @ SV11 @ ( singleton @ SV40 ) )
| ( SV11 = empty_set )
| ( SV11
= ( singleton @ SV40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(316,plain,
! [SV40: $i,SV11: $i] :
( ( ~ ( ~ ( ( SV11 = empty_set )
| ( SV11
= ( singleton @ SV40 ) ) )
| ( subset @ SV11 @ ( singleton @ SV40 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[287]) ).
thf(317,plain,
! [SV41: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV41 )
| ~ ( proper_subset @ SV41 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(318,plain,
! [SV13: $i] :
( ( ( SV13 != empty_set )
| ! [SY80: $i] :
~ ( in @ SY80 @ SV13 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(319,plain,
! [SV13: $i] :
( ( ~ ! [SY81: $i] :
~ ( in @ SY81 @ SV13 )
| ( SV13 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(320,plain,
! [SV42: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV14 ) @ SV42 )
| ( in @ SV14 @ SV42 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(321,plain,
! [SV42: $i,SV14: $i] :
( ( ~ ( ~ ( in @ SV14 @ SV42 )
| ( subset @ ( singleton @ SV14 ) @ SV42 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(322,plain,
! [SV61: $i,SV43: $i,SV15: $i] :
( ( ( ( singleton @ SV15 )
!= ( unordered_pair @ SV43 @ SV61 ) )
= $true )
| ( ( SV43 = SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(323,plain,
! [SV62: $i,SV44: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV44 ) )
= $true )
| ( ( subset @ ( set_difference @ SV16 @ SV62 ) @ ( set_difference @ SV44 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(324,plain,
! [SV63: $i,SV45: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV45 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV17 @ SV63 ) @ ( set_intersection2 @ SV45 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(325,plain,
! [SV46: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV46 )
= $false )
| ( ( ( set_intersection2 @ SV19 @ SV46 )
= SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(326,plain,
! [SV64: $i,SV47: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV20 @ SV47 )
| ~ ( disjoint @ SV47 @ SV64 ) ) )
= $true )
| ( ( disjoint @ SV20 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(327,plain,
! [SV48: $i,SV21: $i] :
( ( ( subset @ ( singleton @ SV21 ) @ ( singleton @ SV48 ) )
= $false )
| ( ( SV21 = SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(328,plain,
! [SV49: $i,SV22: $i] :
( ( ~ ( ~ ( subset @ SV22 @ SV49 )
| ! [SY117: $i] :
( ~ ( in @ SY117 @ SV22 )
| ( in @ SY117 @ SV49 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(329,plain,
! [SV49: $i,SV22: $i] :
( ( ~ ( ~ ! [SY118: $i] :
( ~ ( in @ SY118 @ SV22 )
| ( in @ SY118 @ SV49 ) )
| ( subset @ SV22 @ SV49 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[301]) ).
thf(330,plain,
! [SV65: $i,SV50: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV23 @ SV50 )
| ~ ( subset @ SV50 @ SV65 ) ) )
= $true )
| ( ( subset @ SV23 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(331,plain,
! [SV51: $i,SV24: $i] :
( ( ~ ( ~ ( proper_subset @ SV24 @ SV51 )
| ~ ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(332,plain,
! [SV51: $i,SV24: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) )
| ( proper_subset @ SV24 @ SV51 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(333,plain,
! [SV52: $i,SV26: $i] :
( ( ~ ( ( ( set_difference @ SV26 @ SV52 )
!= empty_set )
| ( subset @ SV26 @ SV52 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(334,plain,
! [SV52: $i,SV26: $i] :
( ( ~ ( ~ ( subset @ SV26 @ SV52 )
| ( ( set_difference @ SV26 @ SV52 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(335,plain,
! [SV66: $i,SV53: $i,SV27: $i] :
( ( ( ( singleton @ SV27 )
!= ( unordered_pair @ SV53 @ SV66 ) )
= $true )
| ( ( SV27 = SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(336,plain,
! [SV54: $i,SV28: $i] :
( ( ~ ( ( SV28 != SV54 )
| ~ ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(337,plain,
! [SV54: $i,SV28: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) )
| ( SV28 = SV54 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(338,plain,
! [SV55: $i,SV29: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV29 ) @ SV55 )
| ( in @ SV29 @ SV55 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(339,plain,
! [SV55: $i,SV29: $i] :
( ( ~ ( ~ ( in @ SV29 @ SV55 )
| ( subset @ ( singleton @ SV29 ) @ SV55 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(340,plain,
! [SV56: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV56 )
= $false )
| ( ( ( set_union2 @ SV30 @ SV56 )
= SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(341,plain,
! [SV31: $i,SV57: $i] :
( ( ~ ( ( SV57
!= ( singleton @ SV31 ) )
| ! [SY121: $i] :
~ ( ~ ( ~ ( in @ SY121 @ SV57 )
| ( SY121 = SV31 ) )
| ~ ( ( SY121 != SV31 )
| ( in @ SY121 @ SV57 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(342,plain,
! [SV31: $i,SV57: $i] :
( ( ~ ( ~ ! [SY122: $i] :
~ ( ~ ( ~ ( in @ SY122 @ SV57 )
| ( SY122 = SV31 ) )
| ~ ( ( SY122 != SV31 )
| ( in @ SY122 @ SV57 ) ) )
| ( SV57
= ( singleton @ SV31 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(343,plain,
! [SV58: $i,SV33: $i] :
( ( ~ ( ( ( set_difference @ SV33 @ SV58 )
!= empty_set )
| ( subset @ SV33 @ SV58 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(344,plain,
! [SV58: $i,SV33: $i] :
( ( ~ ( ~ ( subset @ SV33 @ SV58 )
| ( ( set_difference @ SV33 @ SV58 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(345,plain,
! [SV67: $i,SV59: $i,SV34: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV34 @ SV59 )
| ~ ( subset @ SV34 @ SV67 ) ) )
= $true )
| ( ( subset @ SV34 @ ( set_intersection2 @ SV59 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(346,plain,
! [SV68: $i,SV60: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV35 @ SV60 )
| ~ ( subset @ SV68 @ SV60 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV35 @ SV68 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(347,plain,
! [SV40: $i,SV11: $i] :
( ( ~ ( subset @ SV11 @ ( singleton @ SV40 ) )
| ( SV11 = empty_set )
| ( SV11
= ( singleton @ SV40 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(348,plain,
! [SV40: $i,SV11: $i] :
( ( ~ ( ( SV11 = empty_set )
| ( SV11
= ( singleton @ SV40 ) ) )
| ( subset @ SV11 @ ( singleton @ SV40 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(349,plain,
! [SV41: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV41 ) )
= $true )
| ( ( ~ ( proper_subset @ SV41 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(350,plain,
! [SV13: $i] :
( ( ( SV13 != empty_set )
= $true )
| ( ( ! [SY80: $i] :
~ ( in @ SY80 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(351,plain,
! [SV13: $i] :
( ( ( ~ ! [SY81: $i] :
~ ( in @ SY81 @ SV13 ) )
= $true )
| ( ( SV13 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(352,plain,
! [SV42: $i,SV14: $i] :
( ( ~ ( subset @ ( singleton @ SV14 ) @ SV42 )
| ( in @ SV14 @ SV42 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(353,plain,
! [SV42: $i,SV14: $i] :
( ( ~ ( in @ SV14 @ SV42 )
| ( subset @ ( singleton @ SV14 ) @ SV42 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(354,plain,
! [SV61: $i,SV43: $i,SV15: $i] :
( ( ( ( singleton @ SV15 )
= ( unordered_pair @ SV43 @ SV61 ) )
= $false )
| ( ( SV43 = SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(355,plain,
! [SV62: $i,SV44: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV44 )
= $false )
| ( ( subset @ ( set_difference @ SV16 @ SV62 ) @ ( set_difference @ SV44 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(356,plain,
! [SV63: $i,SV45: $i,SV17: $i] :
( ( ( subset @ SV17 @ SV45 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV17 @ SV63 ) @ ( set_intersection2 @ SV45 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(357,plain,
! [SV64: $i,SV47: $i,SV20: $i] :
( ( ( ~ ( ~ ( subset @ SV20 @ SV47 )
| ~ ( disjoint @ SV47 @ SV64 ) ) )
= $false )
| ( ( disjoint @ SV20 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(358,plain,
! [SV49: $i,SV22: $i] :
( ( ~ ( subset @ SV22 @ SV49 )
| ! [SY117: $i] :
( ~ ( in @ SY117 @ SV22 )
| ( in @ SY117 @ SV49 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(359,plain,
! [SV49: $i,SV22: $i] :
( ( ~ ! [SY118: $i] :
( ~ ( in @ SY118 @ SV22 )
| ( in @ SY118 @ SV49 ) )
| ( subset @ SV22 @ SV49 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(360,plain,
! [SV65: $i,SV50: $i,SV23: $i] :
( ( ( ~ ( ~ ( subset @ SV23 @ SV50 )
| ~ ( subset @ SV50 @ SV65 ) ) )
= $false )
| ( ( subset @ SV23 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(361,plain,
! [SV51: $i,SV24: $i] :
( ( ~ ( proper_subset @ SV24 @ SV51 )
| ~ ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(362,plain,
! [SV51: $i,SV24: $i] :
( ( ~ ~ ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) )
| ( proper_subset @ SV24 @ SV51 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(363,plain,
! [SV52: $i,SV26: $i] :
( ( ( ( set_difference @ SV26 @ SV52 )
!= empty_set )
| ( subset @ SV26 @ SV52 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(364,plain,
! [SV52: $i,SV26: $i] :
( ( ~ ( subset @ SV26 @ SV52 )
| ( ( set_difference @ SV26 @ SV52 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(365,plain,
! [SV66: $i,SV53: $i,SV27: $i] :
( ( ( ( singleton @ SV27 )
= ( unordered_pair @ SV53 @ SV66 ) )
= $false )
| ( ( SV27 = SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(366,plain,
! [SV54: $i,SV28: $i] :
( ( ( SV28 != SV54 )
| ~ ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(367,plain,
! [SV54: $i,SV28: $i] :
( ( ~ ~ ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) )
| ( SV28 = SV54 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(368,plain,
! [SV55: $i,SV29: $i] :
( ( ~ ( subset @ ( singleton @ SV29 ) @ SV55 )
| ( in @ SV29 @ SV55 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(369,plain,
! [SV55: $i,SV29: $i] :
( ( ~ ( in @ SV29 @ SV55 )
| ( subset @ ( singleton @ SV29 ) @ SV55 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(370,plain,
! [SV31: $i,SV57: $i] :
( ( ( SV57
!= ( singleton @ SV31 ) )
| ! [SY121: $i] :
~ ( ~ ( ~ ( in @ SY121 @ SV57 )
| ( SY121 = SV31 ) )
| ~ ( ( SY121 != SV31 )
| ( in @ SY121 @ SV57 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(371,plain,
! [SV31: $i,SV57: $i] :
( ( ~ ! [SY122: $i] :
~ ( ~ ( ~ ( in @ SY122 @ SV57 )
| ( SY122 = SV31 ) )
| ~ ( ( SY122 != SV31 )
| ( in @ SY122 @ SV57 ) ) )
| ( SV57
= ( singleton @ SV31 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(372,plain,
! [SV58: $i,SV33: $i] :
( ( ( ( set_difference @ SV33 @ SV58 )
!= empty_set )
| ( subset @ SV33 @ SV58 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(373,plain,
! [SV58: $i,SV33: $i] :
( ( ~ ( subset @ SV33 @ SV58 )
| ( ( set_difference @ SV33 @ SV58 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(374,plain,
! [SV67: $i,SV59: $i,SV34: $i] :
( ( ( ~ ( ~ ( subset @ SV34 @ SV59 )
| ~ ( subset @ SV34 @ SV67 ) ) )
= $false )
| ( ( subset @ SV34 @ ( set_intersection2 @ SV59 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(375,plain,
! [SV68: $i,SV60: $i,SV35: $i] :
( ( ( ~ ( ~ ( subset @ SV35 @ SV60 )
| ~ ( subset @ SV68 @ SV60 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV35 @ SV68 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(376,plain,
! [SV40: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ ( singleton @ SV40 ) ) )
= $true )
| ( ( ( SV11 = empty_set )
| ( SV11
= ( singleton @ SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(377,plain,
! [SV40: $i,SV11: $i] :
( ( ( ~ ( ( SV11 = empty_set )
| ( SV11
= ( singleton @ SV40 ) ) ) )
= $true )
| ( ( subset @ SV11 @ ( singleton @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(378,plain,
! [SV41: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV41 )
= $false )
