%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU131+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 : n020.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 10:42:59 AM UTC 2026
% Result : Theorem 11.03s 2.06s
% Output : CNFRefutation 11.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 26
% Syntax : Number of formulae : 496 ( 249 unt; 0 typ; 0 def)
% Number of atoms : 3303 (1191 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 6491 (1562 ~;1006 |; 20 &;3836 @)
% ( 25 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 1205 ( 0 ^;1205 !; 0 ?;1205 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY42,type,
sK2_SY42: $i ).
thf(tp_sK3_SY61,type,
sK3_SY61: $i > $i ).
thf(tp_sK4_SY71,type,
sK4_SY71: $i > $i > $i ).
thf(tp_sK5_SY76,type,
sK5_SY76: $i > $i > $i > $i ).
thf(tp_sK6_SY91,type,
sK6_SY91: $i > $i ).
thf(tp_sK7_SY107,type,
sK7_SY107: $i > $i > $i ).
thf(tp_sK8_SY110,type,
sK8_SY110: $i > $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
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(17,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(18,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(19,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(25,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(27,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(32,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(33,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(35,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(37,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(39,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(40,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(41,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(42,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(44,conjecture,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(45,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[44]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[45]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(49,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(51,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(53,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(54,plain,
$true = $true,
inference(unfold_def,[status(thm)],[18]) ).
thf(55,plain,
$true = $true,
inference(unfold_def,[status(thm)],[19]) ).
thf(56,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(57,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(58,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(62,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)],[32]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(65,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(67,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)],[39]) ).
thf(68,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(69,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)],[41]) ).
thf(70,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(72,plain,
( ( ! [SY42: $i] :
( ( ( set_difference @ sK1_A @ SY42 )
= empty_set )
<=> ( subset @ sK1_A @ SY42 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(73,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY42 )
= empty_set )
<=> ( subset @ sK1_A @ sK2_SY42 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[72]) ).
thf(74,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY42 )
= empty_set )
=> ( subset @ sK1_A @ sK2_SY42 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[73]) ).
thf(75,plain,
( ( ( subset @ sK1_A @ sK2_SY42 )
=> ( ( set_difference @ sK1_A @ sK2_SY42 )
= empty_set ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[73]) ).
thf(76,plain,
( ( ~ ( ( ( set_difference @ sK1_A @ sK2_SY42 )
= empty_set )
=> ( subset @ sK1_A @ sK2_SY42 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[74]) ).
thf(77,plain,
( ( ~ ( ( subset @ sK1_A @ sK2_SY42 )
=> ( ( set_difference @ sK1_A @ sK2_SY42 )
= empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[75]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(80,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(81,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(82,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(83,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(84,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(85,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(87,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(88,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(89,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(90,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(91,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(92,plain,
$true = $true,
inference(copy,[status(thm)],[57]) ).
thf(93,plain,
$true = $true,
inference(copy,[status(thm)],[56]) ).
thf(94,plain,
$true = $true,
inference(copy,[status(thm)],[55]) ).
thf(95,plain,
$true = $true,
inference(copy,[status(thm)],[54]) ).
thf(96,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(98,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(99,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(100,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(101,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(102,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(103,plain,
( ( ~ ( ( ( set_difference @ sK1_A @ sK2_SY42 )
= empty_set )
=> ( subset @ sK1_A @ sK2_SY42 ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(104,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)],[88]) ).
thf(105,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(106,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(107,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)],[87]) ).
thf(108,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)],[90]) ).
thf(109,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(112,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)],[89]) ).
thf(113,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)],[82]) ).
thf(114,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(115,plain,
( ( ~ ( ( ( set_difference @ sK1_A @ sK2_SY42 )
!= empty_set )
| ( subset @ sK1_A @ sK2_SY42 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(116,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)],[80]) ).
thf(117,plain,
! [SV1: $i] :
( ( ! [SY43: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY43 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(118,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(119,plain,
! [SV3: $i] :
( ( ! [SY44: $i] : ( subset @ SV3 @ ( set_union2 @ SV3 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(120,plain,
! [SV4: $i] :
( ( ! [SY45: $i] : ( subset @ SV4 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(121,plain,
! [SV5: $i] :
( ( ( set_union2 @ SV5 @ empty_set )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(122,plain,
! [SV6: $i] :
( ( ( set_intersection2 @ SV6 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(123,plain,
! [SV7: $i] :
( ( ( set_difference @ SV7 @ empty_set )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(124,plain,
! [SV8: $i] :
( ( ( set_difference @ empty_set @ SV8 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(125,plain,
! [SV9: $i] :
( ( ! [SY46: $i] :
~ ( ~ ( ( SV9 != SY46 )
| ~ ( ~ ( subset @ SV9 @ SY46 )
| ~ ( subset @ SY46 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV9 @ SY46 )
| ~ ( subset @ SY46 @ SV9 ) )
| ( SV9 = SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(126,plain,
! [SV10: $i] :
( ( ! [SY47: $i] :
( ~ ( subset @ SV10 @ SY47 )
| ( ( set_intersection2 @ SV10 @ SY47 )
= SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(127,plain,
! [SV11: $i] :
( ( ! [SY48: $i,SY49: $i] :
~ ( ~ ( ( SY49
!= ( set_difference @ SV11 @ SY48 ) )
| ! [SY50: $i] :
~ ( ~ ( ~ ( in @ SY50 @ SY49 )
| ~ ( ~ ( in @ SY50 @ SV11 )
| ~ ~ ( in @ SY50 @ SY48 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY50 @ SV11 )
| ~ ~ ( in @ SY50 @ SY48 ) )
| ( in @ SY50 @ SY49 ) ) ) )
| ~ ( ~ ! [SY51: $i] :
~ ( ~ ( ~ ( in @ SY51 @ SY49 )
| ~ ( ~ ( in @ SY51 @ SV11 )
| ~ ~ ( in @ SY51 @ SY48 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY51 @ SV11 )
| ~ ~ ( in @ SY51 @ SY48 ) )
| ( in @ SY51 @ SY49 ) ) )
| ( SY49
= ( set_difference @ SV11 @ SY48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(128,plain,
! [SV12: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ~ ( ~ ( subset @ SV12 @ SY52 )
| ~ ( subset @ SY53 @ SY52 ) )
| ( subset @ ( set_union2 @ SV12 @ SY53 ) @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(129,plain,
! [SV13: $i] :
( ( ! [SY54: $i] :
~ ( ~ ( ~ ( subset @ SV13 @ SY54 )
| ! [SY55: $i] :
( ~ ( in @ SY55 @ SV13 )
| ( in @ SY55 @ SY54 ) ) )
| ~ ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ SV13 )
| ( in @ SY56 @ SY54 ) )
| ( subset @ SV13 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(130,plain,
! [SV14: $i] :
( ( ~ ( subset @ SV14 @ empty_set )
| ( SV14 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(131,plain,
! [SV15: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ~ ( ~ ( subset @ SV15 @ SY57 )
| ~ ( subset @ SY57 @ SY58 ) )
| ( subset @ SV15 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(132,plain,
! [SV16: $i] :
( ( ! [SY59: $i] :
( ~ ( subset @ SV16 @ SY59 )
| ( ( set_union2 @ SV16 @ SY59 )
= SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(133,plain,
! [SV17: $i] :
( ( ~ ( ~ ( ( SV17 != empty_set )
| ! [SY60: $i] :
~ ( in @ SY60 @ SV17 ) )
| ~ ( ~ ! [SY61: $i] :
~ ( in @ SY61 @ SV17 )
| ( SV17 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(134,plain,
! [SV18: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ( subset @ SV18 @ SY62 )
| ( subset @ ( set_intersection2 @ SV18 @ SY63 ) @ ( set_intersection2 @ SY62 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(135,plain,
! [SV19: $i] :
( ( ~ ( empty @ SV19 )
