%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU134+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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:00 AM UTC 2026
% Result : Theorem 1.66s 0.48s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 30
% Syntax : Number of formulae : 576 ( 306 unt; 0 typ; 0 def)
% Number of atoms : 3679 (1359 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 7161 (1680 ~;1098 |; 20 &;4284 @)
% ( 33 <=>; 46 =>; 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 : 1381 ( 0 ^;1381 !; 0 ?;1381 :)
% 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_SY51,type,
sK2_SY51: $i ).
thf(tp_sK3_SY62,type,
sK3_SY62: $i > $i ).
thf(tp_sK4_SY85,type,
sK4_SY85: $i > $i > $i ).
thf(tp_sK5_SY91,type,
sK5_SY91: $i > $i > $i > $i ).
thf(tp_sK6_SY116,type,
sK6_SY116: $i > $i ).
thf(tp_sK7_SY129,type,
sK7_SY129: $i > $i > $i ).
thf(tp_sK8_SY131,type,
sK8_SY131: $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(22,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(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,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(39,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(41,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(42,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(43,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(44,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(47,conjecture,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(48,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[47]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[48]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(51,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(56,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(57,plain,
$true = $true,
inference(unfold_def,[status(thm)],[18]) ).
thf(58,plain,
$true = $true,
inference(unfold_def,[status(thm)],[19]) ).
thf(59,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(60,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(62,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(63,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(66,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(67,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(70,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(71,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(72,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(73,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)],[41]) ).
thf(74,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(75,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)],[43]) ).
thf(76,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(77,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(79,plain,
( ( ! [SY51: $i] :
( ( ( set_difference @ sK1_A @ SY51 )
= empty_set )
<=> ( subset @ sK1_A @ SY51 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[49]) ).
thf(80,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY51 )
= empty_set )
<=> ( subset @ sK1_A @ sK2_SY51 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[79]) ).
thf(81,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY51 )
= empty_set )
=> ( subset @ sK1_A @ sK2_SY51 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[80]) ).
thf(82,plain,
( ( ( subset @ sK1_A @ sK2_SY51 )
=> ( ( set_difference @ sK1_A @ sK2_SY51 )
= empty_set ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[80]) ).
thf(83,plain,
( ( ~ ( ( ( set_difference @ sK1_A @ sK2_SY51 )
= empty_set )
=> ( subset @ sK1_A @ sK2_SY51 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[81]) ).
thf(84,plain,
( ( ~ ( ( subset @ sK1_A @ sK2_SY51 )
=> ( ( set_difference @ sK1_A @ sK2_SY51 )
= empty_set ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[82]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(89,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(90,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(92,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(93,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(97,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(99,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(100,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(101,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)],[62]) ).
thf(102,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(103,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(104,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(105,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(106,plain,
$true = $true,
inference(copy,[status(thm)],[57]) ).
thf(107,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(109,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(110,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(111,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(112,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(113,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(114,plain,
( ( ~ ( ( ( set_difference @ sK1_A @ sK2_SY51 )
= empty_set )
=> ( subset @ sK1_A @ sK2_SY51 ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(115,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
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)],[88]) ).
thf(117,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(118,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_difference @ SX0 @ SX2 ) @ ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(119,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)],[99]) ).
thf(120,plain,
( ( ~ ( ( ( set_difference @ sK1_A @ sK2_SY51 )
!= empty_set )
| ( subset @ sK1_A @ sK2_SY51 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(121,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)],[97]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(123,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(124,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)],[90]) ).
thf(125,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)],[98]) ).
thf(126,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)],[100]) ).
thf(127,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(128,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)],[101]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(131,plain,
! [SV1: $i] :
( ( ! [SY52: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY52 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(132,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(133,plain,
! [SV3: $i] :
( ( ! [SY53: $i] : ( subset @ ( set_difference @ SV3 @ SY53 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(134,plain,
! [SV4: $i] :
( ( ! [SY54: $i] : ( subset @ SV4 @ ( set_union2 @ SV4 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(135,plain,
! [SV5: $i] :
( ( ! [SY55: $i] : ( subset @ SV5 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(136,plain,
! [SV6: $i] :
( ( ( set_union2 @ SV6 @ empty_set )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(137,plain,
! [SV7: $i] :
( ( ( set_intersection2 @ SV7 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(138,plain,
! [SV8: $i] :
( ( ( set_difference @ SV8 @ empty_set )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(139,plain,
! [SV9: $i] :
( ( ( set_difference @ empty_set @ SV9 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(140,plain,
! [SV10: $i] :
( ( ! [SY56: $i] :
( ~ ( subset @ SV10 @ SY56 )
| ( ( set_union2 @ SV10 @ SY56 )
= SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(141,plain,
! [SV11: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ~ ( ~ ( subset @ SV11 @ SY57 )
| ~ ( subset @ SV11 @ SY58 ) )
| ( subset @ SV11 @ ( set_intersection2 @ SY57 @ SY58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(142,plain,
! [SV12: $i] :
( ( ~ ( subset @ SV12 @ empty_set )
| ( SV12 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(143,plain,
! [SV13: $i] :
( ( ! [SY59: $i,SY60: $i] :
( ~ ( subset @ SV13 @ SY59 )
| ( subset @ ( set_difference @ SV13 @ SY60 ) @ ( set_difference @ SY59 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(144,plain,
! [SV14: $i] :
( ( ~ ( ~ ( ( SV14 != empty_set )
| ! [SY61: $i] :
~ ( in @ SY61 @ SV14 ) )
| ~ ( ~ ! [SY62: $i] :
~ ( in @ SY62 @ SV14 )
| ( SV14 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(145,plain,
( ( ( ( set_difference @ sK1_A @ sK2_SY51 )
!= empty_set )
| ( subset @ sK1_A @ sK2_SY51 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(146,plain,
! [SV15: $i] :
( ( ! [SY63: $i,SY64: $i] :
( ~ ~ ( ~ ( subset @ SV15 @ SY63 )
| ~ ( subset @ SY64 @ SY63 ) )
| ( subset @ ( set_union2 @ SV15 @ SY64 ) @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(147,plain,
! [SV16: $i] :
( ( ! [SY65: $i] :
( ~ ( subset @ SV16 @ SY65 )
| ( ( set_intersection2 @ SV16 @ SY65 )
= SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(148,plain,
! [SV17: $i] :
( ( ~ ( empty @ SV17 )
| ( SV17 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(149,plain,
! [SV18: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ( subset @ SV18 @ SY66 )
| ( subset @ ( set_intersection2 @ SV18 @ SY67 ) @ ( set_intersection2 @ SY66 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(150,plain,
! [SV19: $i] :
( ( ! [SY68: $i] :
~ ( ~ ( ( SV19 != SY68 )
| ~ ( ~ ( subset @ SV19 @ SY68 )
| ~ ( subset @ SY68 @ SV19 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV19 @ SY68 )
| ~ ( subset @ SY68 @ SV19 ) )
| ( SV19 = SY68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(151,plain,
! [SV20: $i] :
( ( ! [SY69: $i] :
~ ( ~ ( ~ ( subset @ SV20 @ SY69 )
| ! [SY70: $i] :
( ~ ( in @ SY70 @ SV20 )
| ( in @ SY70 @ SY69 ) ) )
| ~ ( ~ ! [SY71: $i] :
( ~ ( in @ SY71 @ SV20 )
| ( in @ SY71 @ SY69 ) )
| ( subset @ SV20 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(152,plain,
! [SV21: $i] :
( ( ! [SY72: $i] :
~ ( ~ ( ( ( set_difference @ SV21 @ SY72 )
!= empty_set )
| ( subset @ SV21 @ SY72 ) )
| ~ ( ~ ( subset @ SV21 @ SY72 )
| ( ( set_difference @ SV21 @ SY72 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(153,plain,