| ( ( ~ ( proper_subset @ SV41 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(379,plain,
! [SV13: $i] :
( ( ( SV13 = empty_set )
= $false )
| ( ( ! [SY80: $i] :
~ ( in @ SY80 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(380,plain,
! [SV13: $i] :
( ( ( ! [SY81: $i] :
~ ( in @ SY81 @ SV13 ) )
= $false )
| ( ( SV13 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(381,plain,
! [SV42: $i,SV14: $i] :
( ( ( ~ ( subset @ ( singleton @ SV14 ) @ SV42 ) )
= $true )
| ( ( in @ SV14 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(382,plain,
! [SV42: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV42 ) )
= $true )
| ( ( subset @ ( singleton @ SV14 ) @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(383,plain,
! [SV64: $i,SV47: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV47 )
| ~ ( disjoint @ SV47 @ SV64 ) )
= $true )
| ( ( disjoint @ SV20 @ SV64 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(384,plain,
! [SV49: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV49 ) )
= $true )
| ( ( ! [SY117: $i] :
( ~ ( in @ SY117 @ SV22 )
| ( in @ SY117 @ SV49 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(385,plain,
! [SV49: $i,SV22: $i] :
( ( ( ~ ! [SY118: $i] :
( ~ ( in @ SY118 @ SV22 )
| ( in @ SY118 @ SV49 ) ) )
= $true )
| ( ( subset @ SV22 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(386,plain,
! [SV65: $i,SV50: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV50 )
| ~ ( subset @ SV50 @ SV65 ) )
= $true )
| ( ( subset @ SV23 @ SV65 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(387,plain,
! [SV51: $i,SV24: $i] :
( ( ( ~ ( proper_subset @ SV24 @ SV51 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(388,plain,
! [SV51: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) ) )
= $true )
| ( ( proper_subset @ SV24 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(389,plain,
! [SV52: $i,SV26: $i] :
( ( ( ( set_difference @ SV26 @ SV52 )
!= empty_set )
= $true )
| ( ( subset @ SV26 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(390,plain,
! [SV52: $i,SV26: $i] :
( ( ( ~ ( subset @ SV26 @ SV52 ) )
= $true )
| ( ( ( set_difference @ SV26 @ SV52 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(391,plain,
! [SV54: $i,SV28: $i] :
( ( ( SV28 != SV54 )
= $true )
| ( ( ~ ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(392,plain,
! [SV54: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) ) )
= $true )
| ( ( SV28 = SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(393,plain,
! [SV55: $i,SV29: $i] :
( ( ( ~ ( subset @ ( singleton @ SV29 ) @ SV55 ) )
= $true )
| ( ( in @ SV29 @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(394,plain,
! [SV55: $i,SV29: $i] :
( ( ( ~ ( in @ SV29 @ SV55 ) )
= $true )
| ( ( subset @ ( singleton @ SV29 ) @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(395,plain,
! [SV31: $i,SV57: $i] :
( ( ( SV57
!= ( singleton @ SV31 ) )
= $true )
| ( ( ! [SY121: $i] :
~ ( ~ ( ~ ( in @ SY121 @ SV57 )
| ( SY121 = SV31 ) )
| ~ ( ( SY121 != SV31 )
| ( in @ SY121 @ SV57 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(396,plain,
! [SV31: $i,SV57: $i] :
( ( ( ~ ! [SY122: $i] :
~ ( ~ ( ~ ( in @ SY122 @ SV57 )
| ( SY122 = SV31 ) )
| ~ ( ( SY122 != SV31 )
| ( in @ SY122 @ SV57 ) ) ) )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(397,plain,
! [SV58: $i,SV33: $i] :
( ( ( ( set_difference @ SV33 @ SV58 )
!= empty_set )
= $true )
| ( ( subset @ SV33 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(398,plain,
! [SV58: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV58 ) )
= $true )
| ( ( ( set_difference @ SV33 @ SV58 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(399,plain,
! [SV67: $i,SV59: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV59 )
| ~ ( subset @ SV34 @ SV67 ) )
= $true )
| ( ( subset @ SV34 @ ( set_intersection2 @ SV59 @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(400,plain,
! [SV68: $i,SV60: $i,SV35: $i] :
( ( ( ~ ( subset @ SV35 @ SV60 )
| ~ ( subset @ SV68 @ SV60 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV35 @ SV68 ) @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(401,plain,
! [SV40: $i,SV11: $i] :
( ( ( subset @ SV11 @ ( singleton @ SV40 ) )
= $false )
| ( ( ( SV11 = empty_set )
| ( SV11
= ( singleton @ SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(402,plain,
! [SV40: $i,SV11: $i] :
( ( ( ( SV11 = empty_set )
| ( SV11
= ( singleton @ SV40 ) ) )
= $false )
| ( ( subset @ SV11 @ ( singleton @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(403,plain,
! [SV12: $i,SV41: $i] :
( ( ( proper_subset @ SV41 @ SV12 )
= $false )
| ( ( subset @ SV12 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(404,plain,
! [SV13: $i,SV69: $i] :
( ( ( ~ ( in @ SV69 @ SV13 ) )
= $true )
| ( ( SV13 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(405,plain,
! [SV13: $i] :
( ( ( ~ ( in @ ( sK3_SY81 @ SV13 ) @ SV13 ) )
= $false )
| ( ( SV13 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[380]) ).
thf(406,plain,
! [SV42: $i,SV14: $i] :
( ( ( subset @ ( singleton @ SV14 ) @ SV42 )
= $false )
| ( ( in @ SV14 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(407,plain,
! [SV42: $i,SV14: $i] :
( ( ( in @ SV14 @ SV42 )
= $false )
| ( ( subset @ ( singleton @ SV14 ) @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(408,plain,
! [SV64: $i,SV47: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV47 ) )
= $true )
| ( ( ~ ( disjoint @ SV47 @ SV64 ) )
= $true )
| ( ( disjoint @ SV20 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(409,plain,
! [SV49: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV49 )
= $false )
| ( ( ! [SY117: $i] :
( ~ ( in @ SY117 @ SV22 )
| ( in @ SY117 @ SV49 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(410,plain,
! [SV49: $i,SV22: $i] :
( ( ( ! [SY118: $i] :
( ~ ( in @ SY118 @ SV22 )
| ( in @ SY118 @ SV49 ) ) )
= $false )
| ( ( subset @ SV22 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(411,plain,
! [SV65: $i,SV50: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV50 ) )
= $true )
| ( ( ~ ( subset @ SV50 @ SV65 ) )
= $true )
| ( ( subset @ SV23 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(412,plain,
! [SV51: $i,SV24: $i] :
( ( ( proper_subset @ SV24 @ SV51 )
= $false )
| ( ( ~ ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(413,plain,
! [SV51: $i,SV24: $i] :
( ( ( ~ ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) ) )
= $false )
| ( ( proper_subset @ SV24 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(414,plain,
! [SV52: $i,SV26: $i] :
( ( ( ( set_difference @ SV26 @ SV52 )
= empty_set )
= $false )
| ( ( subset @ SV26 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(415,plain,
! [SV52: $i,SV26: $i] :
( ( ( subset @ SV26 @ SV52 )
= $false )
| ( ( ( set_difference @ SV26 @ SV52 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(416,plain,
! [SV54: $i,SV28: $i] :
( ( ( SV28 = SV54 )
= $false )
| ( ( ~ ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(417,plain,
! [SV54: $i,SV28: $i] :
( ( ( ~ ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) ) )
= $false )
| ( ( SV28 = SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(418,plain,
! [SV55: $i,SV29: $i] :
( ( ( subset @ ( singleton @ SV29 ) @ SV55 )
= $false )
| ( ( in @ SV29 @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(419,plain,
! [SV55: $i,SV29: $i] :
( ( ( in @ SV29 @ SV55 )
= $false )
| ( ( subset @ ( singleton @ SV29 ) @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(420,plain,
! [SV31: $i,SV57: $i] :
( ( ( SV57
= ( singleton @ SV31 ) )
= $false )
| ( ( ! [SY121: $i] :
~ ( ~ ( ~ ( in @ SY121 @ SV57 )
| ( SY121 = SV31 ) )
| ~ ( ( SY121 != SV31 )
| ( in @ SY121 @ SV57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(421,plain,
! [SV31: $i,SV57: $i] :
( ( ( ! [SY122: $i] :
~ ( ~ ( ~ ( in @ SY122 @ SV57 )
| ( SY122 = SV31 ) )
| ~ ( ( SY122 != SV31 )
| ( in @ SY122 @ SV57 ) ) ) )
= $false )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(422,plain,
! [SV58: $i,SV33: $i] :
( ( ( ( set_difference @ SV33 @ SV58 )
= empty_set )
= $false )
| ( ( subset @ SV33 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(423,plain,
! [SV58: $i,SV33: $i] :
( ( ( subset @ SV33 @ SV58 )
= $false )
| ( ( ( set_difference @ SV33 @ SV58 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(424,plain,
! [SV67: $i,SV59: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV59 ) )
= $true )
| ( ( ~ ( subset @ SV34 @ SV67 ) )
= $true )
| ( ( subset @ SV34 @ ( set_intersection2 @ SV59 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(425,plain,
! [SV68: $i,SV60: $i,SV35: $i] :
( ( ( ~ ( subset @ SV35 @ SV60 ) )
= $true )
| ( ( ~ ( subset @ SV68 @ SV60 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV35 @ SV68 ) @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(426,plain,
! [SV40: $i,SV11: $i] :
( ( ( SV11 = empty_set )
= $true )
| ( ( SV11
= ( singleton @ SV40 ) )
= $true )
| ( ( subset @ SV11 @ ( singleton @ SV40 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(427,plain,
! [SV40: $i,SV11: $i] :
( ( ( SV11 = empty_set )
= $false )
| ( ( subset @ SV11 @ ( singleton @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(428,plain,
! [SV40: $i,SV11: $i] :
( ( ( SV11
= ( singleton @ SV40 ) )
= $false )
| ( ( subset @ SV11 @ ( singleton @ SV40 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(429,plain,
! [SV13: $i,SV69: $i] :
( ( ( in @ SV69 @ SV13 )
= $false )
| ( ( SV13 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(430,plain,
! [SV13: $i] :
( ( ( in @ ( sK3_SY81 @ SV13 ) @ SV13 )
= $true )
| ( ( SV13 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(431,plain,
! [SV64: $i,SV47: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV47 )
= $false )
| ( ( ~ ( disjoint @ SV47 @ SV64 ) )
= $true )
| ( ( disjoint @ SV20 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(432,plain,
! [SV49: $i,SV22: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ SV22 )
| ( in @ SV70 @ SV49 ) )
= $true )
| ( ( subset @ SV22 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(433,plain,
! [SV22: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK4_SY118 @ SV49 @ SV22 ) @ SV22 )
| ( in @ ( sK4_SY118 @ SV49 @ SV22 ) @ SV49 ) )
= $false )
| ( ( subset @ SV22 @ SV49 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[410]) ).
thf(434,plain,
! [SV65: $i,SV50: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV50 )
= $false )
| ( ( ~ ( subset @ SV50 @ SV65 ) )
= $true )
| ( ( subset @ SV23 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(435,plain,
! [SV51: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) )
= $false )
| ( ( proper_subset @ SV24 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(436,plain,
! [SV51: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV51 )
| ~ ( ( SV24 != SV51 ) ) )
= $true )
| ( ( proper_subset @ SV24 @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(437,plain,
! [SV54: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) )
= $false )
| ( ( SV28 = SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(438,plain,
! [SV54: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV54 )
| ~ ( subset @ SV54 @ SV28 ) )
= $true )
| ( ( SV28 = SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(439,plain,
! [SV31: $i,SV57: $i,SV71: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV71 @ SV57 )
| ( SV71 = SV31 ) )
| ~ ( ( SV71 != SV31 )
| ( in @ SV71 @ SV57 ) ) ) )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(440,plain,
! [SV57: $i,SV31: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 )
| ( ( sK5_SY122 @ SV31 @ SV57 )
= SV31 ) )
| ~ ( ( ( sK5_SY122 @ SV31 @ SV57 )
!= SV31 )
| ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 ) ) ) )
= $false )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[421]) ).