| ( SV19 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(136,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY42 )
!= empty_set )
| ( subset @ sK1_A @ sK2_SY42 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(137,plain,
! [SV20: $i] :
( ( ! [SY64: $i,SY65: $i] :
( ~ ~ ( ~ ( subset @ SV20 @ SY64 )
| ~ ( subset @ SV20 @ SY65 ) )
| ( subset @ SV20 @ ( set_intersection2 @ SY64 @ SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(138,plain,
! [SV21: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV21 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(139,plain,
! [SV22: $i,SV3: $i] :
( ( subset @ SV3 @ ( set_union2 @ SV3 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(140,plain,
! [SV4: $i] :
( ( subset @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(141,plain,
! [SV24: $i,SV9: $i] :
( ( ~ ( ~ ( ( SV9 != SV24 )
| ~ ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) )
| ( SV9 = SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(142,plain,
! [SV25: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV25 )
| ( ( set_intersection2 @ SV10 @ SV25 )
= SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(143,plain,
! [SV26: $i,SV11: $i] :
( ( ! [SY66: $i] :
~ ( ~ ( ( SY66
!= ( set_difference @ SV11 @ SV26 ) )
| ! [SY67: $i] :
~ ( ~ ( ~ ( in @ SY67 @ SY66 )
| ~ ( ~ ( in @ SY67 @ SV11 )
| ~ ~ ( in @ SY67 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY67 @ SV11 )
| ~ ~ ( in @ SY67 @ SV26 ) )
| ( in @ SY67 @ SY66 ) ) ) )
| ~ ( ~ ! [SY68: $i] :
~ ( ~ ( ~ ( in @ SY68 @ SY66 )
| ~ ( ~ ( in @ SY68 @ SV11 )
| ~ ~ ( in @ SY68 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY68 @ SV11 )
| ~ ~ ( in @ SY68 @ SV26 ) )
| ( in @ SY68 @ SY66 ) ) )
| ( SY66
= ( set_difference @ SV11 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(144,plain,
! [SV27: $i,SV12: $i] :
( ( ! [SY69: $i] :
( ~ ~ ( ~ ( subset @ SV12 @ SV27 )
| ~ ( subset @ SY69 @ SV27 ) )
| ( subset @ ( set_union2 @ SV12 @ SY69 ) @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(145,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV13 @ SV28 )
| ! [SY70: $i] :
( ~ ( in @ SY70 @ SV13 )
| ( in @ SY70 @ SV28 ) ) )
| ~ ( ~ ! [SY71: $i] :
( ~ ( in @ SY71 @ SV13 )
| ( in @ SY71 @ SV28 ) )
| ( subset @ SV13 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(146,plain,
! [SV14: $i] :
( ( ( ~ ( subset @ SV14 @ empty_set ) )
= $true )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(147,plain,
! [SV29: $i,SV15: $i] :
( ( ! [SY72: $i] :
( ~ ~ ( ~ ( subset @ SV15 @ SV29 )
| ~ ( subset @ SV29 @ SY72 ) )
| ( subset @ SV15 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(148,plain,
! [SV30: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV30 )
| ( ( set_union2 @ SV16 @ SV30 )
= SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(149,plain,
! [SV17: $i] :
( ( ~ ( ( SV17 != empty_set )
| ! [SY60: $i] :
~ ( in @ SY60 @ SV17 ) )
| ~ ( ~ ! [SY61: $i] :
~ ( in @ SY61 @ SV17 )
| ( SV17 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(150,plain,
! [SV31: $i,SV18: $i] :
( ( ! [SY73: $i] :
( ~ ( subset @ SV18 @ SV31 )
| ( subset @ ( set_intersection2 @ SV18 @ SY73 ) @ ( set_intersection2 @ SV31 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(151,plain,
! [SV19: $i] :
( ( ( ~ ( empty @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(152,plain,
( ( ( set_difference @ sK1_A @ sK2_SY42 )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(153,plain,
( ( subset @ sK1_A @ sK2_SY42 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(154,plain,
! [SV32: $i,SV20: $i] :
( ( ! [SY74: $i] :
( ~ ~ ( ~ ( subset @ SV20 @ SV32 )
| ~ ( subset @ SV20 @ SY74 ) )
| ( subset @ SV20 @ ( set_intersection2 @ SV32 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(155,plain,
! [SV24: $i,SV9: $i] :
( ( ~ ( ( SV9 != SV24 )
| ~ ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) )
| ( SV9 = SV24 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(156,plain,
! [SV25: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV25 ) )
= $true )
| ( ( ( set_intersection2 @ SV10 @ SV25 )
= SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(157,plain,
! [SV26: $i,SV11: $i,SV33: $i] :
( ( ~ ( ~ ( ( SV33
!= ( set_difference @ SV11 @ SV26 ) )
| ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SV33 )
| ~ ( ~ ( in @ SY75 @ SV11 )
| ~ ~ ( in @ SY75 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY75 @ SV11 )
| ~ ~ ( in @ SY75 @ SV26 ) )
| ( in @ SY75 @ SV33 ) ) ) )
| ~ ( ~ ! [SY76: $i] :
~ ( ~ ( ~ ( in @ SY76 @ SV33 )
| ~ ( ~ ( in @ SY76 @ SV11 )
| ~ ~ ( in @ SY76 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY76 @ SV11 )
| ~ ~ ( in @ SY76 @ SV26 ) )
| ( in @ SY76 @ SV33 ) ) )
| ( SV33
= ( set_difference @ SV11 @ SV26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(158,plain,
! [SV34: $i,SV27: $i,SV12: $i] :
( ( ~ ~ ( ~ ( subset @ SV12 @ SV27 )
| ~ ( subset @ SV34 @ SV27 ) )
| ( subset @ ( set_union2 @ SV12 @ SV34 ) @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(159,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ( ~ ( subset @ SV13 @ SV28 )
| ! [SY70: $i] :
( ~ ( in @ SY70 @ SV13 )
| ( in @ SY70 @ SV28 ) ) )
| ~ ( ~ ! [SY71: $i] :
( ~ ( in @ SY71 @ SV13 )
| ( in @ SY71 @ SV28 ) )
| ( subset @ SV13 @ SV28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(160,plain,
! [SV14: $i] :
( ( ( subset @ SV14 @ empty_set )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(161,plain,
! [SV35: $i,SV29: $i,SV15: $i] :
( ( ~ ~ ( ~ ( subset @ SV15 @ SV29 )
| ~ ( subset @ SV29 @ SV35 ) )
| ( subset @ SV15 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(162,plain,
! [SV30: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV30 ) )
= $true )
| ( ( ( set_union2 @ SV16 @ SV30 )
= SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(163,plain,
! [SV17: $i] :
( ( ~ ( ( SV17 != empty_set )
| ! [SY60: $i] :
~ ( in @ SY60 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(164,plain,
! [SV17: $i] :
( ( ~ ( ~ ! [SY61: $i] :
~ ( in @ SY61 @ SV17 )
| ( SV17 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(165,plain,
! [SV36: $i,SV31: $i,SV18: $i] :
( ( ~ ( subset @ SV18 @ SV31 )
| ( subset @ ( set_intersection2 @ SV18 @ SV36 ) @ ( set_intersection2 @ SV31 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(166,plain,
! [SV19: $i] :
( ( ( empty @ SV19 )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(167,plain,
( ( ( set_difference @ sK1_A @ sK2_SY42 )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(168,plain,
! [SV37: $i,SV32: $i,SV20: $i] :
( ( ~ ~ ( ~ ( subset @ SV20 @ SV32 )
| ~ ( subset @ SV20 @ SV37 ) )
| ( subset @ SV20 @ ( set_intersection2 @ SV32 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(169,plain,
! [SV24: $i,SV9: $i] :
( ( ~ ( ( SV9 != SV24 )
| ~ ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(170,plain,
! [SV24: $i,SV9: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) )
| ( SV9 = SV24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[155]) ).
thf(171,plain,
! [SV25: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV25 )
= $false )
| ( ( ( set_intersection2 @ SV10 @ SV25 )
= SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(172,plain,
! [SV26: $i,SV11: $i,SV33: $i] :
( ( ~ ( ( SV33
!= ( set_difference @ SV11 @ SV26 ) )
| ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SV33 )
| ~ ( ~ ( in @ SY75 @ SV11 )
| ~ ~ ( in @ SY75 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY75 @ SV11 )
| ~ ~ ( in @ SY75 @ SV26 ) )
| ( in @ SY75 @ SV33 ) ) ) )
| ~ ( ~ ! [SY76: $i] :
~ ( ~ ( ~ ( in @ SY76 @ SV33 )
| ~ ( ~ ( in @ SY76 @ SV11 )
| ~ ~ ( in @ SY76 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY76 @ SV11 )
| ~ ~ ( in @ SY76 @ SV26 ) )
| ( in @ SY76 @ SV33 ) ) )
| ( SV33
= ( set_difference @ SV11 @ SV26 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(173,plain,
! [SV34: $i,SV27: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV12 @ SV27 )
| ~ ( subset @ SV34 @ SV27 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV12 @ SV34 ) @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(174,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ( ~ ( subset @ SV13 @ SV28 )
| ! [SY70: $i] :
( ~ ( in @ SY70 @ SV13 )
| ( in @ SY70 @ SV28 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(175,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ( ~ ! [SY71: $i] :
( ~ ( in @ SY71 @ SV13 )
| ( in @ SY71 @ SV28 ) )
| ( subset @ SV13 @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(176,plain,
! [SV35: $i,SV29: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV15 @ SV29 )
| ~ ( subset @ SV29 @ SV35 ) ) )
= $true )
| ( ( subset @ SV15 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(177,plain,
! [SV30: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV30 )
= $false )
| ( ( ( set_union2 @ SV16 @ SV30 )
= SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(178,plain,
! [SV17: $i] :
( ( ( SV17 != empty_set )
| ! [SY60: $i] :
~ ( in @ SY60 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(179,plain,
! [SV17: $i] :
( ( ~ ! [SY61: $i] :
~ ( in @ SY61 @ SV17 )
| ( SV17 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(180,plain,
! [SV36: $i,SV31: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV31 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV18 @ SV36 ) @ ( set_intersection2 @ SV31 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(181,plain,
! [SV37: $i,SV32: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV20 @ SV32 )
| ~ ( subset @ SV20 @ SV37 ) ) )
= $true )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV32 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(182,plain,
! [SV24: $i,SV9: $i] :
( ( ( SV9 != SV24 )
| ~ ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(183,plain,
! [SV24: $i,SV9: $i] :
( ( ~ ~ ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) )
| ( SV9 = SV24 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[170]) ).