! [SV22: $i] :
( ( ! [SY73: $i,SY74: $i] :
~ ( ~ ( ( SY74
!= ( set_difference @ SV22 @ SY73 ) )
| ! [SY75: $i] :
~ ( ~ ( ~ ( in @ SY75 @ SY74 )
| ~ ( ~ ( in @ SY75 @ SV22 )
| ~ ~ ( in @ SY75 @ SY73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY75 @ SV22 )
| ~ ~ ( in @ SY75 @ SY73 ) )
| ( in @ SY75 @ SY74 ) ) ) )
| ~ ( ~ ! [SY76: $i] :
~ ( ~ ( ~ ( in @ SY76 @ SY74 )
| ~ ( ~ ( in @ SY76 @ SV22 )
| ~ ~ ( in @ SY76 @ SY73 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY76 @ SV22 )
| ~ ~ ( in @ SY76 @ SY73 ) )
| ( in @ SY76 @ SY74 ) ) )
| ( SY74
= ( set_difference @ SV22 @ SY73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(154,plain,
! [SV23: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ~ ~ ( ~ ( subset @ SV23 @ SY77 )
| ~ ( subset @ SY77 @ SY78 ) )
| ( subset @ SV23 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(155,plain,
! [SV24: $i] :
( ( ! [SY79: $i] :
~ ( ~ ( ~ ( disjoint @ SV24 @ SY79 )
| ( ( set_intersection2 @ SV24 @ SY79 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV24 @ SY79 )
!= empty_set )
| ( disjoint @ SV24 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(156,plain,
! [SV25: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV25 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(157,plain,
! [SV26: $i,SV3: $i] :
( ( subset @ ( set_difference @ SV3 @ SV26 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(158,plain,
! [SV27: $i,SV4: $i] :
( ( subset @ SV4 @ ( set_union2 @ SV4 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(159,plain,
! [SV5: $i] :
( ( subset @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(160,plain,
! [SV29: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV29 )
| ( ( set_union2 @ SV10 @ SV29 )
= SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(161,plain,
! [SV30: $i,SV11: $i] :
( ( ! [SY80: $i] :
( ~ ~ ( ~ ( subset @ SV11 @ SV30 )
| ~ ( subset @ SV11 @ SY80 ) )
| ( subset @ SV11 @ ( set_intersection2 @ SV30 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(162,plain,
! [SV12: $i] :
( ( ( ~ ( subset @ SV12 @ empty_set ) )
= $true )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(163,plain,
! [SV31: $i,SV13: $i] :
( ( ! [SY81: $i] :
( ~ ( subset @ SV13 @ SV31 )
| ( subset @ ( set_difference @ SV13 @ SY81 ) @ ( set_difference @ SV31 @ SY81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(164,plain,
! [SV14: $i] :
( ( ~ ( ( SV14 != empty_set )
| ! [SY61: $i] :
~ ( in @ SY61 @ SV14 ) )
| ~ ( ~ ! [SY62: $i] :
~ ( in @ SY62 @ SV14 )
| ( SV14 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(165,plain,
( ( ( set_difference @ sK1_A @ sK2_SY51 )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(166,plain,
( ( subset @ sK1_A @ sK2_SY51 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(167,plain,
! [SV32: $i,SV15: $i] :
( ( ! [SY82: $i] :
( ~ ~ ( ~ ( subset @ SV15 @ SV32 )
| ~ ( subset @ SY82 @ SV32 ) )
| ( subset @ ( set_union2 @ SV15 @ SY82 ) @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(168,plain,
! [SV33: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV33 )
| ( ( set_intersection2 @ SV16 @ SV33 )
= SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(169,plain,
! [SV17: $i] :
( ( ( ~ ( empty @ SV17 ) )
= $true )
| ( ( SV17 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(170,plain,
! [SV34: $i,SV18: $i] :
( ( ! [SY83: $i] :
( ~ ( subset @ SV18 @ SV34 )
| ( subset @ ( set_intersection2 @ SV18 @ SY83 ) @ ( set_intersection2 @ SV34 @ SY83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(171,plain,
! [SV35: $i,SV19: $i] :
( ( ~ ( ~ ( ( SV19 != SV35 )
| ~ ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) )
| ( SV19 = SV35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(172,plain,
! [SV36: $i,SV20: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV20 @ SV36 )
| ! [SY84: $i] :
( ~ ( in @ SY84 @ SV20 )
| ( in @ SY84 @ SV36 ) ) )
| ~ ( ~ ! [SY85: $i] :
( ~ ( in @ SY85 @ SV20 )
| ( in @ SY85 @ SV36 ) )
| ( subset @ SV20 @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(173,plain,
! [SV37: $i,SV21: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV21 @ SV37 )
!= empty_set )
| ( subset @ SV21 @ SV37 ) )
| ~ ( ~ ( subset @ SV21 @ SV37 )
| ( ( set_difference @ SV21 @ SV37 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(174,plain,
! [SV38: $i,SV22: $i] :
( ( ! [SY86: $i] :
~ ( ~ ( ( SY86
!= ( set_difference @ SV22 @ SV38 ) )
| ! [SY87: $i] :
~ ( ~ ( ~ ( in @ SY87 @ SY86 )
| ~ ( ~ ( in @ SY87 @ SV22 )
| ~ ~ ( in @ SY87 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY87 @ SV22 )
| ~ ~ ( in @ SY87 @ SV38 ) )
| ( in @ SY87 @ SY86 ) ) ) )
| ~ ( ~ ! [SY88: $i] :
~ ( ~ ( ~ ( in @ SY88 @ SY86 )
| ~ ( ~ ( in @ SY88 @ SV22 )
| ~ ~ ( in @ SY88 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY88 @ SV22 )
| ~ ~ ( in @ SY88 @ SV38 ) )
| ( in @ SY88 @ SY86 ) ) )
| ( SY86
= ( set_difference @ SV22 @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(175,plain,
! [SV39: $i,SV23: $i] :
( ( ! [SY89: $i] :
( ~ ~ ( ~ ( subset @ SV23 @ SV39 )
| ~ ( subset @ SV39 @ SY89 ) )
| ( subset @ SV23 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(176,plain,
! [SV40: $i,SV24: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV24 @ SV40 )
| ( ( set_intersection2 @ SV24 @ SV40 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV24 @ SV40 )
!= empty_set )
| ( disjoint @ SV24 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(177,plain,
! [SV29: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV29 ) )
= $true )
| ( ( ( set_union2 @ SV10 @ SV29 )
= SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(178,plain,
! [SV41: $i,SV30: $i,SV11: $i] :
( ( ~ ~ ( ~ ( subset @ SV11 @ SV30 )
| ~ ( subset @ SV11 @ SV41 ) )
| ( subset @ SV11 @ ( set_intersection2 @ SV30 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(179,plain,
! [SV12: $i] :
( ( ( subset @ SV12 @ empty_set )
= $false )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(180,plain,
! [SV42: $i,SV31: $i,SV13: $i] :
( ( ~ ( subset @ SV13 @ SV31 )
| ( subset @ ( set_difference @ SV13 @ SV42 ) @ ( set_difference @ SV31 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(181,plain,
! [SV14: $i] :
( ( ~ ( ( SV14 != empty_set )
| ! [SY61: $i] :
~ ( in @ SY61 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(182,plain,
! [SV14: $i] :
( ( ~ ( ~ ! [SY62: $i] :
~ ( in @ SY62 @ SV14 )
| ( SV14 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(183,plain,
( ( ( set_difference @ sK1_A @ sK2_SY51 )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(184,plain,
! [SV43: $i,SV32: $i,SV15: $i] :
( ( ~ ~ ( ~ ( subset @ SV15 @ SV32 )
| ~ ( subset @ SV43 @ SV32 ) )
| ( subset @ ( set_union2 @ SV15 @ SV43 ) @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(185,plain,
! [SV33: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV33 ) )
= $true )
| ( ( ( set_intersection2 @ SV16 @ SV33 )
= SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(186,plain,
! [SV17: $i] :
( ( ( empty @ SV17 )
= $false )
| ( ( SV17 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(187,plain,
! [SV44: $i,SV34: $i,SV18: $i] :
( ( ~ ( subset @ SV18 @ SV34 )
| ( subset @ ( set_intersection2 @ SV18 @ SV44 ) @ ( set_intersection2 @ SV34 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(188,plain,
! [SV35: $i,SV19: $i] :
( ( ~ ( ( SV19 != SV35 )
| ~ ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) )
| ( SV19 = SV35 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(189,plain,
! [SV36: $i,SV20: $i] :
( ( ~ ( ~ ( subset @ SV20 @ SV36 )
| ! [SY84: $i] :
( ~ ( in @ SY84 @ SV20 )
| ( in @ SY84 @ SV36 ) ) )
| ~ ( ~ ! [SY85: $i] :
( ~ ( in @ SY85 @ SV20 )
| ( in @ SY85 @ SV36 ) )
| ( subset @ SV20 @ SV36 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(190,plain,
! [SV37: $i,SV21: $i] :
( ( ~ ( ( ( set_difference @ SV21 @ SV37 )
!= empty_set )
| ( subset @ SV21 @ SV37 ) )
| ~ ( ~ ( subset @ SV21 @ SV37 )
| ( ( set_difference @ SV21 @ SV37 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(191,plain,
! [SV38: $i,SV22: $i,SV45: $i] :
( ( ~ ( ~ ( ( SV45
!= ( set_difference @ SV22 @ SV38 ) )
| ! [SY90: $i] :
~ ( ~ ( ~ ( in @ SY90 @ SV45 )
| ~ ( ~ ( in @ SY90 @ SV22 )
| ~ ~ ( in @ SY90 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY90 @ SV22 )
| ~ ~ ( in @ SY90 @ SV38 ) )
| ( in @ SY90 @ SV45 ) ) ) )
| ~ ( ~ ! [SY91: $i] :
~ ( ~ ( ~ ( in @ SY91 @ SV45 )
| ~ ( ~ ( in @ SY91 @ SV22 )
| ~ ~ ( in @ SY91 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY91 @ SV22 )
| ~ ~ ( in @ SY91 @ SV38 ) )
| ( in @ SY91 @ SV45 ) ) )
| ( SV45
= ( set_difference @ SV22 @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(192,plain,
! [SV46: $i,SV39: $i,SV23: $i] :
( ( ~ ~ ( ~ ( subset @ SV23 @ SV39 )
| ~ ( subset @ SV39 @ SV46 ) )
| ( subset @ SV23 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(193,plain,
! [SV40: $i,SV24: $i] :
( ( ~ ( ~ ( disjoint @ SV24 @ SV40 )
| ( ( set_intersection2 @ SV24 @ SV40 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV24 @ SV40 )
!= empty_set )
| ( disjoint @ SV24 @ SV40 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(194,plain,
! [SV29: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV29 )
= $false )
| ( ( ( set_union2 @ SV10 @ SV29 )
= SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(195,plain,
! [SV41: $i,SV30: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV11 @ SV30 )
| ~ ( subset @ SV11 @ SV41 ) ) )
= $true )
| ( ( subset @ SV11 @ ( set_intersection2 @ SV30 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(196,plain,
! [SV42: $i,SV31: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV31 ) )
= $true )
| ( ( subset @ ( set_difference @ SV13 @ SV42 ) @ ( set_difference @ SV31 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(197,plain,
! [SV14: $i] :
( ( ( SV14 != empty_set )
| ! [SY61: $i] :
~ ( in @ SY61 @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(198,plain,
! [SV14: $i] :
( ( ~ ! [SY62: $i] :
~ ( in @ SY62 @ SV14 )