thf(441,plain,
! [SV67: $i,SV59: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV59 )
= $false )
| ( ( ~ ( subset @ SV34 @ SV67 ) )
= $true )
| ( ( subset @ SV34 @ ( set_intersection2 @ SV59 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(442,plain,
! [SV68: $i,SV60: $i,SV35: $i] :
( ( ( subset @ SV35 @ SV60 )
= $false )
| ( ( ~ ( subset @ SV68 @ SV60 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV35 @ SV68 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(443,plain,
! [SV20: $i,SV64: $i,SV47: $i] :
( ( ( disjoint @ SV47 @ SV64 )
= $false )
| ( ( subset @ SV20 @ SV47 )
= $false )
| ( ( disjoint @ SV20 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(444,plain,
! [SV49: $i,SV22: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ SV22 ) )
= $true )
| ( ( in @ SV70 @ SV49 )
= $true )
| ( ( subset @ SV22 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(445,plain,
! [SV22: $i,SV49: $i] :
( ( ( ~ ( in @ ( sK4_SY118 @ SV49 @ SV22 ) @ SV22 ) )
= $false )
| ( ( subset @ SV22 @ SV49 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(446,plain,
! [SV22: $i,SV49: $i] :
( ( ( in @ ( sK4_SY118 @ SV49 @ SV22 ) @ SV49 )
= $false )
| ( ( subset @ SV22 @ SV49 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(447,plain,
! [SV23: $i,SV65: $i,SV50: $i] :
( ( ( subset @ SV50 @ SV65 )
= $false )
| ( ( subset @ SV23 @ SV50 )
= $false )
| ( ( subset @ SV23 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(448,plain,
! [SV51: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV51 ) )
= $false )
| ( ( proper_subset @ SV24 @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(449,plain,
! [SV51: $i,SV24: $i] :
( ( ( ~ ( ( SV24 != SV51 ) ) )
= $false )
| ( ( proper_subset @ SV24 @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(450,plain,
! [SV51: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV51 ) )
= $true )
| ( ( ~ ( ( SV24 != SV51 ) ) )
= $true )
| ( ( proper_subset @ SV24 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(451,plain,
! [SV54: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV54 ) )
= $false )
| ( ( SV28 = SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(452,plain,
! [SV28: $i,SV54: $i] :
( ( ( ~ ( subset @ SV54 @ SV28 ) )
= $false )
| ( ( SV28 = SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(453,plain,
! [SV54: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV54 ) )
= $true )
| ( ( ~ ( subset @ SV54 @ SV28 ) )
= $true )
| ( ( SV28 = SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(454,plain,
! [SV31: $i,SV57: $i,SV71: $i] :
( ( ( ~ ( ~ ( in @ SV71 @ SV57 )
| ( SV71 = SV31 ) )
| ~ ( ( SV71 != SV31 )
| ( in @ SV71 @ SV57 ) ) )
= $false )
| ( ( SV57
= ( singleton @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(455,plain,
! [SV57: $i,SV31: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 )
| ( ( sK5_SY122 @ SV31 @ SV57 )
= SV31 ) )
| ~ ( ( ( sK5_SY122 @ SV31 @ SV57 )
!= SV31 )
| ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 ) ) )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(456,plain,
! [SV59: $i,SV67: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV67 )
= $false )
| ( ( subset @ SV34 @ SV59 )
= $false )
| ( ( subset @ SV34 @ ( set_intersection2 @ SV59 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(457,plain,
! [SV35: $i,SV60: $i,SV68: $i] :
( ( ( subset @ SV68 @ SV60 )
= $false )
| ( ( subset @ SV35 @ SV60 )
= $false )
| ( ( subset @ ( set_union2 @ SV35 @ SV68 ) @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(458,plain,
! [SV49: $i,SV22: $i,SV70: $i] :
( ( ( in @ SV70 @ SV22 )
= $false )
| ( ( in @ SV70 @ SV49 )
= $true )
| ( ( subset @ SV22 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(459,plain,
! [SV22: $i,SV49: $i] :
( ( ( in @ ( sK4_SY118 @ SV49 @ SV22 ) @ SV22 )
= $true )
| ( ( subset @ SV22 @ SV49 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(460,plain,
! [SV51: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV51 )
= $true )
| ( ( proper_subset @ SV24 @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(461,plain,
! [SV51: $i,SV24: $i] :
( ( ( SV24 != SV51 )
= $true )
| ( ( proper_subset @ SV24 @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(462,plain,
! [SV51: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV51 )
= $false )
| ( ( ~ ( ( SV24 != SV51 ) ) )
= $true )
| ( ( proper_subset @ SV24 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(463,plain,
! [SV54: $i,SV28: $i] :
( ( ( subset @ SV28 @ SV54 )
= $true )
| ( ( SV28 = SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(464,plain,
! [SV28: $i,SV54: $i] :
( ( ( subset @ SV54 @ SV28 )
= $true )
| ( ( SV28 = SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(465,plain,
! [SV54: $i,SV28: $i] :
( ( ( subset @ SV28 @ SV54 )
= $false )
| ( ( ~ ( subset @ SV54 @ SV28 ) )
= $true )
| ( ( SV28 = SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(466,plain,
! [SV31: $i,SV57: $i,SV71: $i] :
( ( ( ~ ( ~ ( in @ SV71 @ SV57 )
| ( SV71 = SV31 ) ) )
= $false )
| ( ( SV57
= ( singleton @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(467,plain,
! [SV57: $i,SV31: $i,SV71: $i] :
( ( ( ~ ( ( SV71 != SV31 )
| ( in @ SV71 @ SV57 ) ) )
= $false )
| ( ( SV57
= ( singleton @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(468,plain,
! [SV57: $i,SV31: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 )
| ( ( sK5_SY122 @ SV31 @ SV57 )
= SV31 ) ) )
= $true )
| ( ( ~ ( ( ( sK5_SY122 @ SV31 @ SV57 )
!= SV31 )
| ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 ) ) )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(469,plain,
! [SV51: $i,SV24: $i] :
( ( ( SV24 = SV51 )
= $false )
| ( ( proper_subset @ SV24 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(470,plain,
! [SV51: $i,SV24: $i] :
( ( ( SV24 != SV51 )
= $false )
| ( ( subset @ SV24 @ SV51 )
= $false )
| ( ( proper_subset @ SV24 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(471,plain,
! [SV28: $i,SV54: $i] :
( ( ( subset @ SV54 @ SV28 )
= $false )
| ( ( subset @ SV28 @ SV54 )
= $false )
| ( ( SV28 = SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(472,plain,
! [SV31: $i,SV57: $i,SV71: $i] :
( ( ( ~ ( in @ SV71 @ SV57 )
| ( SV71 = SV31 ) )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(473,plain,
! [SV57: $i,SV31: $i,SV71: $i] :
( ( ( ( SV71 != SV31 )
| ( in @ SV71 @ SV57 ) )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(474,plain,
! [SV57: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 )
| ( ( sK5_SY122 @ SV31 @ SV57 )
= SV31 ) )
= $false )
| ( ( ~ ( ( ( sK5_SY122 @ SV31 @ SV57 )
!= SV31 )
| ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 ) ) )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(475,plain,
! [SV51: $i,SV24: $i] :
( ( ( SV24 = SV51 )
= $true )
| ( ( subset @ SV24 @ SV51 )
= $false )
| ( ( proper_subset @ SV24 @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(476,plain,
! [SV31: $i,SV57: $i,SV71: $i] :
( ( ( ~ ( in @ SV71 @ SV57 ) )
= $true )
| ( ( SV71 = SV31 )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(477,plain,
! [SV57: $i,SV31: $i,SV71: $i] :
( ( ( SV71 != SV31 )
= $true )
| ( ( in @ SV71 @ SV57 )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(478,plain,
! [SV57: $i,SV31: $i] :
( ( ( ~ ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 ) )
= $false )
| ( ( ~ ( ( ( sK5_SY122 @ SV31 @ SV57 )
!= SV31 )
| ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 ) ) )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(479,plain,
! [SV57: $i,SV31: $i] :
( ( ( ( sK5_SY122 @ SV31 @ SV57 )
= SV31 )
= $false )
| ( ( ~ ( ( ( sK5_SY122 @ SV31 @ SV57 )
!= SV31 )
| ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 ) ) )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(480,plain,
! [SV31: $i,SV57: $i,SV71: $i] :
( ( ( in @ SV71 @ SV57 )
= $false )
| ( ( SV71 = SV31 )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(481,plain,
! [SV57: $i,SV31: $i,SV71: $i] :
( ( ( SV71 = SV31 )
= $false )
| ( ( in @ SV71 @ SV57 )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(482,plain,
! [SV57: $i,SV31: $i] :
( ( ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 )
= $true )
| ( ( ~ ( ( ( sK5_SY122 @ SV31 @ SV57 )
!= SV31 )
| ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 ) ) )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(483,plain,
! [SV57: $i,SV31: $i] :
( ( ( ( ( sK5_SY122 @ SV31 @ SV57 )
!= SV31 )
| ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 ) )
= $false )
| ( ( ( sK5_SY122 @ SV31 @ SV57 )
= SV31 )
= $false )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(484,plain,
! [SV57: $i,SV31: $i] :
( ( ( ( ( sK5_SY122 @ SV31 @ SV57 )
!= SV31 )
| ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 ) )
= $false )
| ( ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(485,plain,
! [SV57: $i,SV31: $i] :
( ( ( ( sK5_SY122 @ SV31 @ SV57 )
!= SV31 )
= $false )
| ( ( ( sK5_SY122 @ SV31 @ SV57 )
= SV31 )
= $false )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(486,plain,
! [SV57: $i,SV31: $i] :
( ( ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 )
= $false )
| ( ( ( sK5_SY122 @ SV31 @ SV57 )
= SV31 )
= $false )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(487,plain,
! [SV57: $i,SV31: $i] :
( ( ( ( sK5_SY122 @ SV31 @ SV57 )
!= SV31 )
= $false )
| ( ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(488,plain,
! [SV57: $i,SV31: $i] :
( ( ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 )
= $false )
| ( ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(489,plain,
! [SV57: $i,SV31: $i] :
( ( ( ( sK5_SY122 @ SV31 @ SV57 )
= SV31 )
= $true )
| ( ( ( sK5_SY122 @ SV31 @ SV57 )
= SV31 )
= $false )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(490,plain,
! [SV57: $i,SV31: $i] :
( ( ( ( sK5_SY122 @ SV31 @ SV57 )
= SV31 )
= $true )
| ( ( in @ ( sK5_SY122 @ SV31 @ SV57 ) @ SV57 )
= $true )
| ( ( SV57
= ( singleton @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(491,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[154,490,489,488,486,481,480,475,471,469,464,463,460,459,458,457,456,447,446,443,430,429,428,427,426,423,422,419,418,415,414,407,406,403,365,356,355,354,340,327,325,311,304,297,296,295,269,259,258,257,256,229,228,227,226,223,221,186,185,184,183,182,181,180,179,178,177,176]) ).
thf(492,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(493,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(494,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(496,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(497,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(498,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(499,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(500,plain,
( ( ( powerset @ empty_set )
= ( singleton @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(501,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(502,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(503,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(504,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(505,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(506,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(507,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(508,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(509,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(510,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(511,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(512,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(513,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(514,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(515,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(516,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(517,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(518,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(519,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(520,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(521,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(522,plain,
$true = $true,
inference(copy,[status(thm)],[109]) ).
thf(523,plain,
$true = $true,
inference(copy,[status(thm)],[108]) ).
thf(524,plain,
$true = $true,
inference(copy,[status(thm)],[107]) ).
thf(525,plain,
$true = $true,
inference(copy,[status(thm)],[106]) ).
thf(526,plain,
$true = $true,
inference(copy,[status(thm)],[105]) ).
thf(527,plain,
$true = $true,
inference(copy,[status(thm)],[104]) ).
thf(528,plain,
$true = $true,
inference(copy,[status(thm)],[103]) ).
thf(529,plain,
$true = $true,
inference(copy,[status(thm)],[102]) ).
thf(530,plain,
$true = $true,
inference(copy,[status(thm)],[101]) ).
thf(531,plain,
$true = $true,
inference(copy,[status(thm)],[100]) ).
thf(532,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(533,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(534,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(535,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(536,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(537,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(538,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(539,plain,
( ( ~ ( ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) )
=> ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(540,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( disjoint @ SX1 @ SX2 ) )
| ( disjoint @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(541,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(542,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_intersection2 @ SX0 @ SX2 ) @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(543,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(544,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(545,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_difference @ SX0 @ SX2 ) @ ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(546,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(547,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(548,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(549,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ ( singleton @ SX1 ) )
| ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ~ ( ~ ( ( SX0 = empty_set )
| ( SX0
= ( singleton @ SX1 ) ) )
| ( subset @ SX0 @ ( singleton @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(550,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(551,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(552,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(553,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( proper_subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(554,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX0 @ SX2 ) )
| ( subset @ SX0 @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(555,plain,
( ( ~ ( ~ ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) )
| ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(556,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499]) ).