thf(184,plain,
! [SV26: $i,SV11: $i,SV33: $i] :
( ( ~ ( ( SV33
!= ( set_difference @ SV11 @ SV26 ) )
| ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SV33 )
| ~ ( ~ ( in @ SY75 @ SV11 )
| ~ ~ ( in @ SY75 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY75 @ SV11 )
| ~ ~ ( in @ SY75 @ SV26 ) )
| ( in @ SY75 @ SV33 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(185,plain,
! [SV26: $i,SV11: $i,SV33: $i] :
( ( ~ ( ~ ! [SY76: $i] :
~ ( ~ ( ~ ( in @ SY76 @ SV33 )
| ~ ( ~ ( in @ SY76 @ SV11 )
| ~ ~ ( in @ SY76 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY76 @ SV11 )
| ~ ~ ( in @ SY76 @ SV26 ) )
| ( in @ SY76 @ SV33 ) ) )
| ( SV33
= ( set_difference @ SV11 @ SV26 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(186,plain,
! [SV34: $i,SV27: $i,SV12: $i] :
( ( ( ~ ( ~ ( subset @ SV12 @ SV27 )
| ~ ( subset @ SV34 @ SV27 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV12 @ SV34 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(187,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ( subset @ SV13 @ SV28 )
| ! [SY70: $i] :
( ~ ( in @ SY70 @ SV13 )
| ( in @ SY70 @ SV28 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(188,plain,
! [SV28: $i,SV13: $i] :
( ( ~ ! [SY71: $i] :
( ~ ( in @ SY71 @ SV13 )
| ( in @ SY71 @ SV28 ) )
| ( subset @ SV13 @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(189,plain,
! [SV35: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( ~ ( subset @ SV15 @ SV29 )
| ~ ( subset @ SV29 @ SV35 ) ) )
= $false )
| ( ( subset @ SV15 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(190,plain,
! [SV17: $i] :
( ( ( SV17 != empty_set )
= $true )
| ( ( ! [SY60: $i] :
~ ( in @ SY60 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(191,plain,
! [SV17: $i] :
( ( ( ~ ! [SY61: $i] :
~ ( in @ SY61 @ SV17 ) )
= $true )
| ( ( SV17 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(192,plain,
! [SV36: $i,SV31: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV31 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV18 @ SV36 ) @ ( set_intersection2 @ SV31 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(193,plain,
! [SV37: $i,SV32: $i,SV20: $i] :
( ( ( ~ ( ~ ( subset @ SV20 @ SV32 )
| ~ ( subset @ SV20 @ SV37 ) ) )
= $false )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV32 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(194,plain,
! [SV24: $i,SV9: $i] :
( ( ( SV9 != SV24 )
= $true )
| ( ( ~ ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(195,plain,
! [SV24: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) ) )
= $true )
| ( ( SV9 = SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(196,plain,
! [SV26: $i,SV11: $i,SV33: $i] :
( ( ( SV33
!= ( set_difference @ SV11 @ SV26 ) )
| ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SV33 )
| ~ ( ~ ( in @ SY75 @ SV11 )
| ~ ~ ( in @ SY75 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY75 @ SV11 )
| ~ ~ ( in @ SY75 @ SV26 ) )
| ( in @ SY75 @ SV33 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(197,plain,
! [SV26: $i,SV11: $i,SV33: $i] :
( ( ~ ! [SY76: $i] :
~ ( ~ ( ~ ( in @ SY76 @ SV33 )
| ~ ( ~ ( in @ SY76 @ SV11 )
| ~ ~ ( in @ SY76 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY76 @ SV11 )
| ~ ~ ( in @ SY76 @ SV26 ) )
| ( in @ SY76 @ SV33 ) ) )
| ( SV33
= ( set_difference @ SV11 @ SV26 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(198,plain,
! [SV34: $i,SV27: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV27 )
| ~ ( subset @ SV34 @ SV27 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV12 @ SV34 ) @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(199,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV28 ) )
= $true )
| ( ( ! [SY70: $i] :
( ~ ( in @ SY70 @ SV13 )
| ( in @ SY70 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(200,plain,
! [SV28: $i,SV13: $i] :
( ( ( ~ ! [SY71: $i] :
( ~ ( in @ SY71 @ SV13 )
| ( in @ SY71 @ SV28 ) ) )
= $true )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(201,plain,
! [SV35: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV29 )
| ~ ( subset @ SV29 @ SV35 ) )
= $true )
| ( ( subset @ SV15 @ SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(202,plain,
! [SV17: $i] :
( ( ( SV17 = empty_set )
= $false )
| ( ( ! [SY60: $i] :
~ ( in @ SY60 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(203,plain,
! [SV17: $i] :
( ( ( ! [SY61: $i] :
~ ( in @ SY61 @ SV17 ) )
= $false )
| ( ( SV17 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(204,plain,
! [SV37: $i,SV32: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV32 )
| ~ ( subset @ SV20 @ SV37 ) )
= $true )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV32 @ SV37 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(205,plain,
! [SV24: $i,SV9: $i] :
( ( ( SV9 = SV24 )
= $false )
| ( ( ~ ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(206,plain,
! [SV24: $i,SV9: $i] :
( ( ( ~ ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) ) )
= $false )
| ( ( SV9 = SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(207,plain,
! [SV26: $i,SV11: $i,SV33: $i] :
( ( ( SV33
!= ( set_difference @ SV11 @ SV26 ) )
= $true )
| ( ( ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SV33 )
| ~ ( ~ ( in @ SY75 @ SV11 )
| ~ ~ ( in @ SY75 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY75 @ SV11 )
| ~ ~ ( in @ SY75 @ SV26 ) )
| ( in @ SY75 @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(208,plain,
! [SV26: $i,SV11: $i,SV33: $i] :
( ( ( ~ ! [SY76: $i] :
~ ( ~ ( ~ ( in @ SY76 @ SV33 )
| ~ ( ~ ( in @ SY76 @ SV11 )
| ~ ~ ( in @ SY76 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY76 @ SV11 )
| ~ ~ ( in @ SY76 @ SV26 ) )
| ( in @ SY76 @ SV33 ) ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(209,plain,
! [SV34: $i,SV27: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV27 ) )
= $true )
| ( ( ~ ( subset @ SV34 @ SV27 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV12 @ SV34 ) @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(210,plain,
! [SV28: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV28 )
= $false )
| ( ( ! [SY70: $i] :
( ~ ( in @ SY70 @ SV13 )
| ( in @ SY70 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(211,plain,
! [SV28: $i,SV13: $i] :
( ( ( ! [SY71: $i] :
( ~ ( in @ SY71 @ SV13 )
| ( in @ SY71 @ SV28 ) ) )
= $false )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(212,plain,
! [SV35: $i,SV29: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV29 ) )
= $true )
| ( ( ~ ( subset @ SV29 @ SV35 ) )
= $true )
| ( ( subset @ SV15 @ SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(213,plain,
! [SV17: $i,SV38: $i] :
( ( ( ~ ( in @ SV38 @ SV17 ) )
= $true )
| ( ( SV17 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(214,plain,
! [SV17: $i] :
( ( ( ~ ( in @ ( sK3_SY61 @ SV17 ) @ SV17 ) )
= $false )
| ( ( SV17 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[203]) ).
thf(215,plain,
! [SV37: $i,SV32: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV32 ) )
= $true )
| ( ( ~ ( subset @ SV20 @ SV37 ) )
= $true )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV32 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(216,plain,
! [SV24: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) )
= $false )
| ( ( SV9 = SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(217,plain,
! [SV24: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV24 )
| ~ ( subset @ SV24 @ SV9 ) )
= $true )
| ( ( SV9 = SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(218,plain,
! [SV26: $i,SV11: $i,SV33: $i] :
( ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false )
| ( ( ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SV33 )
| ~ ( ~ ( in @ SY75 @ SV11 )
| ~ ~ ( in @ SY75 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY75 @ SV11 )
| ~ ~ ( in @ SY75 @ SV26 ) )
| ( in @ SY75 @ SV33 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(219,plain,
! [SV26: $i,SV11: $i,SV33: $i] :
( ( ( ! [SY76: $i] :
~ ( ~ ( ~ ( in @ SY76 @ SV33 )
| ~ ( ~ ( in @ SY76 @ SV11 )
| ~ ~ ( in @ SY76 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY76 @ SV11 )
| ~ ~ ( in @ SY76 @ SV26 ) )
| ( in @ SY76 @ SV33 ) ) ) )
= $false )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(220,plain,
! [SV34: $i,SV27: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV27 )
= $false )
| ( ( ~ ( subset @ SV34 @ SV27 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV12 @ SV34 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(221,plain,
! [SV28: $i,SV13: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ SV13 )
| ( in @ SV39 @ SV28 ) )
= $true )
| ( ( subset @ SV13 @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(222,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK4_SY71 @ SV28 @ SV13 ) @ SV13 )
| ( in @ ( sK4_SY71 @ SV28 @ SV13 ) @ SV28 ) )
= $false )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[211]) ).