| ( SV14 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(199,plain,
! [SV43: $i,SV32: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV15 @ SV32 )
| ~ ( subset @ SV43 @ SV32 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV15 @ SV43 ) @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(200,plain,
! [SV33: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV33 )
= $false )
| ( ( ( set_intersection2 @ SV16 @ SV33 )
= SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(201,plain,
! [SV44: $i,SV34: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV34 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV18 @ SV44 ) @ ( set_intersection2 @ SV34 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(202,plain,
! [SV35: $i,SV19: $i] :
( ( ~ ( ( SV19 != SV35 )
| ~ ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(203,plain,
! [SV35: $i,SV19: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) )
| ( SV19 = SV35 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(204,plain,
! [SV36: $i,SV20: $i] :
( ( ~ ( ~ ( subset @ SV20 @ SV36 )
| ! [SY84: $i] :
( ~ ( in @ SY84 @ SV20 )
| ( in @ SY84 @ SV36 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(205,plain,
! [SV36: $i,SV20: $i] :
( ( ~ ( ~ ! [SY85: $i] :
( ~ ( in @ SY85 @ SV20 )
| ( in @ SY85 @ SV36 ) )
| ( subset @ SV20 @ SV36 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(206,plain,
! [SV37: $i,SV21: $i] :
( ( ~ ( ( ( set_difference @ SV21 @ SV37 )
!= empty_set )
| ( subset @ SV21 @ SV37 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(207,plain,
! [SV37: $i,SV21: $i] :
( ( ~ ( ~ ( subset @ SV21 @ SV37 )
| ( ( set_difference @ SV21 @ SV37 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(208,plain,
! [SV38: $i,SV22: $i,SV45: $i] :
( ( ~ ( ( SV45
!= ( set_difference @ SV22 @ SV38 ) )
| ! [SY90: $i] :
~ ( ~ ( ~ ( in @ SY90 @ SV45 )
| ~ ( ~ ( in @ SY90 @ SV22 )
| ~ ~ ( in @ SY90 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY90 @ SV22 )
| ~ ~ ( in @ SY90 @ SV38 ) )
| ( in @ SY90 @ SV45 ) ) ) )
| ~ ( ~ ! [SY91: $i] :
~ ( ~ ( ~ ( in @ SY91 @ SV45 )
| ~ ( ~ ( in @ SY91 @ SV22 )
| ~ ~ ( in @ SY91 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY91 @ SV22 )
| ~ ~ ( in @ SY91 @ SV38 ) )
| ( in @ SY91 @ SV45 ) ) )
| ( SV45
= ( set_difference @ SV22 @ SV38 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(209,plain,
! [SV46: $i,SV39: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV23 @ SV39 )
| ~ ( subset @ SV39 @ SV46 ) ) )
= $true )
| ( ( subset @ SV23 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(210,plain,
! [SV40: $i,SV24: $i] :
( ( ~ ( ~ ( disjoint @ SV24 @ SV40 )
| ( ( set_intersection2 @ SV24 @ SV40 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(211,plain,
! [SV40: $i,SV24: $i] :
( ( ~ ( ( ( set_intersection2 @ SV24 @ SV40 )
!= empty_set )
| ( disjoint @ SV24 @ SV40 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(212,plain,
! [SV41: $i,SV30: $i,SV11: $i] :
( ( ( ~ ( ~ ( subset @ SV11 @ SV30 )
| ~ ( subset @ SV11 @ SV41 ) ) )
= $false )
| ( ( subset @ SV11 @ ( set_intersection2 @ SV30 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(213,plain,
! [SV42: $i,SV31: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV31 )
= $false )
| ( ( subset @ ( set_difference @ SV13 @ SV42 ) @ ( set_difference @ SV31 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(214,plain,
! [SV14: $i] :
( ( ( SV14 != empty_set )
= $true )
| ( ( ! [SY61: $i] :
~ ( in @ SY61 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(215,plain,
! [SV14: $i] :
( ( ( ~ ! [SY62: $i] :
~ ( in @ SY62 @ SV14 ) )
= $true )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(216,plain,
! [SV43: $i,SV32: $i,SV15: $i] :
( ( ( ~ ( ~ ( subset @ SV15 @ SV32 )
| ~ ( subset @ SV43 @ SV32 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV15 @ SV43 ) @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(217,plain,
! [SV44: $i,SV34: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV34 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV18 @ SV44 ) @ ( set_intersection2 @ SV34 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(218,plain,
! [SV35: $i,SV19: $i] :
( ( ( SV19 != SV35 )
| ~ ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(219,plain,
! [SV35: $i,SV19: $i] :
( ( ~ ~ ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) )
| ( SV19 = SV35 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(220,plain,
! [SV36: $i,SV20: $i] :
( ( ~ ( subset @ SV20 @ SV36 )
| ! [SY84: $i] :
( ~ ( in @ SY84 @ SV20 )
| ( in @ SY84 @ SV36 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(221,plain,
! [SV36: $i,SV20: $i] :
( ( ~ ! [SY85: $i] :
( ~ ( in @ SY85 @ SV20 )
| ( in @ SY85 @ SV36 ) )
| ( subset @ SV20 @ SV36 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(222,plain,
! [SV37: $i,SV21: $i] :
( ( ( ( set_difference @ SV21 @ SV37 )
!= empty_set )
| ( subset @ SV21 @ SV37 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(223,plain,
! [SV37: $i,SV21: $i] :
( ( ~ ( subset @ SV21 @ SV37 )
| ( ( set_difference @ SV21 @ SV37 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(224,plain,
! [SV38: $i,SV22: $i,SV45: $i] :
( ( ~ ( ( SV45
!= ( set_difference @ SV22 @ SV38 ) )
| ! [SY90: $i] :
~ ( ~ ( ~ ( in @ SY90 @ SV45 )
| ~ ( ~ ( in @ SY90 @ SV22 )
| ~ ~ ( in @ SY90 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY90 @ SV22 )
| ~ ~ ( in @ SY90 @ SV38 ) )
| ( in @ SY90 @ SV45 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(225,plain,
! [SV38: $i,SV22: $i,SV45: $i] :
( ( ~ ( ~ ! [SY91: $i] :
~ ( ~ ( ~ ( in @ SY91 @ SV45 )
| ~ ( ~ ( in @ SY91 @ SV22 )
| ~ ~ ( in @ SY91 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY91 @ SV22 )
| ~ ~ ( in @ SY91 @ SV38 ) )
| ( in @ SY91 @ SV45 ) ) )
| ( SV45
= ( set_difference @ SV22 @ SV38 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[208]) ).
thf(226,plain,
! [SV46: $i,SV39: $i,SV23: $i] :
( ( ( ~ ( ~ ( subset @ SV23 @ SV39 )
| ~ ( subset @ SV39 @ SV46 ) ) )
= $false )
| ( ( subset @ SV23 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(227,plain,
! [SV40: $i,SV24: $i] :
( ( ~ ( disjoint @ SV24 @ SV40 )
| ( ( set_intersection2 @ SV24 @ SV40 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(228,plain,
! [SV40: $i,SV24: $i] :
( ( ( ( set_intersection2 @ SV24 @ SV40 )
!= empty_set )
| ( disjoint @ SV24 @ SV40 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(229,plain,
! [SV41: $i,SV30: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV30 )
| ~ ( subset @ SV11 @ SV41 ) )
= $true )
| ( ( subset @ SV11 @ ( set_intersection2 @ SV30 @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(230,plain,
! [SV14: $i] :
( ( ( SV14 = empty_set )
= $false )
| ( ( ! [SY61: $i] :
~ ( in @ SY61 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(231,plain,
! [SV14: $i] :
( ( ( ! [SY62: $i] :
~ ( in @ SY62 @ SV14 ) )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(232,plain,
! [SV43: $i,SV32: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV32 )
| ~ ( subset @ SV43 @ SV32 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV15 @ SV43 ) @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(233,plain,
! [SV35: $i,SV19: $i] :
( ( ( SV19 != SV35 )
= $true )
| ( ( ~ ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(234,plain,
! [SV35: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) ) )
= $true )
| ( ( SV19 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(235,plain,
! [SV36: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV36 ) )
= $true )
| ( ( ! [SY84: $i] :
( ~ ( in @ SY84 @ SV20 )
| ( in @ SY84 @ SV36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(236,plain,
! [SV36: $i,SV20: $i] :
( ( ( ~ ! [SY85: $i] :
( ~ ( in @ SY85 @ SV20 )
| ( in @ SY85 @ SV36 ) ) )
= $true )
| ( ( subset @ SV20 @ SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(237,plain,
! [SV37: $i,SV21: $i] :
( ( ( ( set_difference @ SV21 @ SV37 )
!= empty_set )
= $true )
| ( ( subset @ SV21 @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(238,plain,
! [SV37: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV37 ) )
= $true )
| ( ( ( set_difference @ SV21 @ SV37 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(239,plain,
! [SV38: $i,SV22: $i,SV45: $i] :
( ( ( SV45
!= ( set_difference @ SV22 @ SV38 ) )
| ! [SY90: $i] :
~ ( ~ ( ~ ( in @ SY90 @ SV45 )
| ~ ( ~ ( in @ SY90 @ SV22 )
| ~ ~ ( in @ SY90 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY90 @ SV22 )
| ~ ~ ( in @ SY90 @ SV38 ) )
| ( in @ SY90 @ SV45 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(240,plain,
! [SV38: $i,SV22: $i,SV45: $i] :
( ( ~ ! [SY91: $i] :
~ ( ~ ( ~ ( in @ SY91 @ SV45 )
| ~ ( ~ ( in @ SY91 @ SV22 )
| ~ ~ ( in @ SY91 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY91 @ SV22 )
| ~ ~ ( in @ SY91 @ SV38 ) )
| ( in @ SY91 @ SV45 ) ) )
| ( SV45
= ( set_difference @ SV22 @ SV38 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(241,plain,
! [SV46: $i,SV39: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV39 )
| ~ ( subset @ SV39 @ SV46 ) )
= $true )
| ( ( subset @ SV23 @ SV46 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(242,plain,
! [SV40: $i,SV24: $i] :
( ( ( ~ ( disjoint @ SV24 @ SV40 ) )
= $true )
| ( ( ( set_intersection2 @ SV24 @ SV40 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(243,plain,
! [SV40: $i,SV24: $i] :
( ( ( ( set_intersection2 @ SV24 @ SV40 )
!= empty_set )
= $true )
| ( ( disjoint @ SV24 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(244,plain,
! [SV41: $i,SV30: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV30 ) )
= $true )
| ( ( ~ ( subset @ SV11 @ SV41 ) )
= $true )
| ( ( subset @ SV11 @ ( set_intersection2 @ SV30 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(245,plain,
! [SV14: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV14 ) )
= $true )
| ( ( SV14 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(246,plain,
! [SV14: $i] :
( ( ( ~ ( in @ ( sK3_SY62 @ SV14 ) @ SV14 ) )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[231]) ).