thf(557,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(558,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(559,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SX0 ) @ SX1 )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( subset @ ( singleton @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(560,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX1 ) )
| ( subset @ ( set_union2 @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(561,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(562,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(563,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(564,plain,
( ( ! [SX0: $i] :
( ( singleton @ SX0 )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(565,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( proper_subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( proper_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(566,plain,
! [SV72: $i] :
( ( ! [SY125: $i] : ( subset @ ( set_intersection2 @ SV72 @ SY125 ) @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(567,plain,
! [SV73: $i] :
( ( subset @ empty_set @ SV73 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(568,plain,
! [SV74: $i] :
( ( ! [SY126: $i] : ( subset @ ( set_difference @ SV74 @ SY126 ) @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(569,plain,
! [SV75: $i] :
( ( ( unordered_pair @ SV75 @ SV75 )
= ( singleton @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(570,plain,
! [SV76: $i] :
( ( ! [SY127: $i] : ( subset @ SV76 @ ( set_union2 @ SV76 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(571,plain,
! [SV77: $i] :
( ( ! [SY128: $i] : ( subset @ SV77 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(572,plain,
! [SV78: $i] :
( ( ( set_union2 @ SV78 @ empty_set )
= SV78 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(573,plain,
! [SV79: $i] :
( ( ( set_intersection2 @ SV79 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(574,plain,
! [SV80: $i] :
( ( ( set_difference @ SV80 @ empty_set )
= SV80 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(575,plain,
! [SV81: $i] :
( ( ( set_difference @ empty_set @ SV81 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(576,plain,
! [SV82: $i] :
( ( ! [SY129: $i,SY130: $i] :
( ~ ~ ( ~ ( subset @ SV82 @ SY129 )
| ~ ( disjoint @ SY129 @ SY130 ) )
| ( disjoint @ SV82 @ SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(577,plain,
! [SV83: $i] :
( ( ! [SY131: $i] :
~ ( ~ ( ( ( set_difference @ SV83 @ SY131 )
!= empty_set )
| ( subset @ SV83 @ SY131 ) )
| ~ ( ~ ( subset @ SV83 @ SY131 )
| ( ( set_difference @ SV83 @ SY131 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(578,plain,
! [SV84: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ~ ( subset @ SV84 @ SY132 )
| ( subset @ ( set_intersection2 @ SV84 @ SY133 ) @ ( set_intersection2 @ SY132 @ SY133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(579,plain,
! [SV85: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ( ( singleton @ SV85 )
!= ( unordered_pair @ SY134 @ SY135 ) )
| ( SV85 = SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(580,plain,
! [SV86: $i] :
( ( ! [SY136: $i] :
~ ( ~ ( ( ( set_difference @ SV86 @ SY136 )
!= empty_set )
| ( subset @ SV86 @ SY136 ) )
| ~ ( ~ ( subset @ SV86 @ SY136 )
| ( ( set_difference @ SV86 @ SY136 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(581,plain,
! [SV87: $i] :
( ( ! [SY137: $i,SY138: $i] :
( ~ ( subset @ SV87 @ SY137 )
| ( subset @ ( set_difference @ SV87 @ SY138 ) @ ( set_difference @ SY137 @ SY138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(582,plain,
! [SV88: $i] :
( ( ! [SY139: $i] :
~ ( ~ ( ~ ( subset @ SV88 @ SY139 )
| ! [SY140: $i] :
( ~ ( in @ SY140 @ SV88 )
| ( in @ SY140 @ SY139 ) ) )
| ~ ( ~ ! [SY141: $i] :
( ~ ( in @ SY141 @ SV88 )
| ( in @ SY141 @ SY139 ) )
| ( subset @ SV88 @ SY139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(583,plain,
! [SV89: $i] :
( ( ~ ( subset @ SV89 @ empty_set )
| ( SV89 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(584,plain,
! [SV90: $i] :
( ( ~ ( empty @ SV90 )
| ( SV90 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(585,plain,
! [SV91: $i] :
( ( ! [SY142: $i] :
~ ( ~ ( ~ ( subset @ SV91 @ ( singleton @ SY142 ) )
| ( SV91 = empty_set )
| ( SV91
= ( singleton @ SY142 ) ) )
| ~ ( ~ ( ( SV91 = empty_set )
| ( SV91
= ( singleton @ SY142 ) ) )
| ( subset @ SV91 @ ( singleton @ SY142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(586,plain,
! [SV92: $i] :
( ( ! [SY143: $i] :
~ ( ~ ( ( SV92 != SY143 )
| ~ ( ~ ( subset @ SV92 @ SY143 )
| ~ ( subset @ SY143 @ SV92 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV92 @ SY143 )
| ~ ( subset @ SY143 @ SV92 ) )
| ( SV92 = SY143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(587,plain,
! [SV93: $i] :
( ( ! [SY144: $i] :
~ ( ~ ( ( SY144
!= ( singleton @ SV93 ) )
| ! [SY145: $i] :
~ ( ~ ( ~ ( in @ SY145 @ SY144 )
| ( SY145 = SV93 ) )
| ~ ( ( SY145 != SV93 )
| ( in @ SY145 @ SY144 ) ) ) )
| ~ ( ~ ! [SY146: $i] :
~ ( ~ ( ~ ( in @ SY146 @ SY144 )
| ( SY146 = SV93 ) )
| ~ ( ( SY146 != SV93 )
| ( in @ SY146 @ SY144 ) ) )
| ( SY144
= ( singleton @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(588,plain,
! [SV94: $i] :
( ( ! [SY147: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV94 ) @ SY147 )
| ( in @ SV94 @ SY147 ) )
| ~ ( ~ ( in @ SV94 @ SY147 )
| ( subset @ ( singleton @ SV94 ) @ SY147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(589,plain,
! [SV95: $i] :
( ( ! [SY148: $i] :
~ ~ ( ~ ( subset @ SV95 @ SY148 )
| ~ ( proper_subset @ SY148 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(590,plain,
! [SV96: $i] :
( ( ! [SY149: $i,SY150: $i] :
( ~ ~ ( ~ ( subset @ SV96 @ SY149 )
| ~ ( subset @ SV96 @ SY150 ) )
| ( subset @ SV96 @ ( set_intersection2 @ SY149 @ SY150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(591,plain,
( ( ~ ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) )
| ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(592,plain,
! [SV97: $i] :
( ( ! [SY151: $i,SY152: $i] :
( ~ ~ ( ~ ( subset @ SV97 @ SY151 )
| ~ ( subset @ SY151 @ SY152 ) )
| ( subset @ SV97 @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(593,plain,
! [SV98: $i] :
( ( ~ ( ~ ( ( SV98 != empty_set )
| ! [SY153: $i] :
~ ( in @ SY153 @ SV98 ) )
| ~ ( ~ ! [SY154: $i] :
~ ( in @ SY154 @ SV98 )
| ( SV98 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(594,plain,
! [SV99: $i] :
( ( ! [SY155: $i,SY156: $i] :
( ( ( singleton @ SV99 )
!= ( unordered_pair @ SY155 @ SY156 ) )
| ( SY155 = SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(595,plain,
! [SV100: $i] :
( ( ! [SY157: $i] :
~ ( ~ ( ~ ( subset @ ( singleton @ SV100 ) @ SY157 )
| ( in @ SV100 @ SY157 ) )
| ~ ( ~ ( in @ SV100 @ SY157 )
| ( subset @ ( singleton @ SV100 ) @ SY157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(596,plain,
! [SV101: $i] :
( ( ! [SY158: $i,SY159: $i] :
( ~ ~ ( ~ ( subset @ SV101 @ SY158 )
| ~ ( subset @ SY159 @ SY158 ) )
| ( subset @ ( set_union2 @ SV101 @ SY159 ) @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(597,plain,
! [SV102: $i] :
( ( ! [SY160: $i] :
( ~ ( subset @ SV102 @ SY160 )
| ( ( set_intersection2 @ SV102 @ SY160 )
= SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(598,plain,
! [SV103: $i] :
( ( ! [SY161: $i] :
( ~ ( subset @ ( singleton @ SV103 ) @ ( singleton @ SY161 ) )
| ( SV103 = SY161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(599,plain,
! [SV104: $i] :
( ( ! [SY162: $i] :
( ~ ( subset @ SV104 @ SY162 )
| ( ( set_union2 @ SV104 @ SY162 )
= SY162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(600,plain,
! [SV105: $i] :
( ( ( singleton @ SV105 )
!= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(601,plain,
! [SV106: $i] :
( ( ! [SY163: $i] :
~ ( ~ ( ~ ( proper_subset @ SV106 @ SY163 )
| ~ ( ~ ( subset @ SV106 @ SY163 )
| ~ ( ( SV106 != SY163 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV106 @ SY163 )
| ~ ( ( SV106 != SY163 ) ) )
| ( proper_subset @ SV106 @ SY163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(602,plain,
! [SV107: $i,SV72: $i] :
( ( subset @ ( set_intersection2 @ SV72 @ SV107 ) @ SV72 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(603,plain,
! [SV108: $i,SV74: $i] :
( ( subset @ ( set_difference @ SV74 @ SV108 ) @ SV74 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(604,plain,
! [SV109: $i,SV76: $i] :
( ( subset @ SV76 @ ( set_union2 @ SV76 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(605,plain,
! [SV77: $i] :
( ( subset @ SV77 @ SV77 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(606,plain,
! [SV111: $i,SV82: $i] :
( ( ! [SY164: $i] :
( ~ ~ ( ~ ( subset @ SV82 @ SV111 )
| ~ ( disjoint @ SV111 @ SY164 ) )
| ( disjoint @ SV82 @ SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(607,plain,
! [SV112: $i,SV83: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV83 @ SV112 )
!= empty_set )
| ( subset @ SV83 @ SV112 ) )
| ~ ( ~ ( subset @ SV83 @ SV112 )
| ( ( set_difference @ SV83 @ SV112 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(608,plain,
! [SV113: $i,SV84: $i] :
( ( ! [SY165: $i] :
( ~ ( subset @ SV84 @ SV113 )
| ( subset @ ( set_intersection2 @ SV84 @ SY165 ) @ ( set_intersection2 @ SV113 @ SY165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(609,plain,
! [SV114: $i,SV85: $i] :
( ( ! [SY166: $i] :
( ( ( singleton @ SV85 )
!= ( unordered_pair @ SV114 @ SY166 ) )
| ( SV85 = SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(610,plain,
! [SV115: $i,SV86: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV86 @ SV115 )
!= empty_set )
| ( subset @ SV86 @ SV115 ) )
| ~ ( ~ ( subset @ SV86 @ SV115 )
| ( ( set_difference @ SV86 @ SV115 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(611,plain,
! [SV116: $i,SV87: $i] :
( ( ! [SY167: $i] :
( ~ ( subset @ SV87 @ SV116 )
| ( subset @ ( set_difference @ SV87 @ SY167 ) @ ( set_difference @ SV116 @ SY167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(612,plain,
! [SV117: $i,SV88: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV88 @ SV117 )
| ! [SY168: $i] :
( ~ ( in @ SY168 @ SV88 )
| ( in @ SY168 @ SV117 ) ) )
| ~ ( ~ ! [SY169: $i] :
( ~ ( in @ SY169 @ SV88 )
| ( in @ SY169 @ SV117 ) )
| ( subset @ SV88 @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(613,plain,
! [SV89: $i] :
( ( ( ~ ( subset @ SV89 @ empty_set ) )
= $true )
| ( ( SV89 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(614,plain,
! [SV90: $i] :
( ( ( ~ ( empty @ SV90 ) )
= $true )
| ( ( SV90 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(615,plain,
! [SV118: $i,SV91: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV91 @ ( singleton @ SV118 ) )
| ( SV91 = empty_set )
| ( SV91
= ( singleton @ SV118 ) ) )
| ~ ( ~ ( ( SV91 = empty_set )
| ( SV91
= ( singleton @ SV118 ) ) )
| ( subset @ SV91 @ ( singleton @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(616,plain,
! [SV119: $i,SV92: $i] :
( ( ~ ( ~ ( ( SV92 != SV119 )
| ~ ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) )
| ( SV92 = SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(617,plain,
! [SV93: $i,SV120: $i] :
( ( ~ ( ~ ( ( SV120
!= ( singleton @ SV93 ) )
| ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV120 )
| ( SY170 = SV93 ) )
| ~ ( ( SY170 != SV93 )
| ( in @ SY170 @ SV120 ) ) ) )
| ~ ( ~ ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV120 )
| ( SY171 = SV93 ) )
| ~ ( ( SY171 != SV93 )
| ( in @ SY171 @ SV120 ) ) )
| ( SV120
= ( singleton @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(618,plain,
! [SV121: $i,SV94: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV94 ) @ SV121 )
| ( in @ SV94 @ SV121 ) )
| ~ ( ~ ( in @ SV94 @ SV121 )
| ( subset @ ( singleton @ SV94 ) @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(619,plain,
! [SV122: $i,SV95: $i] :
( ( ~ ~ ( ~ ( subset @ SV95 @ SV122 )
| ~ ( proper_subset @ SV122 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(620,plain,
! [SV123: $i,SV96: $i] :
( ( ! [SY172: $i] :
( ~ ~ ( ~ ( subset @ SV96 @ SV123 )
| ~ ( subset @ SV96 @ SY172 ) )
| ( subset @ SV96 @ ( set_intersection2 @ SV123 @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(621,plain,
( ( ~ ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[591]) ).