thf(223,plain,
! [SV35: $i,SV29: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV29 )
= $false )
| ( ( ~ ( subset @ SV29 @ SV35 ) )
= $true )
| ( ( subset @ SV15 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(224,plain,
! [SV17: $i,SV38: $i] :
( ( ( in @ SV38 @ SV17 )
= $false )
| ( ( SV17 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(225,plain,
! [SV17: $i] :
( ( ( in @ ( sK3_SY61 @ SV17 ) @ SV17 )
= $true )
| ( ( SV17 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(226,plain,
! [SV37: $i,SV32: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV32 )
= $false )
| ( ( ~ ( subset @ SV20 @ SV37 ) )
= $true )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV32 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(227,plain,
! [SV24: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV24 ) )
= $false )
| ( ( SV9 = SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(228,plain,
! [SV9: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV9 ) )
= $false )
| ( ( SV9 = SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(229,plain,
! [SV24: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV24 ) )
= $true )
| ( ( ~ ( subset @ SV24 @ SV9 ) )
= $true )
| ( ( SV9 = SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(230,plain,
! [SV26: $i,SV11: $i,SV33: $i,SV40: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV40 @ SV33 )
| ~ ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) )
| ( in @ SV40 @ SV33 ) ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(231,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
| ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) ) ) )
= $false )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[219]) ).
thf(232,plain,
! [SV12: $i,SV27: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV27 )
= $false )
| ( ( subset @ SV12 @ SV27 )
= $false )
| ( ( subset @ ( set_union2 @ SV12 @ SV34 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(233,plain,
! [SV28: $i,SV13: $i,SV39: $i] :
( ( ( ~ ( in @ SV39 @ SV13 ) )
= $true )
| ( ( in @ SV39 @ SV28 )
= $true )
| ( ( subset @ SV13 @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(234,plain,
! [SV13: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK4_SY71 @ SV28 @ SV13 ) @ SV13 ) )
= $false )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(235,plain,
! [SV13: $i,SV28: $i] :
( ( ( in @ ( sK4_SY71 @ SV28 @ SV13 ) @ SV28 )
= $false )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(236,plain,
! [SV15: $i,SV35: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV35 )
= $false )
| ( ( subset @ SV15 @ SV29 )
= $false )
| ( ( subset @ SV15 @ SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(237,plain,
! [SV32: $i,SV37: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV37 )
= $false )
| ( ( subset @ SV20 @ SV32 )
= $false )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV32 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(238,plain,
! [SV24: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV24 )
= $true )
| ( ( SV9 = SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(239,plain,
! [SV9: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV9 )
= $true )
| ( ( SV9 = SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(240,plain,
! [SV24: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV24 )
= $false )
| ( ( ~ ( subset @ SV24 @ SV9 ) )
= $true )
| ( ( SV9 = SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(241,plain,
! [SV26: $i,SV11: $i,SV33: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ SV40 @ SV33 )
| ~ ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) )
| ( in @ SV40 @ SV33 ) ) )
= $false )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(242,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
| ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(243,plain,
! [SV28: $i,SV13: $i,SV39: $i] :
( ( ( in @ SV39 @ SV13 )
= $false )
| ( ( in @ SV39 @ SV28 )
= $true )
| ( ( subset @ SV13 @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(244,plain,
! [SV13: $i,SV28: $i] :
( ( ( in @ ( sK4_SY71 @ SV28 @ SV13 ) @ SV13 )
= $true )
| ( ( subset @ SV13 @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(245,plain,
! [SV9: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV9 )
= $false )
| ( ( subset @ SV9 @ SV24 )
= $false )
| ( ( SV9 = SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(246,plain,
! [SV26: $i,SV11: $i,SV33: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ SV40 @ SV33 )
| ~ ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) ) ) )
= $false )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(247,plain,
! [SV33: $i,SV26: $i,SV11: $i,SV40: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) )
| ( in @ SV40 @ SV33 ) ) )
= $false )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(248,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
| ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(249,plain,
! [SV26: $i,SV11: $i,SV33: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV33 )
| ~ ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(250,plain,
! [SV33: $i,SV26: $i,SV11: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) )
| ( in @ SV40 @ SV33 ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(251,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
| ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(252,plain,
! [SV26: $i,SV11: $i,SV33: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV33 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(253,plain,
! [SV33: $i,SV26: $i,SV11: $i,SV40: $i] :
( ( ( ~ ~ ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) ) )
= $true )
| ( ( in @ SV40 @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(254,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(255,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(256,plain,
! [SV26: $i,SV11: $i,SV33: $i,SV40: $i] :
( ( ( in @ SV40 @ SV33 )
= $false )
| ( ( ~ ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(257,plain,
! [SV33: $i,SV26: $i,SV11: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) ) )
= $false )
| ( ( in @ SV40 @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(258,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(259,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(260,plain,
! [SV33: $i,SV26: $i,SV11: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) )
= $false )
| ( ( in @ SV40 @ SV33 )
= $false )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(261,plain,
! [SV33: $i,SV26: $i,SV11: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV11 )
| ~ ~ ( in @ SV40 @ SV26 ) )
= $true )
| ( ( in @ SV40 @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(262,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(263,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(264,plain,
! [SV26: $i,SV33: $i,SV11: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV11 ) )
= $false )
| ( ( in @ SV40 @ SV33 )
= $false )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(265,plain,
! [SV11: $i,SV33: $i,SV26: $i,SV40: $i] :
( ( ( ~ ~ ( in @ SV40 @ SV26 ) )
= $false )
| ( ( in @ SV40 @ SV33 )
= $false )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(266,plain,
! [SV33: $i,SV26: $i,SV11: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV11 ) )
= $true )
| ( ( ~ ~ ( in @ SV40 @ SV26 ) )
= $true )
| ( ( in @ SV40 @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(267,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) ) )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(268,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(269,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(270,plain,
! [SV26: $i,SV33: $i,SV11: $i,SV40: $i] :
( ( ( in @ SV40 @ SV11 )
= $true )
| ( ( in @ SV40 @ SV33 )
= $false )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(271,plain,
! [SV11: $i,SV33: $i,SV26: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV26 ) )
= $true )
| ( ( in @ SV40 @ SV33 )
= $false )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(272,plain,
! [SV33: $i,SV26: $i,SV11: $i,SV40: $i] :
( ( ( in @ SV40 @ SV11 )
= $false )
| ( ( ~ ~ ( in @ SV40 @ SV26 ) )
= $true )
| ( ( in @ SV40 @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(273,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) ) )
= $true )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(274,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(275,plain,
! [SV11: $i,SV33: $i,SV26: $i,SV40: $i] :
( ( ( in @ SV40 @ SV26 )
= $false )
| ( ( in @ SV40 @ SV33 )
= $false )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(276,plain,
! [SV33: $i,SV11: $i,SV26: $i,SV40: $i] :
( ( ( ~ ( in @ SV40 @ SV26 ) )
= $false )
| ( ( in @ SV40 @ SV11 )
= $false )
| ( ( in @ SV40 @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(277,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(278,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $true )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) ) )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(279,plain,
! [SV33: $i,SV11: $i,SV26: $i,SV40: $i] :
( ( ( in @ SV40 @ SV26 )
= $true )
| ( ( in @ SV40 @ SV11 )
= $false )
| ( ( in @ SV40 @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(280,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(281,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(282,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
| ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 ) )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(283,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $true )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(284,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
= $true )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(285,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) ) )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(286,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(287,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV33 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(288,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) ) )
= $true )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(289,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
| ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(290,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 ) )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(291,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(292,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $true )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(293,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 ) )
= $true )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(294,plain,
! [SV33: $i,SV11: $i,SV26: $i] :
( ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV11 )
= $false )
| ( ( in @ ( sK5_SY76 @ SV26 @ SV11 @ SV33 ) @ SV26 )
= $true )
| ( ( SV33
= ( set_difference @ SV11 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(295,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[92,294,292,287,286,283,279,275,270,268,245,244,243,239,238,237,236,235,232,225,224,192,177,171,167,166,160,153,140,139,138,124,123,122,121,118,96,95,94,93]) ).
thf(296,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(297,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(298,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(299,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(300,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(301,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(302,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(303,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(304,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(305,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(306,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(307,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(308,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(309,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(310,plain,
$true = $true,
inference(copy,[status(thm)],[57]) ).
thf(311,plain,
$true = $true,
inference(copy,[status(thm)],[56]) ).
thf(312,plain,
$true = $true,
inference(copy,[status(thm)],[55]) ).
thf(313,plain,
$true = $true,
inference(copy,[status(thm)],[54]) ).
thf(314,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(315,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(316,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(317,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(318,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(319,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(320,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(321,plain,
( ( ~ ( ( subset @ sK1_A @ sK2_SY42 )
=> ( ( set_difference @ sK1_A @ sK2_SY42 )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(322,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)],[300]) ).
thf(323,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(324,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( set_difference @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( set_difference @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(325,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)],[298]) ).
thf(326,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(327,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)],[307]) ).
thf(328,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(329,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)],[306]) ).
thf(330,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(331,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)],[308]) ).
thf(332,plain,
( ( ~ ( ~ ( subset @ sK1_A @ sK2_SY42 )
| ( ( set_difference @ sK1_A @ sK2_SY42 )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(333,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(334,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)],[305]) ).