thf(247,plain,
! [SV43: $i,SV32: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV32 ) )
= $true )
| ( ( ~ ( subset @ SV43 @ SV32 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV15 @ SV43 ) @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(248,plain,
! [SV35: $i,SV19: $i] :
( ( ( SV19 = SV35 )
= $false )
| ( ( ~ ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(249,plain,
! [SV35: $i,SV19: $i] :
( ( ( ~ ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) ) )
= $false )
| ( ( SV19 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(250,plain,
! [SV36: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV36 )
= $false )
| ( ( ! [SY84: $i] :
( ~ ( in @ SY84 @ SV20 )
| ( in @ SY84 @ SV36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(251,plain,
! [SV36: $i,SV20: $i] :
( ( ( ! [SY85: $i] :
( ~ ( in @ SY85 @ SV20 )
| ( in @ SY85 @ SV36 ) ) )
= $false )
| ( ( subset @ SV20 @ SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(252,plain,
! [SV37: $i,SV21: $i] :
( ( ( ( set_difference @ SV21 @ SV37 )
= empty_set )
= $false )
| ( ( subset @ SV21 @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(253,plain,
! [SV37: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV37 )
= $false )
| ( ( ( set_difference @ SV21 @ SV37 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(254,plain,
! [SV38: $i,SV22: $i,SV45: $i] :
( ( ( SV45
!= ( set_difference @ SV22 @ SV38 ) )
= $true )
| ( ( ! [SY90: $i] :
~ ( ~ ( ~ ( in @ SY90 @ SV45 )
| ~ ( ~ ( in @ SY90 @ SV22 )
| ~ ~ ( in @ SY90 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY90 @ SV22 )
| ~ ~ ( in @ SY90 @ SV38 ) )
| ( in @ SY90 @ SV45 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(255,plain,
! [SV38: $i,SV22: $i,SV45: $i] :
( ( ( ~ ! [SY91: $i] :
~ ( ~ ( ~ ( in @ SY91 @ SV45 )
| ~ ( ~ ( in @ SY91 @ SV22 )
| ~ ~ ( in @ SY91 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY91 @ SV22 )
| ~ ~ ( in @ SY91 @ SV38 ) )
| ( in @ SY91 @ SV45 ) ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(256,plain,
! [SV46: $i,SV39: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV39 ) )
= $true )
| ( ( ~ ( subset @ SV39 @ SV46 ) )
= $true )
| ( ( subset @ SV23 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(257,plain,
! [SV40: $i,SV24: $i] :
( ( ( disjoint @ SV24 @ SV40 )
= $false )
| ( ( ( set_intersection2 @ SV24 @ SV40 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(258,plain,
! [SV40: $i,SV24: $i] :
( ( ( ( set_intersection2 @ SV24 @ SV40 )
= empty_set )
= $false )
| ( ( disjoint @ SV24 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(259,plain,
! [SV41: $i,SV30: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV30 )
= $false )
| ( ( ~ ( subset @ SV11 @ SV41 ) )
= $true )
| ( ( subset @ SV11 @ ( set_intersection2 @ SV30 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(260,plain,
! [SV14: $i,SV47: $i] :
( ( ( in @ SV47 @ SV14 )
= $false )
| ( ( SV14 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(261,plain,
! [SV14: $i] :
( ( ( in @ ( sK3_SY62 @ SV14 ) @ SV14 )
= $true )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(262,plain,
! [SV43: $i,SV32: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV32 )
= $false )
| ( ( ~ ( subset @ SV43 @ SV32 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV15 @ SV43 ) @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(263,plain,
! [SV35: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) )
= $false )
| ( ( SV19 = SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(264,plain,
! [SV35: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV35 )
| ~ ( subset @ SV35 @ SV19 ) )
= $true )
| ( ( SV19 = SV35 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(265,plain,
! [SV36: $i,SV20: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV20 )
| ( in @ SV48 @ SV36 ) )
= $true )
| ( ( subset @ SV20 @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(266,plain,
! [SV20: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK4_SY85 @ SV36 @ SV20 ) @ SV20 )
| ( in @ ( sK4_SY85 @ SV36 @ SV20 ) @ SV36 ) )
= $false )
| ( ( subset @ SV20 @ SV36 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[251]) ).
thf(267,plain,
! [SV38: $i,SV22: $i,SV45: $i] :
( ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false )
| ( ( ! [SY90: $i] :
~ ( ~ ( ~ ( in @ SY90 @ SV45 )
| ~ ( ~ ( in @ SY90 @ SV22 )
| ~ ~ ( in @ SY90 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY90 @ SV22 )
| ~ ~ ( in @ SY90 @ SV38 ) )
| ( in @ SY90 @ SV45 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(268,plain,
! [SV38: $i,SV22: $i,SV45: $i] :
( ( ( ! [SY91: $i] :
~ ( ~ ( ~ ( in @ SY91 @ SV45 )
| ~ ( ~ ( in @ SY91 @ SV22 )
| ~ ~ ( in @ SY91 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY91 @ SV22 )
| ~ ~ ( in @ SY91 @ SV38 ) )
| ( in @ SY91 @ SV45 ) ) ) )
= $false )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(269,plain,
! [SV46: $i,SV39: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV39 )
= $false )
| ( ( ~ ( subset @ SV39 @ SV46 ) )
= $true )
| ( ( subset @ SV23 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(270,plain,
! [SV30: $i,SV41: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV41 )
= $false )
| ( ( subset @ SV11 @ SV30 )
= $false )
| ( ( subset @ SV11 @ ( set_intersection2 @ SV30 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(271,plain,
! [SV15: $i,SV32: $i,SV43: $i] :
( ( ( subset @ SV43 @ SV32 )
= $false )
| ( ( subset @ SV15 @ SV32 )
= $false )
| ( ( subset @ ( set_union2 @ SV15 @ SV43 ) @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(272,plain,
! [SV35: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV35 ) )
= $false )
| ( ( SV19 = SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(273,plain,
! [SV19: $i,SV35: $i] :
( ( ( ~ ( subset @ SV35 @ SV19 ) )
= $false )
| ( ( SV19 = SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(274,plain,
! [SV35: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV35 ) )
= $true )
| ( ( ~ ( subset @ SV35 @ SV19 ) )
= $true )
| ( ( SV19 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(275,plain,
! [SV36: $i,SV20: $i,SV48: $i] :
( ( ( ~ ( in @ SV48 @ SV20 ) )
= $true )
| ( ( in @ SV48 @ SV36 )
= $true )
| ( ( subset @ SV20 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(276,plain,
! [SV20: $i,SV36: $i] :
( ( ( ~ ( in @ ( sK4_SY85 @ SV36 @ SV20 ) @ SV20 ) )
= $false )
| ( ( subset @ SV20 @ SV36 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(277,plain,
! [SV20: $i,SV36: $i] :
( ( ( in @ ( sK4_SY85 @ SV36 @ SV20 ) @ SV36 )
= $false )
| ( ( subset @ SV20 @ SV36 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(278,plain,
! [SV38: $i,SV22: $i,SV45: $i,SV49: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV49 @ SV45 )
| ~ ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) )
| ( in @ SV49 @ SV45 ) ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(279,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
| ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) ) ) )
= $false )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[268]) ).
thf(280,plain,
! [SV23: $i,SV46: $i,SV39: $i] :
( ( ( subset @ SV39 @ SV46 )
= $false )
| ( ( subset @ SV23 @ SV39 )
= $false )
| ( ( subset @ SV23 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(281,plain,
! [SV35: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV35 )
= $true )
| ( ( SV19 = SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(282,plain,
! [SV19: $i,SV35: $i] :
( ( ( subset @ SV35 @ SV19 )
= $true )
| ( ( SV19 = SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(283,plain,
! [SV35: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV35 )
= $false )
| ( ( ~ ( subset @ SV35 @ SV19 ) )
= $true )
| ( ( SV19 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(284,plain,
! [SV36: $i,SV20: $i,SV48: $i] :
( ( ( in @ SV48 @ SV20 )
= $false )
| ( ( in @ SV48 @ SV36 )
= $true )
| ( ( subset @ SV20 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(285,plain,
! [SV20: $i,SV36: $i] :
( ( ( in @ ( sK4_SY85 @ SV36 @ SV20 ) @ SV20 )
= $true )
| ( ( subset @ SV20 @ SV36 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(286,plain,
! [SV38: $i,SV22: $i,SV45: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ SV49 @ SV45 )
| ~ ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) )
| ( in @ SV49 @ SV45 ) ) )
= $false )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(287,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
| ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(288,plain,
! [SV19: $i,SV35: $i] :
( ( ( subset @ SV35 @ SV19 )
= $false )
| ( ( subset @ SV19 @ SV35 )
= $false )
| ( ( SV19 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(289,plain,
! [SV38: $i,SV22: $i,SV45: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ SV49 @ SV45 )
| ~ ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) ) ) )
= $false )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(290,plain,
! [SV45: $i,SV38: $i,SV22: $i,SV49: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) )
| ( in @ SV49 @ SV45 ) ) )
= $false )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(291,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
| ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(292,plain,
! [SV38: $i,SV22: $i,SV45: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV45 )
| ~ ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(293,plain,
! [SV45: $i,SV38: $i,SV22: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) )
| ( in @ SV49 @ SV45 ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(294,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
| ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(295,plain,
! [SV38: $i,SV22: $i,SV45: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV45 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(296,plain,
! [SV45: $i,SV38: $i,SV22: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) ) )
= $true )
| ( ( in @ SV49 @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(297,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(298,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(299,plain,
! [SV38: $i,SV22: $i,SV45: $i,SV49: $i] :
( ( ( in @ SV49 @ SV45 )
= $false )
| ( ( ~ ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(300,plain,
! [SV45: $i,SV38: $i,SV22: $i,SV49: $i] :
( ( ( ~ ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) ) )
= $false )
| ( ( in @ SV49 @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(301,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(302,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(303,plain,
! [SV45: $i,SV38: $i,SV22: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) )
= $false )
| ( ( in @ SV49 @ SV45 )
= $false )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(304,plain,
! [SV45: $i,SV38: $i,SV22: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV22 )
| ~ ~ ( in @ SV49 @ SV38 ) )
= $true )
| ( ( in @ SV49 @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(305,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(306,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(307,plain,
! [SV38: $i,SV45: $i,SV22: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV22 ) )
= $false )
| ( ( in @ SV49 @ SV45 )
= $false )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(308,plain,
! [SV22: $i,SV45: $i,SV38: $i,SV49: $i] :
( ( ( ~ ~ ( in @ SV49 @ SV38 ) )
= $false )
| ( ( in @ SV49 @ SV45 )
= $false )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(309,plain,
! [SV45: $i,SV38: $i,SV22: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV22 ) )
= $true )
| ( ( ~ ~ ( in @ SV49 @ SV38 ) )
= $true )
| ( ( in @ SV49 @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(310,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) ) )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(311,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(312,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(313,plain,
! [SV38: $i,SV45: $i,SV22: $i,SV49: $i] :
( ( ( in @ SV49 @ SV22 )
= $true )
| ( ( in @ SV49 @ SV45 )
= $false )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(314,plain,
! [SV22: $i,SV45: $i,SV38: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV38 ) )
= $true )
| ( ( in @ SV49 @ SV45 )
= $false )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(315,plain,
! [SV45: $i,SV38: $i,SV22: $i,SV49: $i] :
( ( ( in @ SV49 @ SV22 )
= $false )
| ( ( ~ ~ ( in @ SV49 @ SV38 ) )
= $true )
| ( ( in @ SV49 @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(316,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) ) )
= $true )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(317,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(318,plain,
! [SV22: $i,SV45: $i,SV38: $i,SV49: $i] :
( ( ( in @ SV49 @ SV38 )
= $false )
| ( ( in @ SV49 @ SV45 )
= $false )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(319,plain,
! [SV45: $i,SV22: $i,SV38: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV38 ) )
= $false )
| ( ( in @ SV49 @ SV22 )
= $false )
| ( ( in @ SV49 @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(320,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(321,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $true )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) ) )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(322,plain,
! [SV45: $i,SV22: $i,SV38: $i,SV49: $i] :
( ( ( in @ SV49 @ SV38 )
= $true )
| ( ( in @ SV49 @ SV22 )
= $false )
| ( ( in @ SV49 @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(323,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 ) )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(324,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(325,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
| ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 ) )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(326,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $true )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(327,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
= $true )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(328,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) ) )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(329,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(330,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV45 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(331,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) ) )
= $true )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(332,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
| ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(333,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 ) )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[332]) ).