thf(622,plain,
( ( subset @ sK1_A @ ( singleton @ sK2_SY73 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[591]) ).
thf(623,plain,
! [SV124: $i,SV97: $i] :
( ( ! [SY173: $i] :
( ~ ~ ( ~ ( subset @ SV97 @ SV124 )
| ~ ( subset @ SV124 @ SY173 ) )
| ( subset @ SV97 @ SY173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(624,plain,
! [SV98: $i] :
( ( ~ ( ( SV98 != empty_set )
| ! [SY153: $i] :
~ ( in @ SY153 @ SV98 ) )
| ~ ( ~ ! [SY154: $i] :
~ ( in @ SY154 @ SV98 )
| ( SV98 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(625,plain,
! [SV125: $i,SV99: $i] :
( ( ! [SY174: $i] :
( ( ( singleton @ SV99 )
!= ( unordered_pair @ SV125 @ SY174 ) )
| ( SV125 = SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(626,plain,
! [SV126: $i,SV100: $i] :
( ( ~ ( ~ ( ~ ( subset @ ( singleton @ SV100 ) @ SV126 )
| ( in @ SV100 @ SV126 ) )
| ~ ( ~ ( in @ SV100 @ SV126 )
| ( subset @ ( singleton @ SV100 ) @ SV126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(627,plain,
! [SV127: $i,SV101: $i] :
( ( ! [SY175: $i] :
( ~ ~ ( ~ ( subset @ SV101 @ SV127 )
| ~ ( subset @ SY175 @ SV127 ) )
| ( subset @ ( set_union2 @ SV101 @ SY175 ) @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(628,plain,
! [SV128: $i,SV102: $i] :
( ( ~ ( subset @ SV102 @ SV128 )
| ( ( set_intersection2 @ SV102 @ SV128 )
= SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(629,plain,
! [SV129: $i,SV103: $i] :
( ( ~ ( subset @ ( singleton @ SV103 ) @ ( singleton @ SV129 ) )
| ( SV103 = SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(630,plain,
! [SV130: $i,SV104: $i] :
( ( ~ ( subset @ SV104 @ SV130 )
| ( ( set_union2 @ SV104 @ SV130 )
= SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(631,plain,
! [SV105: $i] :
( ( ( singleton @ SV105 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(632,plain,
! [SV131: $i,SV106: $i] :
( ( ~ ( ~ ( ~ ( proper_subset @ SV106 @ SV131 )
| ~ ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) )
| ( proper_subset @ SV106 @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(633,plain,
! [SV132: $i,SV111: $i,SV82: $i] :
( ( ~ ~ ( ~ ( subset @ SV82 @ SV111 )
| ~ ( disjoint @ SV111 @ SV132 ) )
| ( disjoint @ SV82 @ SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(634,plain,
! [SV112: $i,SV83: $i] :
( ( ~ ( ( ( set_difference @ SV83 @ SV112 )
!= empty_set )
| ( subset @ SV83 @ SV112 ) )
| ~ ( ~ ( subset @ SV83 @ SV112 )
| ( ( set_difference @ SV83 @ SV112 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(635,plain,
! [SV133: $i,SV113: $i,SV84: $i] :
( ( ~ ( subset @ SV84 @ SV113 )
| ( subset @ ( set_intersection2 @ SV84 @ SV133 ) @ ( set_intersection2 @ SV113 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(636,plain,
! [SV134: $i,SV114: $i,SV85: $i] :
( ( ( ( singleton @ SV85 )
!= ( unordered_pair @ SV114 @ SV134 ) )
| ( SV85 = SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(637,plain,
! [SV115: $i,SV86: $i] :
( ( ~ ( ( ( set_difference @ SV86 @ SV115 )
!= empty_set )
| ( subset @ SV86 @ SV115 ) )
| ~ ( ~ ( subset @ SV86 @ SV115 )
| ( ( set_difference @ SV86 @ SV115 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(638,plain,
! [SV135: $i,SV116: $i,SV87: $i] :
( ( ~ ( subset @ SV87 @ SV116 )
| ( subset @ ( set_difference @ SV87 @ SV135 ) @ ( set_difference @ SV116 @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(639,plain,
! [SV117: $i,SV88: $i] :
( ( ~ ( ~ ( subset @ SV88 @ SV117 )
| ! [SY168: $i] :
( ~ ( in @ SY168 @ SV88 )
| ( in @ SY168 @ SV117 ) ) )
| ~ ( ~ ! [SY169: $i] :
( ~ ( in @ SY169 @ SV88 )
| ( in @ SY169 @ SV117 ) )
| ( subset @ SV88 @ SV117 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(640,plain,
! [SV89: $i] :
( ( ( subset @ SV89 @ empty_set )
= $false )
| ( ( SV89 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(641,plain,
! [SV90: $i] :
( ( ( empty @ SV90 )
= $false )
| ( ( SV90 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(642,plain,
! [SV118: $i,SV91: $i] :
( ( ~ ( ~ ( subset @ SV91 @ ( singleton @ SV118 ) )
| ( SV91 = empty_set )
| ( SV91
= ( singleton @ SV118 ) ) )
| ~ ( ~ ( ( SV91 = empty_set )
| ( SV91
= ( singleton @ SV118 ) ) )
| ( subset @ SV91 @ ( singleton @ SV118 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(643,plain,
! [SV119: $i,SV92: $i] :
( ( ~ ( ( SV92 != SV119 )
| ~ ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) )
| ( SV92 = SV119 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(644,plain,
! [SV93: $i,SV120: $i] :
( ( ~ ( ( SV120
!= ( singleton @ SV93 ) )
| ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV120 )
| ( SY170 = SV93 ) )
| ~ ( ( SY170 != SV93 )
| ( in @ SY170 @ SV120 ) ) ) )
| ~ ( ~ ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV120 )
| ( SY171 = SV93 ) )
| ~ ( ( SY171 != SV93 )
| ( in @ SY171 @ SV120 ) ) )
| ( SV120
= ( singleton @ SV93 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(645,plain,
! [SV121: $i,SV94: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV94 ) @ SV121 )
| ( in @ SV94 @ SV121 ) )
| ~ ( ~ ( in @ SV94 @ SV121 )
| ( subset @ ( singleton @ SV94 ) @ SV121 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(646,plain,
! [SV122: $i,SV95: $i] :
( ( ~ ( ~ ( subset @ SV95 @ SV122 )
| ~ ( proper_subset @ SV122 @ SV95 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(647,plain,
! [SV136: $i,SV123: $i,SV96: $i] :
( ( ~ ~ ( ~ ( subset @ SV96 @ SV123 )
| ~ ( subset @ SV96 @ SV136 ) )
| ( subset @ SV96 @ ( set_intersection2 @ SV123 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(648,plain,
( ( ( sK1_A = empty_set )
| ( sK1_A
= ( singleton @ sK2_SY73 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(649,plain,
! [SV137: $i,SV124: $i,SV97: $i] :
( ( ~ ~ ( ~ ( subset @ SV97 @ SV124 )
| ~ ( subset @ SV124 @ SV137 ) )
| ( subset @ SV97 @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(650,plain,
! [SV98: $i] :
( ( ~ ( ( SV98 != empty_set )
| ! [SY153: $i] :
~ ( in @ SY153 @ SV98 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(651,plain,
! [SV98: $i] :
( ( ~ ( ~ ! [SY154: $i] :
~ ( in @ SY154 @ SV98 )
| ( SV98 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[624]) ).
thf(652,plain,
! [SV138: $i,SV125: $i,SV99: $i] :
( ( ( ( singleton @ SV99 )
!= ( unordered_pair @ SV125 @ SV138 ) )
| ( SV125 = SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(653,plain,
! [SV126: $i,SV100: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV100 ) @ SV126 )
| ( in @ SV100 @ SV126 ) )
| ~ ( ~ ( in @ SV100 @ SV126 )
| ( subset @ ( singleton @ SV100 ) @ SV126 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(654,plain,
! [SV139: $i,SV127: $i,SV101: $i] :
( ( ~ ~ ( ~ ( subset @ SV101 @ SV127 )
| ~ ( subset @ SV139 @ SV127 ) )
| ( subset @ ( set_union2 @ SV101 @ SV139 ) @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(655,plain,
! [SV128: $i,SV102: $i] :
( ( ( ~ ( subset @ SV102 @ SV128 ) )
= $true )
| ( ( ( set_intersection2 @ SV102 @ SV128 )
= SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(656,plain,
! [SV129: $i,SV103: $i] :
( ( ( ~ ( subset @ ( singleton @ SV103 ) @ ( singleton @ SV129 ) ) )
= $true )
| ( ( SV103 = SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(657,plain,
! [SV130: $i,SV104: $i] :
( ( ( ~ ( subset @ SV104 @ SV130 ) )
= $true )
| ( ( ( set_union2 @ SV104 @ SV130 )
= SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(658,plain,
! [SV131: $i,SV106: $i] :
( ( ~ ( ~ ( proper_subset @ SV106 @ SV131 )
| ~ ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) )
| ( proper_subset @ SV106 @ SV131 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(659,plain,
! [SV132: $i,SV111: $i,SV82: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV82 @ SV111 )
| ~ ( disjoint @ SV111 @ SV132 ) ) )
= $true )
| ( ( disjoint @ SV82 @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(660,plain,
! [SV112: $i,SV83: $i] :
( ( ~ ( ( ( set_difference @ SV83 @ SV112 )
!= empty_set )
| ( subset @ SV83 @ SV112 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(661,plain,
! [SV112: $i,SV83: $i] :
( ( ~ ( ~ ( subset @ SV83 @ SV112 )
| ( ( set_difference @ SV83 @ SV112 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[634]) ).
thf(662,plain,
! [SV133: $i,SV113: $i,SV84: $i] :
( ( ( ~ ( subset @ SV84 @ SV113 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV84 @ SV133 ) @ ( set_intersection2 @ SV113 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(663,plain,
! [SV134: $i,SV114: $i,SV85: $i] :
( ( ( ( singleton @ SV85 )
!= ( unordered_pair @ SV114 @ SV134 ) )
= $true )
| ( ( SV85 = SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(664,plain,
! [SV115: $i,SV86: $i] :
( ( ~ ( ( ( set_difference @ SV86 @ SV115 )
!= empty_set )
| ( subset @ SV86 @ SV115 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(665,plain,
! [SV115: $i,SV86: $i] :
( ( ~ ( ~ ( subset @ SV86 @ SV115 )
| ( ( set_difference @ SV86 @ SV115 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[637]) ).
thf(666,plain,
! [SV135: $i,SV116: $i,SV87: $i] :
( ( ( ~ ( subset @ SV87 @ SV116 ) )
= $true )
| ( ( subset @ ( set_difference @ SV87 @ SV135 ) @ ( set_difference @ SV116 @ SV135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(667,plain,
! [SV117: $i,SV88: $i] :
( ( ~ ( ~ ( subset @ SV88 @ SV117 )
| ! [SY168: $i] :
( ~ ( in @ SY168 @ SV88 )
| ( in @ SY168 @ SV117 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(668,plain,
! [SV117: $i,SV88: $i] :
( ( ~ ( ~ ! [SY169: $i] :
( ~ ( in @ SY169 @ SV88 )
| ( in @ SY169 @ SV117 ) )
| ( subset @ SV88 @ SV117 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(669,plain,
! [SV118: $i,SV91: $i] :
( ( ~ ( ~ ( subset @ SV91 @ ( singleton @ SV118 ) )
| ( SV91 = empty_set )
| ( SV91
= ( singleton @ SV118 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(670,plain,
! [SV118: $i,SV91: $i] :
( ( ~ ( ~ ( ( SV91 = empty_set )
| ( SV91
= ( singleton @ SV118 ) ) )
| ( subset @ SV91 @ ( singleton @ SV118 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[642]) ).