thf(335,plain,
! [SV41: $i] :
( ( ! [SY77: $i] : ( subset @ ( set_intersection2 @ SV41 @ SY77 ) @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(336,plain,
! [SV42: $i] :
( ( subset @ empty_set @ SV42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(337,plain,
! [SV43: $i] :
( ( ! [SY78: $i] : ( subset @ SV43 @ ( set_union2 @ SV43 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(338,plain,
! [SV44: $i] :
( ( ! [SY79: $i] : ( subset @ SV44 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(339,plain,
! [SV45: $i] :
( ( ( set_union2 @ SV45 @ empty_set )
= SV45 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(340,plain,
! [SV46: $i] :
( ( ( set_intersection2 @ SV46 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(341,plain,
! [SV47: $i] :
( ( ( set_difference @ SV47 @ empty_set )
= SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(342,plain,
! [SV48: $i] :
( ( ( set_difference @ empty_set @ SV48 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(343,plain,
! [SV49: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ~ ( subset @ SV49 @ SY80 )
| ( subset @ ( set_intersection2 @ SV49 @ SY81 ) @ ( set_intersection2 @ SY80 @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(344,plain,
! [SV50: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ~ ~ ( ~ ( subset @ SV50 @ SY82 )
| ~ ( subset @ SY82 @ SY83 ) )
| ( subset @ SV50 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(345,plain,
! [SV51: $i] :
( ( ! [SY84: $i,SY85: $i] :
~ ( ~ ( ( SY85
!= ( set_difference @ SV51 @ SY84 ) )
| ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ SY85 )
| ~ ( ~ ( in @ SY86 @ SV51 )
| ~ ~ ( in @ SY86 @ SY84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY86 @ SV51 )
| ~ ~ ( in @ SY86 @ SY84 ) )
| ( in @ SY86 @ SY85 ) ) ) )
| ~ ( ~ ! [SY87: $i] :
~ ( ~ ( ~ ( in @ SY87 @ SY85 )
| ~ ( ~ ( in @ SY87 @ SV51 )
| ~ ~ ( in @ SY87 @ SY84 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY87 @ SV51 )
| ~ ~ ( in @ SY87 @ SY84 ) )
| ( in @ SY87 @ SY85 ) ) )
| ( SY85
= ( set_difference @ SV51 @ SY84 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(346,plain,
! [SV52: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ~ ( ~ ( subset @ SV52 @ SY88 )
| ~ ( subset @ SV52 @ SY89 ) )
| ( subset @ SV52 @ ( set_intersection2 @ SY88 @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(347,plain,
! [SV53: $i] :
( ( ~ ( empty @ SV53 )
| ( SV53 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(348,plain,
! [SV54: $i] :
( ( ~ ( ~ ( ( SV54 != empty_set )
| ! [SY90: $i] :
~ ( in @ SY90 @ SV54 ) )
| ~ ( ~ ! [SY91: $i] :
~ ( in @ SY91 @ SV54 )
| ( SV54 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(349,plain,
! [SV55: $i] :
( ( ! [SY92: $i] :
( ~ ( subset @ SV55 @ SY92 )
| ( ( set_union2 @ SV55 @ SY92 )
= SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(350,plain,
! [SV56: $i] :
( ( ! [SY93: $i] :
~ ( ~ ( ( SV56 != SY93 )
| ~ ( ~ ( subset @ SV56 @ SY93 )
| ~ ( subset @ SY93 @ SV56 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV56 @ SY93 )
| ~ ( subset @ SY93 @ SV56 ) )
| ( SV56 = SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(351,plain,
! [SV57: $i] :
( ( ! [SY94: $i] :
( ~ ( subset @ SV57 @ SY94 )
| ( ( set_intersection2 @ SV57 @ SY94 )
= SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(352,plain,
! [SV58: $i] :
( ( ! [SY95: $i] :
~ ( ~ ( ~ ( subset @ SV58 @ SY95 )
| ! [SY96: $i] :
( ~ ( in @ SY96 @ SV58 )
| ( in @ SY96 @ SY95 ) ) )
| ~ ( ~ ! [SY97: $i] :
( ~ ( in @ SY97 @ SV58 )
| ( in @ SY97 @ SY95 ) )
| ( subset @ SV58 @ SY95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(353,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY42 )
| ( ( set_difference @ sK1_A @ sK2_SY42 )
= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(354,plain,
! [SV59: $i] :
( ( ~ ( subset @ SV59 @ empty_set )
| ( SV59 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(355,plain,
! [SV60: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ~ ~ ( ~ ( subset @ SV60 @ SY98 )
| ~ ( subset @ SY99 @ SY98 ) )
| ( subset @ ( set_union2 @ SV60 @ SY99 ) @ SY98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(356,plain,
! [SV61: $i,SV41: $i] :
( ( subset @ ( set_intersection2 @ SV41 @ SV61 ) @ SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(357,plain,
! [SV62: $i,SV43: $i] :
( ( subset @ SV43 @ ( set_union2 @ SV43 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(358,plain,
! [SV44: $i] :
( ( subset @ SV44 @ SV44 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(359,plain,
! [SV64: $i,SV49: $i] :
( ( ! [SY100: $i] :
( ~ ( subset @ SV49 @ SV64 )
| ( subset @ ( set_intersection2 @ SV49 @ SY100 ) @ ( set_intersection2 @ SV64 @ SY100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(360,plain,
! [SV65: $i,SV50: $i] :
( ( ! [SY101: $i] :
( ~ ~ ( ~ ( subset @ SV50 @ SV65 )
| ~ ( subset @ SV65 @ SY101 ) )
| ( subset @ SV50 @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(361,plain,
! [SV66: $i,SV51: $i] :
( ( ! [SY102: $i] :
~ ( ~ ( ( SY102
!= ( set_difference @ SV51 @ SV66 ) )
| ! [SY103: $i] :
~ ( ~ ( ~ ( in @ SY103 @ SY102 )
| ~ ( ~ ( in @ SY103 @ SV51 )
| ~ ~ ( in @ SY103 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY103 @ SV51 )
| ~ ~ ( in @ SY103 @ SV66 ) )
| ( in @ SY103 @ SY102 ) ) ) )
| ~ ( ~ ! [SY104: $i] :
~ ( ~ ( ~ ( in @ SY104 @ SY102 )
| ~ ( ~ ( in @ SY104 @ SV51 )
| ~ ~ ( in @ SY104 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY104 @ SV51 )
| ~ ~ ( in @ SY104 @ SV66 ) )
| ( in @ SY104 @ SY102 ) ) )
| ( SY102
= ( set_difference @ SV51 @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(362,plain,
! [SV67: $i,SV52: $i] :
( ( ! [SY105: $i] :
( ~ ~ ( ~ ( subset @ SV52 @ SV67 )
| ~ ( subset @ SV52 @ SY105 ) )
| ( subset @ SV52 @ ( set_intersection2 @ SV67 @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(363,plain,
! [SV53: $i] :
( ( ( ~ ( empty @ SV53 ) )
= $true )
| ( ( SV53 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(364,plain,
! [SV54: $i] :
( ( ~ ( ( SV54 != empty_set )
| ! [SY90: $i] :
~ ( in @ SY90 @ SV54 ) )
| ~ ( ~ ! [SY91: $i] :
~ ( in @ SY91 @ SV54 )
| ( SV54 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(365,plain,
! [SV68: $i,SV55: $i] :
( ( ~ ( subset @ SV55 @ SV68 )
| ( ( set_union2 @ SV55 @ SV68 )
= SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(366,plain,
! [SV69: $i,SV56: $i] :
( ( ~ ( ~ ( ( SV56 != SV69 )
| ~ ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) )
| ( SV56 = SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(367,plain,
! [SV70: $i,SV57: $i] :
( ( ~ ( subset @ SV57 @ SV70 )
| ( ( set_intersection2 @ SV57 @ SV70 )
= SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(368,plain,
! [SV71: $i,SV58: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV58 @ SV71 )
| ! [SY106: $i] :
( ~ ( in @ SY106 @ SV58 )
| ( in @ SY106 @ SV71 ) ) )
| ~ ( ~ ! [SY107: $i] :
( ~ ( in @ SY107 @ SV58 )
| ( in @ SY107 @ SV71 ) )
| ( subset @ SV58 @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(369,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY42 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(370,plain,
( ( ( set_difference @ sK1_A @ sK2_SY42 )
= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(371,plain,
! [SV59: $i] :
( ( ( ~ ( subset @ SV59 @ empty_set ) )
= $true )
| ( ( SV59 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(372,plain,
! [SV72: $i,SV60: $i] :
( ( ! [SY108: $i] :
( ~ ~ ( ~ ( subset @ SV60 @ SV72 )
| ~ ( subset @ SY108 @ SV72 ) )
| ( subset @ ( set_union2 @ SV60 @ SY108 ) @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(373,plain,
! [SV73: $i,SV64: $i,SV49: $i] :
( ( ~ ( subset @ SV49 @ SV64 )
| ( subset @ ( set_intersection2 @ SV49 @ SV73 ) @ ( set_intersection2 @ SV64 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(374,plain,
! [SV74: $i,SV65: $i,SV50: $i] :
( ( ~ ~ ( ~ ( subset @ SV50 @ SV65 )
| ~ ( subset @ SV65 @ SV74 ) )
| ( subset @ SV50 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(375,plain,
! [SV66: $i,SV51: $i,SV75: $i] :
( ( ~ ( ~ ( ( SV75
!= ( set_difference @ SV51 @ SV66 ) )
| ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SV75 )
| ~ ( ~ ( in @ SY109 @ SV51 )
| ~ ~ ( in @ SY109 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY109 @ SV51 )
| ~ ~ ( in @ SY109 @ SV66 ) )
| ( in @ SY109 @ SV75 ) ) ) )
| ~ ( ~ ! [SY110: $i] :
~ ( ~ ( ~ ( in @ SY110 @ SV75 )
| ~ ( ~ ( in @ SY110 @ SV51 )
| ~ ~ ( in @ SY110 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY110 @ SV51 )
| ~ ~ ( in @ SY110 @ SV66 ) )
| ( in @ SY110 @ SV75 ) ) )
| ( SV75
= ( set_difference @ SV51 @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(376,plain,
! [SV76: $i,SV67: $i,SV52: $i] :
( ( ~ ~ ( ~ ( subset @ SV52 @ SV67 )
| ~ ( subset @ SV52 @ SV76 ) )
| ( subset @ SV52 @ ( set_intersection2 @ SV67 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(377,plain,
! [SV53: $i] :
( ( ( empty @ SV53 )
= $false )
| ( ( SV53 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(378,plain,
! [SV54: $i] :
( ( ~ ( ( SV54 != empty_set )
| ! [SY90: $i] :
~ ( in @ SY90 @ SV54 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(379,plain,
! [SV54: $i] :
( ( ~ ( ~ ! [SY91: $i] :
~ ( in @ SY91 @ SV54 )
| ( SV54 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[364]) ).