thf(334,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[332]) ).
thf(335,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $true )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(336,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( ~ ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 ) )
= $true )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(337,plain,
! [SV45: $i,SV22: $i,SV38: $i] :
( ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV22 )
= $false )
| ( ( in @ ( sK5_SY91 @ SV38 @ SV22 @ SV45 ) @ SV38 )
= $true )
| ( ( SV45
= ( set_difference @ SV22 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(338,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[103,337,335,330,329,326,322,318,313,311,288,285,284,282,281,280,277,271,270,261,260,258,257,253,252,217,213,200,194,186,183,179,166,159,158,157,156,139,138,137,136,132,107,106,105,104]) ).
thf(339,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(340,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(341,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(342,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(343,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(344,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(345,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(346,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(347,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(348,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(349,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(350,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(351,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(352,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(353,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(354,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(355,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)],[62]) ).
thf(356,plain,
( ( ! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(357,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(358,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(359,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(360,plain,
$true = $true,
inference(copy,[status(thm)],[57]) ).
thf(361,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(362,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(363,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(364,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(365,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(366,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(367,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(368,plain,
( ( ~ ( ( subset @ sK1_A @ sK2_SY51 )
=> ( ( set_difference @ sK1_A @ sK2_SY51 )
= empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(369,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_difference @ SX0 @ SX2 ) @ ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(370,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)],[351]) ).
thf(371,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)],[352]) ).
thf(372,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(373,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(374,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(375,plain,
( ( ~ ( ~ ( subset @ sK1_A @ sK2_SY51 )
| ( ( set_difference @ sK1_A @ sK2_SY51 )
= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(376,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)],[342]) ).
thf(377,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(378,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ SX0 @ SX1 )
!= empty_set )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( ( set_difference @ SX0 @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(379,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)],[344]) ).
thf(380,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( disjoint @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SX0 @ SX1 )
!= empty_set )
| ( disjoint @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(381,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)],[355]) ).
thf(382,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)],[353]) ).
thf(383,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(384,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)],[354]) ).
thf(385,plain,
! [SV50: $i] :
( ( ! [SY92: $i] : ( subset @ ( set_intersection2 @ SV50 @ SY92 ) @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(386,plain,
! [SV51: $i] :
( ( subset @ empty_set @ SV51 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(387,plain,
! [SV52: $i] :
( ( ! [SY93: $i] : ( subset @ ( set_difference @ SV52 @ SY93 ) @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(388,plain,
! [SV53: $i] :
( ( ! [SY94: $i] : ( subset @ SV53 @ ( set_union2 @ SV53 @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(389,plain,
! [SV54: $i] :
( ( ! [SY95: $i] : ( subset @ SV54 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(390,plain,
! [SV55: $i] :
( ( ( set_union2 @ SV55 @ empty_set )
= SV55 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(391,plain,
! [SV56: $i] :
( ( ( set_intersection2 @ SV56 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(392,plain,
! [SV57: $i] :
( ( ( set_difference @ SV57 @ empty_set )
= SV57 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(393,plain,
! [SV58: $i] :
( ( ( set_difference @ empty_set @ SV58 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(394,plain,
! [SV59: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( subset @ SV59 @ SY96 )
| ( subset @ ( set_difference @ SV59 @ SY97 ) @ ( set_difference @ SY96 @ SY97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(395,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)],[370]) ).
thf(396,plain,
! [SV61: $i] :
( ( ! [SY100: $i] :
~ ( ~ ( ( SV61 != SY100 )
| ~ ( ~ ( subset @ SV61 @ SY100 )
| ~ ( subset @ SY100 @ SV61 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV61 @ SY100 )
| ~ ( subset @ SY100 @ SV61 ) )
| ( SV61 = SY100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(397,plain,
! [SV62: $i] :
( ( ~ ( empty @ SV62 )
| ( SV62 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(398,plain,
! [SV63: $i] :
( ( ! [SY101: $i,SY102: $i] :
( ~ ~ ( ~ ( subset @ SV63 @ SY101 )
| ~ ( subset @ SY101 @ SY102 ) )
| ( subset @ SV63 @ SY102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(399,plain,
! [SV64: $i] :
( ( ! [SY103: $i] :
( ~ ( subset @ SV64 @ SY103 )
| ( ( set_union2 @ SV64 @ SY103 )
= SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(400,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY51 )
| ( ( set_difference @ sK1_A @ sK2_SY51 )
= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(401,plain,
! [SV65: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ~ ~ ( ~ ( subset @ SV65 @ SY104 )
| ~ ( subset @ SV65 @ SY105 ) )
| ( subset @ SV65 @ ( set_intersection2 @ SY104 @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(402,plain,
! [SV66: $i] :
( ( ! [SY106: $i] :
( ~ ( subset @ SV66 @ SY106 )
| ( ( set_intersection2 @ SV66 @ SY106 )
= SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(403,plain,
! [SV67: $i] :
( ( ! [SY107: $i] :
~ ( ~ ( ( ( set_difference @ SV67 @ SY107 )
!= empty_set )
| ( subset @ SV67 @ SY107 ) )
| ~ ( ~ ( subset @ SV67 @ SY107 )
| ( ( set_difference @ SV67 @ SY107 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(404,plain,
! [SV68: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ~ ( subset @ SV68 @ SY108 )
| ( subset @ ( set_intersection2 @ SV68 @ SY109 ) @ ( set_intersection2 @ SY108 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(405,plain,
! [SV69: $i] :
( ( ! [SY110: $i] :
~ ( ~ ( ~ ( disjoint @ SV69 @ SY110 )
| ( ( set_intersection2 @ SV69 @ SY110 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV69 @ SY110 )
!= empty_set )
| ( disjoint @ SV69 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(406,plain,
! [SV70: $i] :
( ( ! [SY111: $i,SY112: $i] :
~ ( ~ ( ( SY112
!= ( set_difference @ SV70 @ SY111 ) )
| ! [SY113: $i] :
~ ( ~ ( ~ ( in @ SY113 @ SY112 )
| ~ ( ~ ( in @ SY113 @ SV70 )
| ~ ~ ( in @ SY113 @ SY111 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY113 @ SV70 )
| ~ ~ ( in @ SY113 @ SY111 ) )
| ( in @ SY113 @ SY112 ) ) ) )
| ~ ( ~ ! [SY114: $i] :
~ ( ~ ( ~ ( in @ SY114 @ SY112 )
| ~ ( ~ ( in @ SY114 @ SV70 )
| ~ ~ ( in @ SY114 @ SY111 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY114 @ SV70 )
| ~ ~ ( in @ SY114 @ SY111 ) )
| ( in @ SY114 @ SY112 ) ) )
| ( SY112
= ( set_difference @ SV70 @ SY111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(407,plain,
! [SV71: $i] :
( ( ~ ( ~ ( ( SV71 != empty_set )
| ! [SY115: $i] :
~ ( in @ SY115 @ SV71 ) )
| ~ ( ~ ! [SY116: $i] :
~ ( in @ SY116 @ SV71 )
| ( SV71 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(408,plain,
! [SV72: $i] :
( ( ~ ( subset @ SV72 @ empty_set )
| ( SV72 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(409,plain,
! [SV73: $i] :
( ( ! [SY117: $i] :
~ ( ~ ( ~ ( subset @ SV73 @ SY117 )
| ! [SY118: $i] :
( ~ ( in @ SY118 @ SV73 )
| ( in @ SY118 @ SY117 ) ) )
| ~ ( ~ ! [SY119: $i] :
( ~ ( in @ SY119 @ SV73 )
| ( in @ SY119 @ SY117 ) )