thf(671,plain,
! [SV119: $i,SV92: $i] :
( ( ~ ( ( SV92 != SV119 )
| ~ ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(672,plain,
! [SV119: $i,SV92: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) )
| ( SV92 = SV119 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[643]) ).
thf(673,plain,
! [SV93: $i,SV120: $i] :
( ( ~ ( ( SV120
!= ( singleton @ SV93 ) )
| ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV120 )
| ( SY170 = SV93 ) )
| ~ ( ( SY170 != SV93 )
| ( in @ SY170 @ SV120 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(674,plain,
! [SV93: $i,SV120: $i] :
( ( ~ ( ~ ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV120 )
| ( SY171 = SV93 ) )
| ~ ( ( SY171 != SV93 )
| ( in @ SY171 @ SV120 ) ) )
| ( SV120
= ( singleton @ SV93 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(675,plain,
! [SV121: $i,SV94: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV94 ) @ SV121 )
| ( in @ SV94 @ SV121 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(676,plain,
! [SV121: $i,SV94: $i] :
( ( ~ ( ~ ( in @ SV94 @ SV121 )
| ( subset @ ( singleton @ SV94 ) @ SV121 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[645]) ).
thf(677,plain,
! [SV122: $i,SV95: $i] :
( ( ~ ( subset @ SV95 @ SV122 )
| ~ ( proper_subset @ SV122 @ SV95 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[646]) ).
thf(678,plain,
! [SV136: $i,SV123: $i,SV96: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV96 @ SV123 )
| ~ ( subset @ SV96 @ SV136 ) ) )
= $true )
| ( ( subset @ SV96 @ ( set_intersection2 @ SV123 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(679,plain,
( ( ( sK1_A = empty_set )
= $true )
| ( ( sK1_A
= ( singleton @ sK2_SY73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(680,plain,
! [SV137: $i,SV124: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV97 @ SV124 )
| ~ ( subset @ SV124 @ SV137 ) ) )
= $true )
| ( ( subset @ SV97 @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(681,plain,
! [SV98: $i] :
( ( ( SV98 != empty_set )
| ! [SY153: $i] :
~ ( in @ SY153 @ SV98 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(682,plain,
! [SV98: $i] :
( ( ~ ! [SY154: $i] :
~ ( in @ SY154 @ SV98 )
| ( SV98 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(683,plain,
! [SV138: $i,SV125: $i,SV99: $i] :
( ( ( ( singleton @ SV99 )
!= ( unordered_pair @ SV125 @ SV138 ) )
= $true )
| ( ( SV125 = SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(684,plain,
! [SV126: $i,SV100: $i] :
( ( ~ ( ~ ( subset @ ( singleton @ SV100 ) @ SV126 )
| ( in @ SV100 @ SV126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(685,plain,
! [SV126: $i,SV100: $i] :
( ( ~ ( ~ ( in @ SV100 @ SV126 )
| ( subset @ ( singleton @ SV100 ) @ SV126 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(686,plain,
! [SV139: $i,SV127: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV101 @ SV127 )
| ~ ( subset @ SV139 @ SV127 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV101 @ SV139 ) @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(687,plain,
! [SV128: $i,SV102: $i] :
( ( ( subset @ SV102 @ SV128 )
= $false )
| ( ( ( set_intersection2 @ SV102 @ SV128 )
= SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(688,plain,
! [SV129: $i,SV103: $i] :
( ( ( subset @ ( singleton @ SV103 ) @ ( singleton @ SV129 ) )
= $false )
| ( ( SV103 = SV129 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(689,plain,
! [SV130: $i,SV104: $i] :
( ( ( subset @ SV104 @ SV130 )
= $false )
| ( ( ( set_union2 @ SV104 @ SV130 )
= SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(690,plain,
! [SV131: $i,SV106: $i] :
( ( ~ ( ~ ( proper_subset @ SV106 @ SV131 )
| ~ ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[658]) ).
thf(691,plain,
! [SV131: $i,SV106: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) )
| ( proper_subset @ SV106 @ SV131 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[658]) ).
thf(692,plain,
! [SV132: $i,SV111: $i,SV82: $i] :
( ( ( ~ ( ~ ( subset @ SV82 @ SV111 )
| ~ ( disjoint @ SV111 @ SV132 ) ) )
= $false )
| ( ( disjoint @ SV82 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(693,plain,
! [SV112: $i,SV83: $i] :
( ( ( ( set_difference @ SV83 @ SV112 )
!= empty_set )
| ( subset @ SV83 @ SV112 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[660]) ).
thf(694,plain,
! [SV112: $i,SV83: $i] :
( ( ~ ( subset @ SV83 @ SV112 )
| ( ( set_difference @ SV83 @ SV112 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[661]) ).
thf(695,plain,
! [SV133: $i,SV113: $i,SV84: $i] :
( ( ( subset @ SV84 @ SV113 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV84 @ SV133 ) @ ( set_intersection2 @ SV113 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(696,plain,
! [SV134: $i,SV114: $i,SV85: $i] :
( ( ( ( singleton @ SV85 )
= ( unordered_pair @ SV114 @ SV134 ) )
= $false )
| ( ( SV85 = SV114 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(697,plain,
! [SV115: $i,SV86: $i] :
( ( ( ( set_difference @ SV86 @ SV115 )
!= empty_set )
| ( subset @ SV86 @ SV115 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[664]) ).
thf(698,plain,
! [SV115: $i,SV86: $i] :
( ( ~ ( subset @ SV86 @ SV115 )
| ( ( set_difference @ SV86 @ SV115 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[665]) ).
thf(699,plain,
! [SV135: $i,SV116: $i,SV87: $i] :
( ( ( subset @ SV87 @ SV116 )
= $false )
| ( ( subset @ ( set_difference @ SV87 @ SV135 ) @ ( set_difference @ SV116 @ SV135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(700,plain,
! [SV117: $i,SV88: $i] :
( ( ~ ( subset @ SV88 @ SV117 )
| ! [SY168: $i] :
( ~ ( in @ SY168 @ SV88 )
| ( in @ SY168 @ SV117 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[667]) ).
thf(701,plain,
! [SV117: $i,SV88: $i] :
( ( ~ ! [SY169: $i] :
( ~ ( in @ SY169 @ SV88 )
| ( in @ SY169 @ SV117 ) )
| ( subset @ SV88 @ SV117 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[668]) ).
thf(702,plain,
! [SV118: $i,SV91: $i] :
( ( ~ ( subset @ SV91 @ ( singleton @ SV118 ) )
| ( SV91 = empty_set )
| ( SV91
= ( singleton @ SV118 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[669]) ).
thf(703,plain,
! [SV118: $i,SV91: $i] :
( ( ~ ( ( SV91 = empty_set )
| ( SV91
= ( singleton @ SV118 ) ) )
| ( subset @ SV91 @ ( singleton @ SV118 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[670]) ).
thf(704,plain,
! [SV119: $i,SV92: $i] :
( ( ( SV92 != SV119 )
| ~ ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[671]) ).
thf(705,plain,
! [SV119: $i,SV92: $i] :
( ( ~ ~ ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) )
| ( SV92 = SV119 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[672]) ).
thf(706,plain,
! [SV93: $i,SV120: $i] :
( ( ( SV120
!= ( singleton @ SV93 ) )
| ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV120 )
| ( SY170 = SV93 ) )
| ~ ( ( SY170 != SV93 )
| ( in @ SY170 @ SV120 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[673]) ).
thf(707,plain,
! [SV93: $i,SV120: $i] :
( ( ~ ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV120 )
| ( SY171 = SV93 ) )
| ~ ( ( SY171 != SV93 )
| ( in @ SY171 @ SV120 ) ) )
| ( SV120
= ( singleton @ SV93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[674]) ).
thf(708,plain,
! [SV121: $i,SV94: $i] :
( ( ~ ( subset @ ( singleton @ SV94 ) @ SV121 )
| ( in @ SV94 @ SV121 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[675]) ).
thf(709,plain,
! [SV121: $i,SV94: $i] :
( ( ~ ( in @ SV94 @ SV121 )
| ( subset @ ( singleton @ SV94 ) @ SV121 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[676]) ).
thf(710,plain,
! [SV122: $i,SV95: $i] :
( ( ( ~ ( subset @ SV95 @ SV122 ) )
= $true )
| ( ( ~ ( proper_subset @ SV122 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(711,plain,
! [SV136: $i,SV123: $i,SV96: $i] :
( ( ( ~ ( ~ ( subset @ SV96 @ SV123 )
| ~ ( subset @ SV96 @ SV136 ) ) )
= $false )
| ( ( subset @ SV96 @ ( set_intersection2 @ SV123 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(712,plain,
! [SV137: $i,SV124: $i,SV97: $i] :
( ( ( ~ ( ~ ( subset @ SV97 @ SV124 )
| ~ ( subset @ SV124 @ SV137 ) ) )
= $false )
| ( ( subset @ SV97 @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(713,plain,
! [SV98: $i] :
( ( ( SV98 != empty_set )
= $true )
| ( ( ! [SY153: $i] :
~ ( in @ SY153 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(714,plain,
! [SV98: $i] :
( ( ( ~ ! [SY154: $i] :
~ ( in @ SY154 @ SV98 ) )
= $true )
| ( ( SV98 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(715,plain,
! [SV138: $i,SV125: $i,SV99: $i] :
( ( ( ( singleton @ SV99 )
= ( unordered_pair @ SV125 @ SV138 ) )
= $false )
| ( ( SV125 = SV138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(716,plain,
! [SV126: $i,SV100: $i] :
( ( ~ ( subset @ ( singleton @ SV100 ) @ SV126 )
| ( in @ SV100 @ SV126 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[684]) ).
thf(717,plain,
! [SV126: $i,SV100: $i] :
( ( ~ ( in @ SV100 @ SV126 )
| ( subset @ ( singleton @ SV100 ) @ SV126 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(718,plain,
! [SV139: $i,SV127: $i,SV101: $i] :
( ( ( ~ ( ~ ( subset @ SV101 @ SV127 )
| ~ ( subset @ SV139 @ SV127 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV101 @ SV139 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(719,plain,
! [SV131: $i,SV106: $i] :
( ( ~ ( proper_subset @ SV106 @ SV131 )
| ~ ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[690]) ).
thf(720,plain,
! [SV131: $i,SV106: $i] :
( ( ~ ~ ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) )
| ( proper_subset @ SV106 @ SV131 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(721,plain,
! [SV132: $i,SV111: $i,SV82: $i] :
( ( ( ~ ( subset @ SV82 @ SV111 )
| ~ ( disjoint @ SV111 @ SV132 ) )
= $true )
| ( ( disjoint @ SV82 @ SV132 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(722,plain,
! [SV112: $i,SV83: $i] :
( ( ( ( set_difference @ SV83 @ SV112 )
!= empty_set )
= $true )
| ( ( subset @ SV83 @ SV112 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[693]) ).
thf(723,plain,
! [SV112: $i,SV83: $i] :
( ( ( ~ ( subset @ SV83 @ SV112 ) )
= $true )
| ( ( ( set_difference @ SV83 @ SV112 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(724,plain,
! [SV115: $i,SV86: $i] :
( ( ( ( set_difference @ SV86 @ SV115 )
!= empty_set )
= $true )
| ( ( subset @ SV86 @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(725,plain,
! [SV115: $i,SV86: $i] :
( ( ( ~ ( subset @ SV86 @ SV115 ) )
= $true )
| ( ( ( set_difference @ SV86 @ SV115 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(726,plain,
! [SV117: $i,SV88: $i] :
( ( ( ~ ( subset @ SV88 @ SV117 ) )
= $true )
| ( ( ! [SY168: $i] :
( ~ ( in @ SY168 @ SV88 )
| ( in @ SY168 @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(727,plain,
! [SV117: $i,SV88: $i] :
( ( ( ~ ! [SY169: $i] :
( ~ ( in @ SY169 @ SV88 )
| ( in @ SY169 @ SV117 ) ) )
= $true )
| ( ( subset @ SV88 @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(728,plain,
! [SV118: $i,SV91: $i] :
( ( ( ~ ( subset @ SV91 @ ( singleton @ SV118 ) ) )
= $true )
| ( ( ( SV91 = empty_set )
| ( SV91
= ( singleton @ SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(729,plain,
! [SV118: $i,SV91: $i] :
( ( ( ~ ( ( SV91 = empty_set )
| ( SV91
= ( singleton @ SV118 ) ) ) )
= $true )
| ( ( subset @ SV91 @ ( singleton @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(730,plain,
! [SV119: $i,SV92: $i] :
( ( ( SV92 != SV119 )
= $true )
| ( ( ~ ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(731,plain,
! [SV119: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) ) )
= $true )
| ( ( SV92 = SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(732,plain,
! [SV93: $i,SV120: $i] :
( ( ( SV120
!= ( singleton @ SV93 ) )
= $true )
| ( ( ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV120 )
| ( SY170 = SV93 ) )
| ~ ( ( SY170 != SV93 )
| ( in @ SY170 @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[706]) ).