thf(380,plain,
! [SV68: $i,SV55: $i] :
( ( ( ~ ( subset @ SV55 @ SV68 ) )
= $true )
| ( ( ( set_union2 @ SV55 @ SV68 )
= SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(381,plain,
! [SV69: $i,SV56: $i] :
( ( ~ ( ( SV56 != SV69 )
| ~ ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) )
| ( SV56 = SV69 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(382,plain,
! [SV70: $i,SV57: $i] :
( ( ( ~ ( subset @ SV57 @ SV70 ) )
= $true )
| ( ( ( set_intersection2 @ SV57 @ SV70 )
= SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(383,plain,
! [SV71: $i,SV58: $i] :
( ( ~ ( ~ ( subset @ SV58 @ SV71 )
| ! [SY106: $i] :
( ~ ( in @ SY106 @ SV58 )
| ( in @ SY106 @ SV71 ) ) )
| ~ ( ~ ! [SY107: $i] :
( ~ ( in @ SY107 @ SV58 )
| ( in @ SY107 @ SV71 ) )
| ( subset @ SV58 @ SV71 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(384,plain,
( ( subset @ sK1_A @ sK2_SY42 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(385,plain,
! [SV59: $i] :
( ( ( subset @ SV59 @ empty_set )
= $false )
| ( ( SV59 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(386,plain,
! [SV77: $i,SV72: $i,SV60: $i] :
( ( ~ ~ ( ~ ( subset @ SV60 @ SV72 )
| ~ ( subset @ SV77 @ SV72 ) )
| ( subset @ ( set_union2 @ SV60 @ SV77 ) @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(387,plain,
! [SV73: $i,SV64: $i,SV49: $i] :
( ( ( ~ ( subset @ SV49 @ SV64 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV49 @ SV73 ) @ ( set_intersection2 @ SV64 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(388,plain,
! [SV74: $i,SV65: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV50 @ SV65 )
| ~ ( subset @ SV65 @ SV74 ) ) )
= $true )
| ( ( subset @ SV50 @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(389,plain,
! [SV66: $i,SV51: $i,SV75: $i] :
( ( ~ ( ( SV75
!= ( set_difference @ SV51 @ SV66 ) )
| ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SV75 )
| ~ ( ~ ( in @ SY109 @ SV51 )
| ~ ~ ( in @ SY109 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY109 @ SV51 )
| ~ ~ ( in @ SY109 @ SV66 ) )
| ( in @ SY109 @ SV75 ) ) ) )
| ~ ( ~ ! [SY110: $i] :
~ ( ~ ( ~ ( in @ SY110 @ SV75 )
| ~ ( ~ ( in @ SY110 @ SV51 )
| ~ ~ ( in @ SY110 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY110 @ SV51 )
| ~ ~ ( in @ SY110 @ SV66 ) )
| ( in @ SY110 @ SV75 ) ) )
| ( SV75
= ( set_difference @ SV51 @ SV66 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(390,plain,
! [SV76: $i,SV67: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV52 @ SV67 )
| ~ ( subset @ SV52 @ SV76 ) ) )
= $true )
| ( ( subset @ SV52 @ ( set_intersection2 @ SV67 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(391,plain,
! [SV54: $i] :
( ( ( SV54 != empty_set )
| ! [SY90: $i] :
~ ( in @ SY90 @ SV54 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(392,plain,
! [SV54: $i] :
( ( ~ ! [SY91: $i] :
~ ( in @ SY91 @ SV54 )
| ( SV54 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(393,plain,
! [SV68: $i,SV55: $i] :
( ( ( subset @ SV55 @ SV68 )
= $false )
| ( ( ( set_union2 @ SV55 @ SV68 )
= SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(394,plain,
! [SV69: $i,SV56: $i] :
( ( ~ ( ( SV56 != SV69 )
| ~ ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(395,plain,
! [SV69: $i,SV56: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) )
| ( SV56 = SV69 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[381]) ).
thf(396,plain,
! [SV70: $i,SV57: $i] :
( ( ( subset @ SV57 @ SV70 )
= $false )
| ( ( ( set_intersection2 @ SV57 @ SV70 )
= SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(397,plain,
! [SV71: $i,SV58: $i] :
( ( ~ ( ~ ( subset @ SV58 @ SV71 )
| ! [SY106: $i] :
( ~ ( in @ SY106 @ SV58 )
| ( in @ SY106 @ SV71 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(398,plain,
! [SV71: $i,SV58: $i] :
( ( ~ ( ~ ! [SY107: $i] :
( ~ ( in @ SY107 @ SV58 )
| ( in @ SY107 @ SV71 ) )
| ( subset @ SV58 @ SV71 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(399,plain,
! [SV77: $i,SV72: $i,SV60: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV60 @ SV72 )
| ~ ( subset @ SV77 @ SV72 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV60 @ SV77 ) @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(400,plain,
! [SV73: $i,SV64: $i,SV49: $i] :
( ( ( subset @ SV49 @ SV64 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV49 @ SV73 ) @ ( set_intersection2 @ SV64 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(401,plain,
! [SV74: $i,SV65: $i,SV50: $i] :
( ( ( ~ ( ~ ( subset @ SV50 @ SV65 )
| ~ ( subset @ SV65 @ SV74 ) ) )
= $false )
| ( ( subset @ SV50 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(402,plain,
! [SV66: $i,SV51: $i,SV75: $i] :
( ( ~ ( ( SV75
!= ( set_difference @ SV51 @ SV66 ) )
| ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SV75 )
| ~ ( ~ ( in @ SY109 @ SV51 )
| ~ ~ ( in @ SY109 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY109 @ SV51 )
| ~ ~ ( in @ SY109 @ SV66 ) )
| ( in @ SY109 @ SV75 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(403,plain,
! [SV66: $i,SV51: $i,SV75: $i] :
( ( ~ ( ~ ! [SY110: $i] :
~ ( ~ ( ~ ( in @ SY110 @ SV75 )
| ~ ( ~ ( in @ SY110 @ SV51 )
| ~ ~ ( in @ SY110 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY110 @ SV51 )
| ~ ~ ( in @ SY110 @ SV66 ) )
| ( in @ SY110 @ SV75 ) ) )
| ( SV75
= ( set_difference @ SV51 @ SV66 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(404,plain,
! [SV76: $i,SV67: $i,SV52: $i] :
( ( ( ~ ( ~ ( subset @ SV52 @ SV67 )
| ~ ( subset @ SV52 @ SV76 ) ) )
= $false )
| ( ( subset @ SV52 @ ( set_intersection2 @ SV67 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(405,plain,
! [SV54: $i] :
( ( ( SV54 != empty_set )
= $true )
| ( ( ! [SY90: $i] :
~ ( in @ SY90 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(406,plain,
! [SV54: $i] :
( ( ( ~ ! [SY91: $i] :
~ ( in @ SY91 @ SV54 ) )
= $true )
| ( ( SV54 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(407,plain,
! [SV69: $i,SV56: $i] :
( ( ( SV56 != SV69 )
| ~ ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(408,plain,
! [SV69: $i,SV56: $i] :
( ( ~ ~ ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) )
| ( SV56 = SV69 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(409,plain,
! [SV71: $i,SV58: $i] :
( ( ~ ( subset @ SV58 @ SV71 )
| ! [SY106: $i] :
( ~ ( in @ SY106 @ SV58 )
| ( in @ SY106 @ SV71 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(410,plain,
! [SV71: $i,SV58: $i] :
( ( ~ ! [SY107: $i] :
( ~ ( in @ SY107 @ SV58 )
| ( in @ SY107 @ SV71 ) )
| ( subset @ SV58 @ SV71 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[398]) ).