| ( subset @ SV73 @ SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(410,plain,
! [SV74: $i,SV50: $i] :
( ( subset @ ( set_intersection2 @ SV50 @ SV74 ) @ SV50 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(411,plain,
! [SV75: $i,SV52: $i] :
( ( subset @ ( set_difference @ SV52 @ SV75 ) @ SV52 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(412,plain,
! [SV76: $i,SV53: $i] :
( ( subset @ SV53 @ ( set_union2 @ SV53 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(413,plain,
! [SV54: $i] :
( ( subset @ SV54 @ SV54 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(414,plain,
! [SV78: $i,SV59: $i] :
( ( ! [SY120: $i] :
( ~ ( subset @ SV59 @ SV78 )
| ( subset @ ( set_difference @ SV59 @ SY120 ) @ ( set_difference @ SV78 @ SY120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(415,plain,
! [SV79: $i,SV60: $i] :
( ( ! [SY121: $i] :
( ~ ~ ( ~ ( subset @ SV60 @ SV79 )
| ~ ( subset @ SY121 @ SV79 ) )
| ( subset @ ( set_union2 @ SV60 @ SY121 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(416,plain,
! [SV80: $i,SV61: $i] :
( ( ~ ( ~ ( ( SV61 != SV80 )
| ~ ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) )
| ( SV61 = SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(417,plain,
! [SV62: $i] :
( ( ( ~ ( empty @ SV62 ) )
= $true )
| ( ( SV62 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(418,plain,
! [SV81: $i,SV63: $i] :
( ( ! [SY122: $i] :
( ~ ~ ( ~ ( subset @ SV63 @ SV81 )
| ~ ( subset @ SV81 @ SY122 ) )
| ( subset @ SV63 @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(419,plain,
! [SV82: $i,SV64: $i] :
( ( ~ ( subset @ SV64 @ SV82 )
| ( ( set_union2 @ SV64 @ SV82 )
= SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(420,plain,
( ( ~ ( subset @ sK1_A @ sK2_SY51 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(421,plain,
( ( ( set_difference @ sK1_A @ sK2_SY51 )
= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(422,plain,
! [SV83: $i,SV65: $i] :
( ( ! [SY123: $i] :
( ~ ~ ( ~ ( subset @ SV65 @ SV83 )
| ~ ( subset @ SV65 @ SY123 ) )
| ( subset @ SV65 @ ( set_intersection2 @ SV83 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(423,plain,
! [SV84: $i,SV66: $i] :
( ( ~ ( subset @ SV66 @ SV84 )
| ( ( set_intersection2 @ SV66 @ SV84 )
= SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(424,plain,
! [SV85: $i,SV67: $i] :
( ( ~ ( ~ ( ( ( set_difference @ SV67 @ SV85 )
!= empty_set )
| ( subset @ SV67 @ SV85 ) )
| ~ ( ~ ( subset @ SV67 @ SV85 )
| ( ( set_difference @ SV67 @ SV85 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(425,plain,
! [SV86: $i,SV68: $i] :
( ( ! [SY124: $i] :
( ~ ( subset @ SV68 @ SV86 )
| ( subset @ ( set_intersection2 @ SV68 @ SY124 ) @ ( set_intersection2 @ SV86 @ SY124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(426,plain,
! [SV87: $i,SV69: $i] :
( ( ~ ( ~ ( ~ ( disjoint @ SV69 @ SV87 )
| ( ( set_intersection2 @ SV69 @ SV87 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV69 @ SV87 )
!= empty_set )
| ( disjoint @ SV69 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(427,plain,
! [SV88: $i,SV70: $i] :
( ( ! [SY125: $i] :
~ ( ~ ( ( SY125
!= ( set_difference @ SV70 @ SV88 ) )
| ! [SY126: $i] :
~ ( ~ ( ~ ( in @ SY126 @ SY125 )
| ~ ( ~ ( in @ SY126 @ SV70 )
| ~ ~ ( in @ SY126 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY126 @ SV70 )
| ~ ~ ( in @ SY126 @ SV88 ) )
| ( in @ SY126 @ SY125 ) ) ) )
| ~ ( ~ ! [SY127: $i] :
~ ( ~ ( ~ ( in @ SY127 @ SY125 )
| ~ ( ~ ( in @ SY127 @ SV70 )
| ~ ~ ( in @ SY127 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY127 @ SV70 )
| ~ ~ ( in @ SY127 @ SV88 ) )
| ( in @ SY127 @ SY125 ) ) )
| ( SY125
= ( set_difference @ SV70 @ SV88 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(428,plain,
! [SV71: $i] :
( ( ~ ( ( SV71 != empty_set )
| ! [SY115: $i] :
~ ( in @ SY115 @ SV71 ) )
| ~ ( ~ ! [SY116: $i] :
~ ( in @ SY116 @ SV71 )
| ( SV71 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(429,plain,
! [SV72: $i] :
( ( ( ~ ( subset @ SV72 @ empty_set ) )
= $true )
| ( ( SV72 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(430,plain,
! [SV89: $i,SV73: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV73 @ SV89 )
| ! [SY128: $i] :
( ~ ( in @ SY128 @ SV73 )
| ( in @ SY128 @ SV89 ) ) )
| ~ ( ~ ! [SY129: $i] :
( ~ ( in @ SY129 @ SV73 )
| ( in @ SY129 @ SV89 ) )
| ( subset @ SV73 @ SV89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(431,plain,
! [SV90: $i,SV78: $i,SV59: $i] :
( ( ~ ( subset @ SV59 @ SV78 )
| ( subset @ ( set_difference @ SV59 @ SV90 ) @ ( set_difference @ SV78 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(432,plain,
! [SV91: $i,SV79: $i,SV60: $i] :
( ( ~ ~ ( ~ ( subset @ SV60 @ SV79 )
| ~ ( subset @ SV91 @ SV79 ) )
| ( subset @ ( set_union2 @ SV60 @ SV91 ) @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(433,plain,
! [SV80: $i,SV61: $i] :
( ( ~ ( ( SV61 != SV80 )
| ~ ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) )
| ( SV61 = SV80 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(434,plain,
! [SV62: $i] :
( ( ( empty @ SV62 )
= $false )
| ( ( SV62 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(435,plain,
! [SV92: $i,SV81: $i,SV63: $i] :
( ( ~ ~ ( ~ ( subset @ SV63 @ SV81 )
| ~ ( subset @ SV81 @ SV92 ) )
| ( subset @ SV63 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(436,plain,
! [SV82: $i,SV64: $i] :
( ( ( ~ ( subset @ SV64 @ SV82 ) )
= $true )
| ( ( ( set_union2 @ SV64 @ SV82 )
= SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(437,plain,
( ( subset @ sK1_A @ sK2_SY51 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(438,plain,
! [SV93: $i,SV83: $i,SV65: $i] :
( ( ~ ~ ( ~ ( subset @ SV65 @ SV83 )
| ~ ( subset @ SV65 @ SV93 ) )
| ( subset @ SV65 @ ( set_intersection2 @ SV83 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(439,plain,
! [SV84: $i,SV66: $i] :
( ( ( ~ ( subset @ SV66 @ SV84 ) )
= $true )
| ( ( ( set_intersection2 @ SV66 @ SV84 )
= SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(440,plain,
! [SV85: $i,SV67: $i] :
( ( ~ ( ( ( set_difference @ SV67 @ SV85 )
!= empty_set )
| ( subset @ SV67 @ SV85 ) )
| ~ ( ~ ( subset @ SV67 @ SV85 )
| ( ( set_difference @ SV67 @ SV85 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(441,plain,
! [SV94: $i,SV86: $i,SV68: $i] :
( ( ~ ( subset @ SV68 @ SV86 )
| ( subset @ ( set_intersection2 @ SV68 @ SV94 ) @ ( set_intersection2 @ SV86 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(442,plain,
! [SV87: $i,SV69: $i] :
( ( ~ ( ~ ( disjoint @ SV69 @ SV87 )
| ( ( set_intersection2 @ SV69 @ SV87 )
= empty_set ) )
| ~ ( ( ( set_intersection2 @ SV69 @ SV87 )
!= empty_set )
| ( disjoint @ SV69 @ SV87 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(443,plain,
! [SV88: $i,SV70: $i,SV95: $i] :
( ( ~ ( ~ ( ( SV95
!= ( set_difference @ SV70 @ SV88 ) )
| ! [SY130: $i] :
~ ( ~ ( ~ ( in @ SY130 @ SV95 )
| ~ ( ~ ( in @ SY130 @ SV70 )
| ~ ~ ( in @ SY130 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY130 @ SV70 )
| ~ ~ ( in @ SY130 @ SV88 ) )
| ( in @ SY130 @ SV95 ) ) ) )
| ~ ( ~ ! [SY131: $i] :
~ ( ~ ( ~ ( in @ SY131 @ SV95 )
| ~ ( ~ ( in @ SY131 @ SV70 )
| ~ ~ ( in @ SY131 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY131 @ SV70 )
| ~ ~ ( in @ SY131 @ SV88 ) )
| ( in @ SY131 @ SV95 ) ) )
| ( SV95
= ( set_difference @ SV70 @ SV88 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(444,plain,
! [SV71: $i] :
( ( ~ ( ( SV71 != empty_set )
| ! [SY115: $i] :
~ ( in @ SY115 @ SV71 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(445,plain,
! [SV71: $i] :
( ( ~ ( ~ ! [SY116: $i] :
~ ( in @ SY116 @ SV71 )
| ( SV71 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(446,plain,
! [SV72: $i] :
( ( ( subset @ SV72 @ empty_set )
= $false )
| ( ( SV72 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(447,plain,
! [SV89: $i,SV73: $i] :
( ( ~ ( ~ ( subset @ SV73 @ SV89 )
| ! [SY128: $i] :
( ~ ( in @ SY128 @ SV73 )
| ( in @ SY128 @ SV89 ) ) )
| ~ ( ~ ! [SY129: $i] :
( ~ ( in @ SY129 @ SV73 )
| ( in @ SY129 @ SV89 ) )
| ( subset @ SV73 @ SV89 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(448,plain,
! [SV90: $i,SV78: $i,SV59: $i] :
( ( ( ~ ( subset @ SV59 @ SV78 ) )
= $true )
| ( ( subset @ ( set_difference @ SV59 @ SV90 ) @ ( set_difference @ SV78 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(449,plain,
! [SV91: $i,SV79: $i,SV60: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV60 @ SV79 )
| ~ ( subset @ SV91 @ SV79 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV60 @ SV91 ) @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(450,plain,
! [SV80: $i,SV61: $i] :
( ( ~ ( ( SV61 != SV80 )
| ~ ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(451,plain,
! [SV80: $i,SV61: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) )
| ( SV61 = SV80 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(452,plain,
! [SV92: $i,SV81: $i,SV63: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV63 @ SV81 )
| ~ ( subset @ SV81 @ SV92 ) ) )
= $true )
| ( ( subset @ SV63 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(453,plain,
! [SV82: $i,SV64: $i] :
( ( ( subset @ SV64 @ SV82 )
= $false )
| ( ( ( set_union2 @ SV64 @ SV82 )
= SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(454,plain,