thf(733,plain,
! [SV93: $i,SV120: $i] :
( ( ( ~ ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV120 )
| ( SY171 = SV93 ) )
| ~ ( ( SY171 != SV93 )
| ( in @ SY171 @ SV120 ) ) ) )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(734,plain,
! [SV121: $i,SV94: $i] :
( ( ( ~ ( subset @ ( singleton @ SV94 ) @ SV121 ) )
= $true )
| ( ( in @ SV94 @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(735,plain,
! [SV121: $i,SV94: $i] :
( ( ( ~ ( in @ SV94 @ SV121 ) )
= $true )
| ( ( subset @ ( singleton @ SV94 ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(736,plain,
! [SV122: $i,SV95: $i] :
( ( ( subset @ SV95 @ SV122 )
= $false )
| ( ( ~ ( proper_subset @ SV122 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(737,plain,
! [SV136: $i,SV123: $i,SV96: $i] :
( ( ( ~ ( subset @ SV96 @ SV123 )
| ~ ( subset @ SV96 @ SV136 ) )
= $true )
| ( ( subset @ SV96 @ ( set_intersection2 @ SV123 @ SV136 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[711]) ).
thf(738,plain,
! [SV137: $i,SV124: $i,SV97: $i] :
( ( ( ~ ( subset @ SV97 @ SV124 )
| ~ ( subset @ SV124 @ SV137 ) )
= $true )
| ( ( subset @ SV97 @ SV137 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[712]) ).
thf(739,plain,
! [SV98: $i] :
( ( ( SV98 = empty_set )
= $false )
| ( ( ! [SY153: $i] :
~ ( in @ SY153 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(740,plain,
! [SV98: $i] :
( ( ( ! [SY154: $i] :
~ ( in @ SY154 @ SV98 ) )
= $false )
| ( ( SV98 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(741,plain,
! [SV126: $i,SV100: $i] :
( ( ( ~ ( subset @ ( singleton @ SV100 ) @ SV126 ) )
= $true )
| ( ( in @ SV100 @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(742,plain,
! [SV126: $i,SV100: $i] :
( ( ( ~ ( in @ SV100 @ SV126 ) )
= $true )
| ( ( subset @ ( singleton @ SV100 ) @ SV126 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[717]) ).
thf(743,plain,
! [SV139: $i,SV127: $i,SV101: $i] :
( ( ( ~ ( subset @ SV101 @ SV127 )
| ~ ( subset @ SV139 @ SV127 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV101 @ SV139 ) @ SV127 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[718]) ).
thf(744,plain,
! [SV131: $i,SV106: $i] :
( ( ( ~ ( proper_subset @ SV106 @ SV131 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(745,plain,
! [SV131: $i,SV106: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) ) )
= $true )
| ( ( proper_subset @ SV106 @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(746,plain,
! [SV132: $i,SV111: $i,SV82: $i] :
( ( ( ~ ( subset @ SV82 @ SV111 ) )
= $true )
| ( ( ~ ( disjoint @ SV111 @ SV132 ) )
= $true )
| ( ( disjoint @ SV82 @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(747,plain,
! [SV112: $i,SV83: $i] :
( ( ( ( set_difference @ SV83 @ SV112 )
= empty_set )
= $false )
| ( ( subset @ SV83 @ SV112 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(748,plain,
! [SV112: $i,SV83: $i] :
( ( ( subset @ SV83 @ SV112 )
= $false )
| ( ( ( set_difference @ SV83 @ SV112 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(749,plain,
! [SV115: $i,SV86: $i] :
( ( ( ( set_difference @ SV86 @ SV115 )
= empty_set )
= $false )
| ( ( subset @ SV86 @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(750,plain,
! [SV115: $i,SV86: $i] :
( ( ( subset @ SV86 @ SV115 )
= $false )
| ( ( ( set_difference @ SV86 @ SV115 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(751,plain,
! [SV117: $i,SV88: $i] :
( ( ( subset @ SV88 @ SV117 )
= $false )
| ( ( ! [SY168: $i] :
( ~ ( in @ SY168 @ SV88 )
| ( in @ SY168 @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(752,plain,
! [SV117: $i,SV88: $i] :
( ( ( ! [SY169: $i] :
( ~ ( in @ SY169 @ SV88 )
| ( in @ SY169 @ SV117 ) ) )
= $false )
| ( ( subset @ SV88 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(753,plain,
! [SV118: $i,SV91: $i] :
( ( ( subset @ SV91 @ ( singleton @ SV118 ) )
= $false )
| ( ( ( SV91 = empty_set )
| ( SV91
= ( singleton @ SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(754,plain,
! [SV118: $i,SV91: $i] :
( ( ( ( SV91 = empty_set )
| ( SV91
= ( singleton @ SV118 ) ) )
= $false )
| ( ( subset @ SV91 @ ( singleton @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(755,plain,
! [SV119: $i,SV92: $i] :
( ( ( SV92 = SV119 )
= $false )
| ( ( ~ ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(756,plain,
! [SV119: $i,SV92: $i] :
( ( ( ~ ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) ) )
= $false )
| ( ( SV92 = SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(757,plain,
! [SV93: $i,SV120: $i] :
( ( ( SV120
= ( singleton @ SV93 ) )
= $false )
| ( ( ! [SY170: $i] :
~ ( ~ ( ~ ( in @ SY170 @ SV120 )
| ( SY170 = SV93 ) )
| ~ ( ( SY170 != SV93 )
| ( in @ SY170 @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(758,plain,
! [SV93: $i,SV120: $i] :
( ( ( ! [SY171: $i] :
~ ( ~ ( ~ ( in @ SY171 @ SV120 )
| ( SY171 = SV93 ) )
| ~ ( ( SY171 != SV93 )
| ( in @ SY171 @ SV120 ) ) ) )
= $false )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(759,plain,
! [SV121: $i,SV94: $i] :
( ( ( subset @ ( singleton @ SV94 ) @ SV121 )
= $false )
| ( ( in @ SV94 @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(760,plain,
! [SV121: $i,SV94: $i] :
( ( ( in @ SV94 @ SV121 )
= $false )
| ( ( subset @ ( singleton @ SV94 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(761,plain,
! [SV95: $i,SV122: $i] :
( ( ( proper_subset @ SV122 @ SV95 )
= $false )
| ( ( subset @ SV95 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(762,plain,
! [SV136: $i,SV123: $i,SV96: $i] :
( ( ( ~ ( subset @ SV96 @ SV123 ) )
= $true )
| ( ( ~ ( subset @ SV96 @ SV136 ) )
= $true )
| ( ( subset @ SV96 @ ( set_intersection2 @ SV123 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(763,plain,
! [SV137: $i,SV124: $i,SV97: $i] :
( ( ( ~ ( subset @ SV97 @ SV124 ) )
= $true )
| ( ( ~ ( subset @ SV124 @ SV137 ) )
= $true )
| ( ( subset @ SV97 @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[738]) ).
thf(764,plain,
! [SV98: $i,SV140: $i] :
( ( ( ~ ( in @ SV140 @ SV98 ) )
= $true )
| ( ( SV98 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(765,plain,
! [SV98: $i] :
( ( ( ~ ( in @ ( sK6_SY154 @ SV98 ) @ SV98 ) )
= $false )
| ( ( SV98 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[740]) ).
thf(766,plain,
! [SV126: $i,SV100: $i] :
( ( ( subset @ ( singleton @ SV100 ) @ SV126 )
= $false )
| ( ( in @ SV100 @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(767,plain,
! [SV126: $i,SV100: $i] :
( ( ( in @ SV100 @ SV126 )
= $false )
| ( ( subset @ ( singleton @ SV100 ) @ SV126 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(768,plain,
! [SV139: $i,SV127: $i,SV101: $i] :
( ( ( ~ ( subset @ SV101 @ SV127 ) )
= $true )
| ( ( ~ ( subset @ SV139 @ SV127 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV101 @ SV139 ) @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[743]) ).
thf(769,plain,
! [SV131: $i,SV106: $i] :
( ( ( proper_subset @ SV106 @ SV131 )
= $false )
| ( ( ~ ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(770,plain,
! [SV131: $i,SV106: $i] :
( ( ( ~ ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) ) )
= $false )
| ( ( proper_subset @ SV106 @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(771,plain,
! [SV132: $i,SV111: $i,SV82: $i] :
( ( ( subset @ SV82 @ SV111 )
= $false )
| ( ( ~ ( disjoint @ SV111 @ SV132 ) )
= $true )
| ( ( disjoint @ SV82 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(772,plain,
! [SV117: $i,SV88: $i,SV141: $i] :
( ( ( ~ ( in @ SV141 @ SV88 )
| ( in @ SV141 @ SV117 ) )
= $true )
| ( ( subset @ SV88 @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(773,plain,
! [SV88: $i,SV117: $i] :
( ( ( ~ ( in @ ( sK7_SY169 @ SV117 @ SV88 ) @ SV88 )
| ( in @ ( sK7_SY169 @ SV117 @ SV88 ) @ SV117 ) )
= $false )
| ( ( subset @ SV88 @ SV117 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[752]) ).
thf(774,plain,
! [SV118: $i,SV91: $i] :
( ( ( SV91 = empty_set )
= $true )
| ( ( SV91
= ( singleton @ SV118 ) )
= $true )
| ( ( subset @ SV91 @ ( singleton @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(775,plain,
! [SV118: $i,SV91: $i] :
( ( ( SV91 = empty_set )
= $false )
| ( ( subset @ SV91 @ ( singleton @ SV118 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(776,plain,
! [SV118: $i,SV91: $i] :
( ( ( SV91
= ( singleton @ SV118 ) )
= $false )
| ( ( subset @ SV91 @ ( singleton @ SV118 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(777,plain,
! [SV119: $i,SV92: $i] :
( ( ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) )
= $false )
| ( ( SV92 = SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(778,plain,
! [SV119: $i,SV92: $i] :
( ( ( ~ ( subset @ SV92 @ SV119 )
| ~ ( subset @ SV119 @ SV92 ) )
= $true )
| ( ( SV92 = SV119 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[756]) ).
thf(779,plain,
! [SV93: $i,SV120: $i,SV142: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV142 @ SV120 )
| ( SV142 = SV93 ) )
| ~ ( ( SV142 != SV93 )
| ( in @ SV142 @ SV120 ) ) ) )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(780,plain,
! [SV120: $i,SV93: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 )
| ( ( sK8_SY171 @ SV93 @ SV120 )
= SV93 ) )
| ~ ( ( ( sK8_SY171 @ SV93 @ SV120 )
!= SV93 )
| ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 ) ) ) )
= $false )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[758]) ).
thf(781,plain,
! [SV136: $i,SV123: $i,SV96: $i] :
( ( ( subset @ SV96 @ SV123 )
= $false )
| ( ( ~ ( subset @ SV96 @ SV136 ) )
= $true )
| ( ( subset @ SV96 @ ( set_intersection2 @ SV123 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(782,plain,
! [SV137: $i,SV124: $i,SV97: $i] :
( ( ( subset @ SV97 @ SV124 )
= $false )
| ( ( ~ ( subset @ SV124 @ SV137 ) )
= $true )
| ( ( subset @ SV97 @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(783,plain,
! [SV98: $i,SV140: $i] :
( ( ( in @ SV140 @ SV98 )
= $false )
| ( ( SV98 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(784,plain,
! [SV98: $i] :
( ( ( in @ ( sK6_SY154 @ SV98 ) @ SV98 )
= $true )
| ( ( SV98 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[765]) ).
thf(785,plain,
! [SV139: $i,SV127: $i,SV101: $i] :
( ( ( subset @ SV101 @ SV127 )
= $false )
| ( ( ~ ( subset @ SV139 @ SV127 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV101 @ SV139 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(786,plain,
! [SV131: $i,SV106: $i] :
( ( ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) )
= $false )
| ( ( proper_subset @ SV106 @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(787,plain,
! [SV131: $i,SV106: $i] :
( ( ( ~ ( subset @ SV106 @ SV131 )
| ~ ( ( SV106 != SV131 ) ) )
= $true )
| ( ( proper_subset @ SV106 @ SV131 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[770]) ).