thf(411,plain,
! [SV77: $i,SV72: $i,SV60: $i] :
( ( ( ~ ( ~ ( subset @ SV60 @ SV72 )
| ~ ( subset @ SV77 @ SV72 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV60 @ SV77 ) @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(412,plain,
! [SV74: $i,SV65: $i,SV50: $i] :
( ( ( ~ ( subset @ SV50 @ SV65 )
| ~ ( subset @ SV65 @ SV74 ) )
= $true )
| ( ( subset @ SV50 @ SV74 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(413,plain,
! [SV66: $i,SV51: $i,SV75: $i] :
( ( ( SV75
!= ( set_difference @ SV51 @ SV66 ) )
| ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SV75 )
| ~ ( ~ ( in @ SY109 @ SV51 )
| ~ ~ ( in @ SY109 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY109 @ SV51 )
| ~ ~ ( in @ SY109 @ SV66 ) )
| ( in @ SY109 @ SV75 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(414,plain,
! [SV66: $i,SV51: $i,SV75: $i] :
( ( ~ ! [SY110: $i] :
~ ( ~ ( ~ ( in @ SY110 @ SV75 )
| ~ ( ~ ( in @ SY110 @ SV51 )
| ~ ~ ( in @ SY110 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY110 @ SV51 )
| ~ ~ ( in @ SY110 @ SV66 ) )
| ( in @ SY110 @ SV75 ) ) )
| ( SV75
= ( set_difference @ SV51 @ SV66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(415,plain,
! [SV76: $i,SV67: $i,SV52: $i] :
( ( ( ~ ( subset @ SV52 @ SV67 )
| ~ ( subset @ SV52 @ SV76 ) )
= $true )
| ( ( subset @ SV52 @ ( set_intersection2 @ SV67 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(416,plain,
! [SV54: $i] :
( ( ( SV54 = empty_set )
= $false )
| ( ( ! [SY90: $i] :
~ ( in @ SY90 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(417,plain,
! [SV54: $i] :
( ( ( ! [SY91: $i] :
~ ( in @ SY91 @ SV54 ) )
= $false )
| ( ( SV54 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(418,plain,
! [SV69: $i,SV56: $i] :
( ( ( SV56 != SV69 )
= $true )
| ( ( ~ ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(419,plain,
! [SV69: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) ) )
= $true )
| ( ( SV56 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(420,plain,
! [SV71: $i,SV58: $i] :
( ( ( ~ ( subset @ SV58 @ SV71 ) )
= $true )
| ( ( ! [SY106: $i] :
( ~ ( in @ SY106 @ SV58 )
| ( in @ SY106 @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(421,plain,
! [SV71: $i,SV58: $i] :
( ( ( ~ ! [SY107: $i] :
( ~ ( in @ SY107 @ SV58 )
| ( in @ SY107 @ SV71 ) ) )
= $true )
| ( ( subset @ SV58 @ SV71 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(422,plain,
! [SV77: $i,SV72: $i,SV60: $i] :
( ( ( ~ ( subset @ SV60 @ SV72 )
| ~ ( subset @ SV77 @ SV72 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV60 @ SV77 ) @ SV72 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(423,plain,
! [SV74: $i,SV65: $i,SV50: $i] :
( ( ( ~ ( subset @ SV50 @ SV65 ) )
= $true )
| ( ( ~ ( subset @ SV65 @ SV74 ) )
= $true )
| ( ( subset @ SV50 @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(424,plain,
! [SV66: $i,SV51: $i,SV75: $i] :
( ( ( SV75
!= ( set_difference @ SV51 @ SV66 ) )
= $true )
| ( ( ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SV75 )
| ~ ( ~ ( in @ SY109 @ SV51 )
| ~ ~ ( in @ SY109 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY109 @ SV51 )
| ~ ~ ( in @ SY109 @ SV66 ) )
| ( in @ SY109 @ SV75 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(425,plain,
! [SV66: $i,SV51: $i,SV75: $i] :
( ( ( ~ ! [SY110: $i] :
~ ( ~ ( ~ ( in @ SY110 @ SV75 )
| ~ ( ~ ( in @ SY110 @ SV51 )
| ~ ~ ( in @ SY110 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY110 @ SV51 )
| ~ ~ ( in @ SY110 @ SV66 ) )
| ( in @ SY110 @ SV75 ) ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(426,plain,
! [SV76: $i,SV67: $i,SV52: $i] :
( ( ( ~ ( subset @ SV52 @ SV67 ) )
= $true )
| ( ( ~ ( subset @ SV52 @ SV76 ) )
= $true )
| ( ( subset @ SV52 @ ( set_intersection2 @ SV67 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(427,plain,
! [SV54: $i,SV78: $i] :
( ( ( ~ ( in @ SV78 @ SV54 ) )
= $true )
| ( ( SV54 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(428,plain,
! [SV54: $i] :
( ( ( ~ ( in @ ( sK6_SY91 @ SV54 ) @ SV54 ) )
= $false )
| ( ( SV54 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[417]) ).
thf(429,plain,
! [SV69: $i,SV56: $i] :
( ( ( SV56 = SV69 )
= $false )
| ( ( ~ ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(430,plain,
! [SV69: $i,SV56: $i] :
( ( ( ~ ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) ) )
= $false )
| ( ( SV56 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(431,plain,
! [SV71: $i,SV58: $i] :
( ( ( subset @ SV58 @ SV71 )
= $false )
| ( ( ! [SY106: $i] :
( ~ ( in @ SY106 @ SV58 )
| ( in @ SY106 @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(432,plain,
! [SV71: $i,SV58: $i] :
( ( ( ! [SY107: $i] :
( ~ ( in @ SY107 @ SV58 )
| ( in @ SY107 @ SV71 ) ) )
= $false )
| ( ( subset @ SV58 @ SV71 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(433,plain,
! [SV77: $i,SV72: $i,SV60: $i] :
( ( ( ~ ( subset @ SV60 @ SV72 ) )
= $true )
| ( ( ~ ( subset @ SV77 @ SV72 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV60 @ SV77 ) @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(434,plain,
! [SV74: $i,SV65: $i,SV50: $i] :
( ( ( subset @ SV50 @ SV65 )
= $false )
| ( ( ~ ( subset @ SV65 @ SV74 ) )
= $true )
| ( ( subset @ SV50 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(435,plain,
! [SV66: $i,SV51: $i,SV75: $i] :
( ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false )
| ( ( ! [SY109: $i] :
~ ( ~ ( ~ ( in @ SY109 @ SV75 )
| ~ ( ~ ( in @ SY109 @ SV51 )
| ~ ~ ( in @ SY109 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY109 @ SV51 )
| ~ ~ ( in @ SY109 @ SV66 ) )
| ( in @ SY109 @ SV75 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(436,plain,
! [SV66: $i,SV51: $i,SV75: $i] :
( ( ( ! [SY110: $i] :
~ ( ~ ( ~ ( in @ SY110 @ SV75 )
| ~ ( ~ ( in @ SY110 @ SV51 )
| ~ ~ ( in @ SY110 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY110 @ SV51 )
| ~ ~ ( in @ SY110 @ SV66 ) )
| ( in @ SY110 @ SV75 ) ) ) )
= $false )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(437,plain,
! [SV76: $i,SV67: $i,SV52: $i] :
( ( ( subset @ SV52 @ SV67 )
= $false )
| ( ( ~ ( subset @ SV52 @ SV76 ) )
= $true )
| ( ( subset @ SV52 @ ( set_intersection2 @ SV67 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(438,plain,
! [SV54: $i,SV78: $i] :
( ( ( in @ SV78 @ SV54 )
= $false )
| ( ( SV54 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(439,plain,
! [SV54: $i] :
( ( ( in @ ( sK6_SY91 @ SV54 ) @ SV54 )
= $true )
| ( ( SV54 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(440,plain,
! [SV69: $i,SV56: $i] :
( ( ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) )
= $false )
| ( ( SV56 = SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(441,plain,
! [SV69: $i,SV56: $i] :
( ( ( ~ ( subset @ SV56 @ SV69 )
| ~ ( subset @ SV69 @ SV56 ) )
= $true )
| ( ( SV56 = SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(442,plain,
! [SV71: $i,SV58: $i,SV79: $i] :
( ( ( ~ ( in @ SV79 @ SV58 )
| ( in @ SV79 @ SV71 ) )
= $true )
| ( ( subset @ SV58 @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(443,plain,
! [SV58: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK7_SY107 @ SV71 @ SV58 ) @ SV58 )
| ( in @ ( sK7_SY107 @ SV71 @ SV58 ) @ SV71 ) )
= $false )
| ( ( subset @ SV58 @ SV71 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[432]) ).
thf(444,plain,
! [SV77: $i,SV72: $i,SV60: $i] :
( ( ( subset @ SV60 @ SV72 )
= $false )
| ( ( ~ ( subset @ SV77 @ SV72 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV60 @ SV77 ) @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(445,plain,
! [SV50: $i,SV74: $i,SV65: $i] :
( ( ( subset @ SV65 @ SV74 )
= $false )
| ( ( subset @ SV50 @ SV65 )
= $false )
| ( ( subset @ SV50 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(446,plain,
! [SV66: $i,SV51: $i,SV75: $i,SV80: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV80 @ SV75 )
| ~ ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) )
| ( in @ SV80 @ SV75 ) ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(447,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
| ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) ) ) )
= $false )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[436]) ).