! [SV93: $i,SV83: $i,SV65: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV65 @ SV83 )
| ~ ( subset @ SV65 @ SV93 ) ) )
= $true )
| ( ( subset @ SV65 @ ( set_intersection2 @ SV83 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(455,plain,
! [SV84: $i,SV66: $i] :
( ( ( subset @ SV66 @ SV84 )
= $false )
| ( ( ( set_intersection2 @ SV66 @ SV84 )
= SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(456,plain,
! [SV85: $i,SV67: $i] :
( ( ~ ( ( ( set_difference @ SV67 @ SV85 )
!= empty_set )
| ( subset @ SV67 @ SV85 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(457,plain,
! [SV85: $i,SV67: $i] :
( ( ~ ( ~ ( subset @ SV67 @ SV85 )
| ( ( set_difference @ SV67 @ SV85 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(458,plain,
! [SV94: $i,SV86: $i,SV68: $i] :
( ( ( ~ ( subset @ SV68 @ SV86 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV68 @ SV94 ) @ ( set_intersection2 @ SV86 @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(459,plain,
! [SV87: $i,SV69: $i] :
( ( ~ ( ~ ( disjoint @ SV69 @ SV87 )
| ( ( set_intersection2 @ SV69 @ SV87 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(460,plain,
! [SV87: $i,SV69: $i] :
( ( ~ ( ( ( set_intersection2 @ SV69 @ SV87 )
!= empty_set )
| ( disjoint @ SV69 @ SV87 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(461,plain,
! [SV88: $i,SV70: $i,SV95: $i] :
( ( ~ ( ( SV95
!= ( set_difference @ SV70 @ SV88 ) )
| ! [SY130: $i] :
~ ( ~ ( ~ ( in @ SY130 @ SV95 )
| ~ ( ~ ( in @ SY130 @ SV70 )
| ~ ~ ( in @ SY130 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY130 @ SV70 )
| ~ ~ ( in @ SY130 @ SV88 ) )
| ( in @ SY130 @ SV95 ) ) ) )
| ~ ( ~ ! [SY131: $i] :
~ ( ~ ( ~ ( in @ SY131 @ SV95 )
| ~ ( ~ ( in @ SY131 @ SV70 )
| ~ ~ ( in @ SY131 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY131 @ SV70 )
| ~ ~ ( in @ SY131 @ SV88 ) )
| ( in @ SY131 @ SV95 ) ) )
| ( SV95
= ( set_difference @ SV70 @ SV88 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(462,plain,
! [SV71: $i] :
( ( ( SV71 != empty_set )
| ! [SY115: $i] :
~ ( in @ SY115 @ SV71 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(463,plain,
! [SV71: $i] :
( ( ~ ! [SY116: $i] :
~ ( in @ SY116 @ SV71 )
| ( SV71 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(464,plain,
! [SV89: $i,SV73: $i] :
( ( ~ ( ~ ( subset @ SV73 @ SV89 )
| ! [SY128: $i] :
( ~ ( in @ SY128 @ SV73 )
| ( in @ SY128 @ SV89 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(465,plain,
! [SV89: $i,SV73: $i] :
( ( ~ ( ~ ! [SY129: $i] :
( ~ ( in @ SY129 @ SV73 )
| ( in @ SY129 @ SV89 ) )
| ( subset @ SV73 @ SV89 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[447]) ).
thf(466,plain,
! [SV90: $i,SV78: $i,SV59: $i] :
( ( ( subset @ SV59 @ SV78 )
= $false )
| ( ( subset @ ( set_difference @ SV59 @ SV90 ) @ ( set_difference @ SV78 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(467,plain,
! [SV91: $i,SV79: $i,SV60: $i] :
( ( ( ~ ( ~ ( subset @ SV60 @ SV79 )
| ~ ( subset @ SV91 @ SV79 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV60 @ SV91 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(468,plain,
! [SV80: $i,SV61: $i] :
( ( ( SV61 != SV80 )
| ~ ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(469,plain,
! [SV80: $i,SV61: $i] :
( ( ~ ~ ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) )
| ( SV61 = SV80 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(470,plain,
! [SV92: $i,SV81: $i,SV63: $i] :
( ( ( ~ ( ~ ( subset @ SV63 @ SV81 )
| ~ ( subset @ SV81 @ SV92 ) ) )
= $false )
| ( ( subset @ SV63 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(471,plain,
! [SV93: $i,SV83: $i,SV65: $i] :
( ( ( ~ ( ~ ( subset @ SV65 @ SV83 )
| ~ ( subset @ SV65 @ SV93 ) ) )
= $false )
| ( ( subset @ SV65 @ ( set_intersection2 @ SV83 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(472,plain,
! [SV85: $i,SV67: $i] :
( ( ( ( set_difference @ SV67 @ SV85 )
!= empty_set )
| ( subset @ SV67 @ SV85 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[456]) ).
thf(473,plain,
! [SV85: $i,SV67: $i] :
( ( ~ ( subset @ SV67 @ SV85 )
| ( ( set_difference @ SV67 @ SV85 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(474,plain,
! [SV94: $i,SV86: $i,SV68: $i] :
( ( ( subset @ SV68 @ SV86 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV68 @ SV94 ) @ ( set_intersection2 @ SV86 @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(475,plain,
! [SV87: $i,SV69: $i] :
( ( ~ ( disjoint @ SV69 @ SV87 )
| ( ( set_intersection2 @ SV69 @ SV87 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(476,plain,
! [SV87: $i,SV69: $i] :
( ( ( ( set_intersection2 @ SV69 @ SV87 )
!= empty_set )
| ( disjoint @ SV69 @ SV87 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(477,plain,
! [SV88: $i,SV70: $i,SV95: $i] :
( ( ~ ( ( SV95
!= ( set_difference @ SV70 @ SV88 ) )
| ! [SY130: $i] :
~ ( ~ ( ~ ( in @ SY130 @ SV95 )
| ~ ( ~ ( in @ SY130 @ SV70 )
| ~ ~ ( in @ SY130 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY130 @ SV70 )
| ~ ~ ( in @ SY130 @ SV88 ) )
| ( in @ SY130 @ SV95 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(478,plain,
! [SV88: $i,SV70: $i,SV95: $i] :
( ( ~ ( ~ ! [SY131: $i] :
~ ( ~ ( ~ ( in @ SY131 @ SV95 )
| ~ ( ~ ( in @ SY131 @ SV70 )
| ~ ~ ( in @ SY131 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY131 @ SV70 )
| ~ ~ ( in @ SY131 @ SV88 ) )
| ( in @ SY131 @ SV95 ) ) )
| ( SV95
= ( set_difference @ SV70 @ SV88 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(479,plain,
! [SV71: $i] :
( ( ( SV71 != empty_set )
= $true )
| ( ( ! [SY115: $i] :
~ ( in @ SY115 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(480,plain,
! [SV71: $i] :
( ( ( ~ ! [SY116: $i] :
~ ( in @ SY116 @ SV71 ) )
= $true )
| ( ( SV71 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(481,plain,
! [SV89: $i,SV73: $i] :
( ( ~ ( subset @ SV73 @ SV89 )
| ! [SY128: $i] :
( ~ ( in @ SY128 @ SV73 )
| ( in @ SY128 @ SV89 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(482,plain,
! [SV89: $i,SV73: $i] :
( ( ~ ! [SY129: $i] :
( ~ ( in @ SY129 @ SV73 )
| ( in @ SY129 @ SV89 ) )
| ( subset @ SV73 @ SV89 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(483,plain,
! [SV91: $i,SV79: $i,SV60: $i] :
( ( ( ~ ( subset @ SV60 @ SV79 )
| ~ ( subset @ SV91 @ SV79 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV60 @ SV91 ) @ SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(484,plain,
! [SV80: $i,SV61: $i] :
( ( ( SV61 != SV80 )
= $true )
| ( ( ~ ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(485,plain,
! [SV80: $i,SV61: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) ) )
= $true )
| ( ( SV61 = SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(486,plain,
! [SV92: $i,SV81: $i,SV63: $i] :
( ( ( ~ ( subset @ SV63 @ SV81 )
| ~ ( subset @ SV81 @ SV92 ) )
= $true )
| ( ( subset @ SV63 @ SV92 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(487,plain,
! [SV93: $i,SV83: $i,SV65: $i] :
( ( ( ~ ( subset @ SV65 @ SV83 )
| ~ ( subset @ SV65 @ SV93 ) )
= $true )
| ( ( subset @ SV65 @ ( set_intersection2 @ SV83 @ SV93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(488,plain,
! [SV85: $i,SV67: $i] :
( ( ( ( set_difference @ SV67 @ SV85 )
!= empty_set )
= $true )
| ( ( subset @ SV67 @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(489,plain,
! [SV85: $i,SV67: $i] :
( ( ( ~ ( subset @ SV67 @ SV85 ) )
= $true )
| ( ( ( set_difference @ SV67 @ SV85 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(490,plain,
! [SV87: $i,SV69: $i] :
( ( ( ~ ( disjoint @ SV69 @ SV87 ) )
= $true )
| ( ( ( set_intersection2 @ SV69 @ SV87 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(491,plain,
! [SV87: $i,SV69: $i] :
( ( ( ( set_intersection2 @ SV69 @ SV87 )
!= empty_set )
= $true )
| ( ( disjoint @ SV69 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(492,plain,
! [SV88: $i,SV70: $i,SV95: $i] :
( ( ( SV95
!= ( set_difference @ SV70 @ SV88 ) )
| ! [SY130: $i] :
~ ( ~ ( ~ ( in @ SY130 @ SV95 )
| ~ ( ~ ( in @ SY130 @ SV70 )
| ~ ~ ( in @ SY130 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY130 @ SV70 )
| ~ ~ ( in @ SY130 @ SV88 ) )
| ( in @ SY130 @ SV95 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(493,plain,
! [SV88: $i,SV70: $i,SV95: $i] :
( ( ~ ! [SY131: $i] :
~ ( ~ ( ~ ( in @ SY131 @ SV95 )
| ~ ( ~ ( in @ SY131 @ SV70 )
| ~ ~ ( in @ SY131 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY131 @ SV70 )
| ~ ~ ( in @ SY131 @ SV88 ) )
| ( in @ SY131 @ SV95 ) ) )
| ( SV95
= ( set_difference @ SV70 @ SV88 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(494,plain,
! [SV71: $i] :
( ( ( SV71 = empty_set )
= $false )
| ( ( ! [SY115: $i] :
~ ( in @ SY115 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(495,plain,
! [SV71: $i] :
( ( ( ! [SY116: $i] :
~ ( in @ SY116 @ SV71 ) )
= $false )
| ( ( SV71 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(496,plain,
! [SV89: $i,SV73: $i] :
( ( ( ~ ( subset @ SV73 @ SV89 ) )
= $true )
| ( ( ! [SY128: $i] :
( ~ ( in @ SY128 @ SV73 )
| ( in @ SY128 @ SV89 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(497,plain,
! [SV89: $i,SV73: $i] :
( ( ( ~ ! [SY129: $i] :
( ~ ( in @ SY129 @ SV73 )
| ( in @ SY129 @ SV89 ) ) )
= $true )
| ( ( subset @ SV73 @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[482]) ).