thf(788,plain,
! [SV82: $i,SV132: $i,SV111: $i] :
( ( ( disjoint @ SV111 @ SV132 )
= $false )
| ( ( subset @ SV82 @ SV111 )
= $false )
| ( ( disjoint @ SV82 @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(789,plain,
! [SV117: $i,SV88: $i,SV141: $i] :
( ( ( ~ ( in @ SV141 @ SV88 ) )
= $true )
| ( ( in @ SV141 @ SV117 )
= $true )
| ( ( subset @ SV88 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(790,plain,
! [SV88: $i,SV117: $i] :
( ( ( ~ ( in @ ( sK7_SY169 @ SV117 @ SV88 ) @ SV88 ) )
= $false )
| ( ( subset @ SV88 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(791,plain,
! [SV88: $i,SV117: $i] :
( ( ( in @ ( sK7_SY169 @ SV117 @ SV88 ) @ SV117 )
= $false )
| ( ( subset @ SV88 @ SV117 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(792,plain,
! [SV119: $i,SV92: $i] :
( ( ( ~ ( subset @ SV92 @ SV119 ) )
= $false )
| ( ( SV92 = SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[777]) ).
thf(793,plain,
! [SV92: $i,SV119: $i] :
( ( ( ~ ( subset @ SV119 @ SV92 ) )
= $false )
| ( ( SV92 = SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[777]) ).
thf(794,plain,
! [SV119: $i,SV92: $i] :
( ( ( ~ ( subset @ SV92 @ SV119 ) )
= $true )
| ( ( ~ ( subset @ SV119 @ SV92 ) )
= $true )
| ( ( SV92 = SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(795,plain,
! [SV93: $i,SV120: $i,SV142: $i] :
( ( ( ~ ( ~ ( in @ SV142 @ SV120 )
| ( SV142 = SV93 ) )
| ~ ( ( SV142 != SV93 )
| ( in @ SV142 @ SV120 ) ) )
= $false )
| ( ( SV120
= ( singleton @ SV93 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(796,plain,
! [SV120: $i,SV93: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 )
| ( ( sK8_SY171 @ SV93 @ SV120 )
= SV93 ) )
| ~ ( ( ( sK8_SY171 @ SV93 @ SV120 )
!= SV93 )
| ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 ) ) )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[780]) ).
thf(797,plain,
! [SV123: $i,SV136: $i,SV96: $i] :
( ( ( subset @ SV96 @ SV136 )
= $false )
| ( ( subset @ SV96 @ SV123 )
= $false )
| ( ( subset @ SV96 @ ( set_intersection2 @ SV123 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(798,plain,
! [SV97: $i,SV137: $i,SV124: $i] :
( ( ( subset @ SV124 @ SV137 )
= $false )
| ( ( subset @ SV97 @ SV124 )
= $false )
| ( ( subset @ SV97 @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(799,plain,
! [SV101: $i,SV127: $i,SV139: $i] :
( ( ( subset @ SV139 @ SV127 )
= $false )
| ( ( subset @ SV101 @ SV127 )
= $false )
| ( ( subset @ ( set_union2 @ SV101 @ SV139 ) @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(800,plain,
! [SV131: $i,SV106: $i] :
( ( ( ~ ( subset @ SV106 @ SV131 ) )
= $false )
| ( ( proper_subset @ SV106 @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(801,plain,
! [SV131: $i,SV106: $i] :
( ( ( ~ ( ( SV106 != SV131 ) ) )
= $false )
| ( ( proper_subset @ SV106 @ SV131 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(802,plain,
! [SV131: $i,SV106: $i] :
( ( ( ~ ( subset @ SV106 @ SV131 ) )
= $true )
| ( ( ~ ( ( SV106 != SV131 ) ) )
= $true )
| ( ( proper_subset @ SV106 @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[787]) ).
thf(803,plain,
! [SV117: $i,SV88: $i,SV141: $i] :
( ( ( in @ SV141 @ SV88 )
= $false )
| ( ( in @ SV141 @ SV117 )
= $true )
| ( ( subset @ SV88 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(804,plain,
! [SV88: $i,SV117: $i] :
( ( ( in @ ( sK7_SY169 @ SV117 @ SV88 ) @ SV88 )
= $true )
| ( ( subset @ SV88 @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(805,plain,
! [SV119: $i,SV92: $i] :
( ( ( subset @ SV92 @ SV119 )
= $true )
| ( ( SV92 = SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(806,plain,
! [SV92: $i,SV119: $i] :
( ( ( subset @ SV119 @ SV92 )
= $true )
| ( ( SV92 = SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(807,plain,
! [SV119: $i,SV92: $i] :
( ( ( subset @ SV92 @ SV119 )
= $false )
| ( ( ~ ( subset @ SV119 @ SV92 ) )
= $true )
| ( ( SV92 = SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(808,plain,
! [SV93: $i,SV120: $i,SV142: $i] :
( ( ( ~ ( ~ ( in @ SV142 @ SV120 )
| ( SV142 = SV93 ) ) )
= $false )
| ( ( SV120
= ( singleton @ SV93 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[795]) ).
thf(809,plain,
! [SV120: $i,SV93: $i,SV142: $i] :
( ( ( ~ ( ( SV142 != SV93 )
| ( in @ SV142 @ SV120 ) ) )
= $false )
| ( ( SV120
= ( singleton @ SV93 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[795]) ).
thf(810,plain,
! [SV120: $i,SV93: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 )
| ( ( sK8_SY171 @ SV93 @ SV120 )
= SV93 ) ) )
= $true )
| ( ( ~ ( ( ( sK8_SY171 @ SV93 @ SV120 )
!= SV93 )
| ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 ) ) )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(811,plain,
! [SV131: $i,SV106: $i] :
( ( ( subset @ SV106 @ SV131 )
= $true )
| ( ( proper_subset @ SV106 @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(812,plain,
! [SV131: $i,SV106: $i] :
( ( ( SV106 != SV131 )
= $true )
| ( ( proper_subset @ SV106 @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(813,plain,
! [SV131: $i,SV106: $i] :
( ( ( subset @ SV106 @ SV131 )
= $false )
| ( ( ~ ( ( SV106 != SV131 ) ) )
= $true )
| ( ( proper_subset @ SV106 @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(814,plain,
! [SV92: $i,SV119: $i] :
( ( ( subset @ SV119 @ SV92 )
= $false )
| ( ( subset @ SV92 @ SV119 )
= $false )
| ( ( SV92 = SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(815,plain,
! [SV93: $i,SV120: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ SV120 )
| ( SV142 = SV93 ) )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(816,plain,
! [SV120: $i,SV93: $i,SV142: $i] :
( ( ( ( SV142 != SV93 )
| ( in @ SV142 @ SV120 ) )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(817,plain,
! [SV120: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 )
| ( ( sK8_SY171 @ SV93 @ SV120 )
= SV93 ) )
= $false )
| ( ( ~ ( ( ( sK8_SY171 @ SV93 @ SV120 )
!= SV93 )
| ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 ) ) )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(818,plain,
! [SV131: $i,SV106: $i] :
( ( ( SV106 = SV131 )
= $false )
| ( ( proper_subset @ SV106 @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(819,plain,
! [SV131: $i,SV106: $i] :
( ( ( SV106 != SV131 )
= $false )
| ( ( subset @ SV106 @ SV131 )
= $false )
| ( ( proper_subset @ SV106 @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(820,plain,
! [SV93: $i,SV120: $i,SV142: $i] :
( ( ( ~ ( in @ SV142 @ SV120 ) )
= $true )
| ( ( SV142 = SV93 )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(821,plain,
! [SV120: $i,SV93: $i,SV142: $i] :
( ( ( SV142 != SV93 )
= $true )
| ( ( in @ SV142 @ SV120 )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(822,plain,
! [SV120: $i,SV93: $i] :
( ( ( ~ ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 ) )
= $false )
| ( ( ~ ( ( ( sK8_SY171 @ SV93 @ SV120 )
!= SV93 )
| ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 ) ) )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(823,plain,
! [SV120: $i,SV93: $i] :
( ( ( ( sK8_SY171 @ SV93 @ SV120 )
= SV93 )
= $false )
| ( ( ~ ( ( ( sK8_SY171 @ SV93 @ SV120 )
!= SV93 )
| ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 ) ) )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[817]) ).
thf(824,plain,
! [SV131: $i,SV106: $i] :
( ( ( SV106 = SV131 )
= $true )
| ( ( subset @ SV106 @ SV131 )
= $false )
| ( ( proper_subset @ SV106 @ SV131 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(825,plain,
! [SV93: $i,SV120: $i,SV142: $i] :
( ( ( in @ SV142 @ SV120 )
= $false )
| ( ( SV142 = SV93 )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(826,plain,
! [SV120: $i,SV93: $i,SV142: $i] :
( ( ( SV142 = SV93 )
= $false )
| ( ( in @ SV142 @ SV120 )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[821]) ).
thf(827,plain,
! [SV120: $i,SV93: $i] :
( ( ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 )
= $true )
| ( ( ~ ( ( ( sK8_SY171 @ SV93 @ SV120 )
!= SV93 )
| ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 ) ) )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(828,plain,
! [SV120: $i,SV93: $i] :
( ( ( ( ( sK8_SY171 @ SV93 @ SV120 )
!= SV93 )
| ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 ) )
= $false )
| ( ( ( sK8_SY171 @ SV93 @ SV120 )
= SV93 )
= $false )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(829,plain,
! [SV120: $i,SV93: $i] :
( ( ( ( ( sK8_SY171 @ SV93 @ SV120 )
!= SV93 )
| ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 ) )
= $false )
| ( ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(830,plain,
! [SV120: $i,SV93: $i] :
( ( ( ( sK8_SY171 @ SV93 @ SV120 )
!= SV93 )
= $false )
| ( ( ( sK8_SY171 @ SV93 @ SV120 )
= SV93 )
= $false )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[828]) ).
thf(831,plain,
! [SV120: $i,SV93: $i] :
( ( ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 )
= $false )
| ( ( ( sK8_SY171 @ SV93 @ SV120 )
= SV93 )
= $false )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[828]) ).
thf(832,plain,
! [SV120: $i,SV93: $i] :
( ( ( ( sK8_SY171 @ SV93 @ SV120 )
!= SV93 )
= $false )
| ( ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[829]) ).
thf(833,plain,
! [SV120: $i,SV93: $i] :
( ( ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 )
= $false )
| ( ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[829]) ).
thf(834,plain,
! [SV120: $i,SV93: $i] :
( ( ( ( sK8_SY171 @ SV93 @ SV120 )
= SV93 )
= $true )
| ( ( ( sK8_SY171 @ SV93 @ SV120 )
= SV93 )
= $false )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(835,plain,
! [SV120: $i,SV93: $i] :
( ( ( ( sK8_SY171 @ SV93 @ SV120 )
= SV93 )
= $true )
| ( ( in @ ( sK8_SY171 @ SV93 @ SV120 ) @ SV120 )
= $true )
| ( ( SV120
= ( singleton @ SV93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(836,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[500,835,834,833,831,826,825,824,818,814,811,806,805,804,803,799,798,797,791,788,784,783,776,775,774,767,766,761,760,759,750,749,748,747,715,699,696,695,689,688,687,679,641,640,631,622,605,604,603,602,575,574,573,572,569,567,532,531,530,529,528,527,526,525,524,523,522]) ).
thf(837,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[836,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU160+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.17 % Computer : n016.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Oct 6 15:07:14 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.96/0.56
% 1.96/0.56 No.of.Axioms: 47
% 1.96/0.56
% 1.96/0.56 Length.of.Defs: 0
% 1.96/0.56
% 1.96/0.56 Contains.Choice.Funs: false
% 1.96/0.56 ......................
% 1.96/0.56
% 1.96/0.56 ********************************
% 1.96/0.56 * All subproblems solved! *
% 1.96/0.56 ********************************
% 1.96/0.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:47,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:836,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.96/0.56
% 1.96/0.56 %**** Beginning of derivation protocol ****
% 1.96/0.56 % SZS output start CNFRefutation
% See solution above
% 1.96/0.56
% 1.96/0.56 %**** End of derivation protocol ****
% 1.96/0.56 %**** no. of clauses in derivation: 795 ****
% 1.96/0.56 %**** clause counter: 836 ****
% 1.96/0.56
% 1.96/0.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:47,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:836,loop_count:0,foatp_calls:1,translation:fof_full)
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