thf(448,plain,
! [SV67: $i,SV76: $i,SV52: $i] :
( ( ( subset @ SV52 @ SV76 )
= $false )
| ( ( subset @ SV52 @ SV67 )
= $false )
| ( ( subset @ SV52 @ ( set_intersection2 @ SV67 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(449,plain,
! [SV69: $i,SV56: $i] :
( ( ( ~ ( subset @ SV56 @ SV69 ) )
= $false )
| ( ( SV56 = SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(450,plain,
! [SV56: $i,SV69: $i] :
( ( ( ~ ( subset @ SV69 @ SV56 ) )
= $false )
| ( ( SV56 = SV69 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(451,plain,
! [SV69: $i,SV56: $i] :
( ( ( ~ ( subset @ SV56 @ SV69 ) )
= $true )
| ( ( ~ ( subset @ SV69 @ SV56 ) )
= $true )
| ( ( SV56 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(452,plain,
! [SV71: $i,SV58: $i,SV79: $i] :
( ( ( ~ ( in @ SV79 @ SV58 ) )
= $true )
| ( ( in @ SV79 @ SV71 )
= $true )
| ( ( subset @ SV58 @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(453,plain,
! [SV58: $i,SV71: $i] :
( ( ( ~ ( in @ ( sK7_SY107 @ SV71 @ SV58 ) @ SV58 ) )
= $false )
| ( ( subset @ SV58 @ SV71 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(454,plain,
! [SV58: $i,SV71: $i] :
( ( ( in @ ( sK7_SY107 @ SV71 @ SV58 ) @ SV71 )
= $false )
| ( ( subset @ SV58 @ SV71 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(455,plain,
! [SV60: $i,SV72: $i,SV77: $i] :
( ( ( subset @ SV77 @ SV72 )
= $false )
| ( ( subset @ SV60 @ SV72 )
= $false )
| ( ( subset @ ( set_union2 @ SV60 @ SV77 ) @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(456,plain,
! [SV66: $i,SV51: $i,SV75: $i,SV80: $i] :
( ( ( ~ ( ~ ( in @ SV80 @ SV75 )
| ~ ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) )
| ( in @ SV80 @ SV75 ) ) )
= $false )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(457,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
| ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(458,plain,
! [SV69: $i,SV56: $i] :
( ( ( subset @ SV56 @ SV69 )
= $true )
| ( ( SV56 = SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(459,plain,
! [SV56: $i,SV69: $i] :
( ( ( subset @ SV69 @ SV56 )
= $true )
| ( ( SV56 = SV69 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(460,plain,
! [SV69: $i,SV56: $i] :
( ( ( subset @ SV56 @ SV69 )
= $false )
| ( ( ~ ( subset @ SV69 @ SV56 ) )
= $true )
| ( ( SV56 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(461,plain,
! [SV71: $i,SV58: $i,SV79: $i] :
( ( ( in @ SV79 @ SV58 )
= $false )
| ( ( in @ SV79 @ SV71 )
= $true )
| ( ( subset @ SV58 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(462,plain,
! [SV58: $i,SV71: $i] :
( ( ( in @ ( sK7_SY107 @ SV71 @ SV58 ) @ SV58 )
= $true )
| ( ( subset @ SV58 @ SV71 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(463,plain,
! [SV66: $i,SV51: $i,SV75: $i,SV80: $i] :
( ( ( ~ ( ~ ( in @ SV80 @ SV75 )
| ~ ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) ) ) )
= $false )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(464,plain,
! [SV75: $i,SV66: $i,SV51: $i,SV80: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) )
| ( in @ SV80 @ SV75 ) ) )
= $false )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(465,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
| ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(466,plain,
! [SV56: $i,SV69: $i] :
( ( ( subset @ SV69 @ SV56 )
= $false )
| ( ( subset @ SV56 @ SV69 )
= $false )
| ( ( SV56 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(467,plain,
! [SV66: $i,SV51: $i,SV75: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV75 )
| ~ ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(468,plain,
! [SV75: $i,SV66: $i,SV51: $i,SV80: $i] :
( ( ( ~ ~ ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) )
| ( in @ SV80 @ SV75 ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(469,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
| ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(470,plain,
! [SV66: $i,SV51: $i,SV75: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV75 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(471,plain,
! [SV75: $i,SV66: $i,SV51: $i,SV80: $i] :
( ( ( ~ ~ ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) ) )
= $true )
| ( ( in @ SV80 @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(472,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(473,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(474,plain,
! [SV66: $i,SV51: $i,SV75: $i,SV80: $i] :
( ( ( in @ SV80 @ SV75 )
= $false )
| ( ( ~ ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(475,plain,
! [SV75: $i,SV66: $i,SV51: $i,SV80: $i] :
( ( ( ~ ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) ) )
= $false )
| ( ( in @ SV80 @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(476,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(477,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(478,plain,
! [SV75: $i,SV66: $i,SV51: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) )
= $false )
| ( ( in @ SV80 @ SV75 )
= $false )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(479,plain,
! [SV75: $i,SV66: $i,SV51: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV51 )
| ~ ~ ( in @ SV80 @ SV66 ) )
= $true )
| ( ( in @ SV80 @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(480,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(481,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(482,plain,
! [SV66: $i,SV75: $i,SV51: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV51 ) )
= $false )
| ( ( in @ SV80 @ SV75 )
= $false )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(483,plain,
! [SV51: $i,SV75: $i,SV66: $i,SV80: $i] :
( ( ( ~ ~ ( in @ SV80 @ SV66 ) )
= $false )
| ( ( in @ SV80 @ SV75 )
= $false )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(484,plain,
! [SV75: $i,SV66: $i,SV51: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV51 ) )
= $true )
| ( ( ~ ~ ( in @ SV80 @ SV66 ) )
= $true )
| ( ( in @ SV80 @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(485,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) ) )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(486,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(487,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(488,plain,
! [SV66: $i,SV75: $i,SV51: $i,SV80: $i] :
( ( ( in @ SV80 @ SV51 )
= $true )
| ( ( in @ SV80 @ SV75 )
= $false )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(489,plain,
! [SV51: $i,SV75: $i,SV66: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV66 ) )
= $true )
| ( ( in @ SV80 @ SV75 )
= $false )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(490,plain,
! [SV75: $i,SV66: $i,SV51: $i,SV80: $i] :
( ( ( in @ SV80 @ SV51 )
= $false )
| ( ( ~ ~ ( in @ SV80 @ SV66 ) )
= $true )
| ( ( in @ SV80 @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(491,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) ) )
= $true )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(492,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(493,plain,
! [SV51: $i,SV75: $i,SV66: $i,SV80: $i] :
( ( ( in @ SV80 @ SV66 )
= $false )
| ( ( in @ SV80 @ SV75 )
= $false )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(494,plain,
! [SV75: $i,SV51: $i,SV66: $i,SV80: $i] :
( ( ( ~ ( in @ SV80 @ SV66 ) )
= $false )
| ( ( in @ SV80 @ SV51 )
= $false )
| ( ( in @ SV80 @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(495,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(496,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $true )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) ) )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(497,plain,
! [SV75: $i,SV51: $i,SV66: $i,SV80: $i] :
( ( ( in @ SV80 @ SV66 )
= $true )
| ( ( in @ SV80 @ SV51 )
= $false )
| ( ( in @ SV80 @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(498,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 ) )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(499,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[495]) ).
thf(500,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
| ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 ) )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(501,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $true )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(502,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
= $true )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(503,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) ) )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(504,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(505,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV75 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(506,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) ) )
= $true )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(507,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
| ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(508,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 ) )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(509,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(510,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $true )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(511,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( ~ ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 ) )
= $true )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(512,plain,
! [SV75: $i,SV51: $i,SV66: $i] :
( ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV51 )
= $false )
| ( ( in @ ( sK8_SY110 @ SV66 @ SV51 @ SV75 ) @ SV66 )
= $true )
| ( ( SV75
= ( set_difference @ SV51 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(513,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[310,512,510,505,504,501,497,493,488,486,466,462,461,459,458,455,454,448,445,439,438,400,396,393,385,384,377,370,358,357,356,342,341,340,339,336,314,313,312,311]) ).
thf(514,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[513,295]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU131+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:02:06 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.03/2.06
% 11.03/2.06 No.of.Axioms: 25
% 11.03/2.06
% 11.03/2.06 Length.of.Defs: 0
% 11.03/2.06
% 11.03/2.06 Contains.Choice.Funs: false
% 11.03/2.06 ...............
% 11.03/2.06
% 11.03/2.06 ********************************
% 11.03/2.06 * All subproblems solved! *
% 11.03/2.06 ********************************
% 11.03/2.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:25,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:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:513,loop_count:0,foatp_calls:1,translation:fof_full)
% 11.03/2.06
% 11.03/2.06 %**** Beginning of derivation protocol ****
% 11.03/2.06 % SZS output start CNFRefutation
% See solution above
% 11.03/2.06
% 11.03/2.06 %**** End of derivation protocol ****
% 11.03/2.06 %**** no. of clauses in derivation: 496 ****
% 11.03/2.06 %**** clause counter: 513 ****
% 11.03/2.06
% 11.03/2.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:25,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:298,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:513,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------