thf(498,plain,
! [SV91: $i,SV79: $i,SV60: $i] :
( ( ( ~ ( subset @ SV60 @ SV79 ) )
= $true )
| ( ( ~ ( subset @ SV91 @ SV79 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV60 @ SV91 ) @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[483]) ).
thf(499,plain,
! [SV80: $i,SV61: $i] :
( ( ( SV61 = SV80 )
= $false )
| ( ( ~ ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(500,plain,
! [SV80: $i,SV61: $i] :
( ( ( ~ ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) ) )
= $false )
| ( ( SV61 = SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(501,plain,
! [SV92: $i,SV81: $i,SV63: $i] :
( ( ( ~ ( subset @ SV63 @ SV81 ) )
= $true )
| ( ( ~ ( subset @ SV81 @ SV92 ) )
= $true )
| ( ( subset @ SV63 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(502,plain,
! [SV93: $i,SV83: $i,SV65: $i] :
( ( ( ~ ( subset @ SV65 @ SV83 ) )
= $true )
| ( ( ~ ( subset @ SV65 @ SV93 ) )
= $true )
| ( ( subset @ SV65 @ ( set_intersection2 @ SV83 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(503,plain,
! [SV85: $i,SV67: $i] :
( ( ( ( set_difference @ SV67 @ SV85 )
= empty_set )
= $false )
| ( ( subset @ SV67 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(504,plain,
! [SV85: $i,SV67: $i] :
( ( ( subset @ SV67 @ SV85 )
= $false )
| ( ( ( set_difference @ SV67 @ SV85 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(505,plain,
! [SV87: $i,SV69: $i] :
( ( ( disjoint @ SV69 @ SV87 )
= $false )
| ( ( ( set_intersection2 @ SV69 @ SV87 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(506,plain,
! [SV87: $i,SV69: $i] :
( ( ( ( set_intersection2 @ SV69 @ SV87 )
= empty_set )
= $false )
| ( ( disjoint @ SV69 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(507,plain,
! [SV88: $i,SV70: $i,SV95: $i] :
( ( ( SV95
!= ( set_difference @ SV70 @ SV88 ) )
= $true )
| ( ( ! [SY130: $i] :
~ ( ~ ( ~ ( in @ SY130 @ SV95 )
| ~ ( ~ ( in @ SY130 @ SV70 )
| ~ ~ ( in @ SY130 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY130 @ SV70 )
| ~ ~ ( in @ SY130 @ SV88 ) )
| ( in @ SY130 @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(508,plain,
! [SV88: $i,SV70: $i,SV95: $i] :
( ( ( ~ ! [SY131: $i] :
~ ( ~ ( ~ ( in @ SY131 @ SV95 )
| ~ ( ~ ( in @ SY131 @ SV70 )
| ~ ~ ( in @ SY131 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY131 @ SV70 )
| ~ ~ ( in @ SY131 @ SV88 ) )
| ( in @ SY131 @ SV95 ) ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(509,plain,
! [SV71: $i,SV96: $i] :
( ( ( ~ ( in @ SV96 @ SV71 ) )
= $true )
| ( ( SV71 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(510,plain,
! [SV71: $i] :
( ( ( ~ ( in @ ( sK6_SY116 @ SV71 ) @ SV71 ) )
= $false )
| ( ( SV71 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[495]) ).
thf(511,plain,
! [SV89: $i,SV73: $i] :
( ( ( subset @ SV73 @ SV89 )
= $false )
| ( ( ! [SY128: $i] :
( ~ ( in @ SY128 @ SV73 )
| ( in @ SY128 @ SV89 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(512,plain,
! [SV89: $i,SV73: $i] :
( ( ( ! [SY129: $i] :
( ~ ( in @ SY129 @ SV73 )
| ( in @ SY129 @ SV89 ) ) )
= $false )
| ( ( subset @ SV73 @ SV89 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(513,plain,
! [SV91: $i,SV79: $i,SV60: $i] :
( ( ( subset @ SV60 @ SV79 )
= $false )
| ( ( ~ ( subset @ SV91 @ SV79 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV60 @ SV91 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(514,plain,
! [SV80: $i,SV61: $i] :
( ( ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) )
= $false )
| ( ( SV61 = SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(515,plain,
! [SV80: $i,SV61: $i] :
( ( ( ~ ( subset @ SV61 @ SV80 )
| ~ ( subset @ SV80 @ SV61 ) )
= $true )
| ( ( SV61 = SV80 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(516,plain,
! [SV92: $i,SV81: $i,SV63: $i] :
( ( ( subset @ SV63 @ SV81 )
= $false )
| ( ( ~ ( subset @ SV81 @ SV92 ) )
= $true )
| ( ( subset @ SV63 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(517,plain,
! [SV93: $i,SV83: $i,SV65: $i] :
( ( ( subset @ SV65 @ SV83 )
= $false )
| ( ( ~ ( subset @ SV65 @ SV93 ) )
= $true )
| ( ( subset @ SV65 @ ( set_intersection2 @ SV83 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(518,plain,
! [SV88: $i,SV70: $i,SV95: $i] :
( ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false )
| ( ( ! [SY130: $i] :
~ ( ~ ( ~ ( in @ SY130 @ SV95 )
| ~ ( ~ ( in @ SY130 @ SV70 )
| ~ ~ ( in @ SY130 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY130 @ SV70 )
| ~ ~ ( in @ SY130 @ SV88 ) )
| ( in @ SY130 @ SV95 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(519,plain,
! [SV88: $i,SV70: $i,SV95: $i] :
( ( ( ! [SY131: $i] :
~ ( ~ ( ~ ( in @ SY131 @ SV95 )
| ~ ( ~ ( in @ SY131 @ SV70 )
| ~ ~ ( in @ SY131 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY131 @ SV70 )
| ~ ~ ( in @ SY131 @ SV88 ) )
| ( in @ SY131 @ SV95 ) ) ) )
= $false )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(520,plain,
! [SV71: $i,SV96: $i] :
( ( ( in @ SV96 @ SV71 )
= $false )
| ( ( SV71 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(521,plain,
! [SV71: $i] :
( ( ( in @ ( sK6_SY116 @ SV71 ) @ SV71 )
= $true )
| ( ( SV71 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(522,plain,
! [SV89: $i,SV73: $i,SV97: $i] :
( ( ( ~ ( in @ SV97 @ SV73 )
| ( in @ SV97 @ SV89 ) )
= $true )
| ( ( subset @ SV73 @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(523,plain,
! [SV73: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK7_SY129 @ SV89 @ SV73 ) @ SV73 )
| ( in @ ( sK7_SY129 @ SV89 @ SV73 ) @ SV89 ) )
= $false )
| ( ( subset @ SV73 @ SV89 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[512]) ).
thf(524,plain,
! [SV60: $i,SV79: $i,SV91: $i] :
( ( ( subset @ SV91 @ SV79 )
= $false )
| ( ( subset @ SV60 @ SV79 )
= $false )
| ( ( subset @ ( set_union2 @ SV60 @ SV91 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(525,plain,
! [SV80: $i,SV61: $i] :
( ( ( ~ ( subset @ SV61 @ SV80 ) )
= $false )
| ( ( SV61 = SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(526,plain,
! [SV61: $i,SV80: $i] :
( ( ( ~ ( subset @ SV80 @ SV61 ) )
= $false )
| ( ( SV61 = SV80 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[514]) ).
thf(527,plain,
! [SV80: $i,SV61: $i] :
( ( ( ~ ( subset @ SV61 @ SV80 ) )
= $true )
| ( ( ~ ( subset @ SV80 @ SV61 ) )
= $true )
| ( ( SV61 = SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(528,plain,
! [SV63: $i,SV92: $i,SV81: $i] :
( ( ( subset @ SV81 @ SV92 )
= $false )
| ( ( subset @ SV63 @ SV81 )
= $false )
| ( ( subset @ SV63 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(529,plain,
! [SV83: $i,SV93: $i,SV65: $i] :
( ( ( subset @ SV65 @ SV93 )
= $false )
| ( ( subset @ SV65 @ SV83 )
= $false )
| ( ( subset @ SV65 @ ( set_intersection2 @ SV83 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(530,plain,
! [SV88: $i,SV70: $i,SV95: $i,SV98: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV98 @ SV95 )
| ~ ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) )
| ( in @ SV98 @ SV95 ) ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(531,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
| ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) ) ) )
= $false )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[519]) ).
thf(532,plain,
! [SV89: $i,SV73: $i,SV97: $i] :
( ( ( ~ ( in @ SV97 @ SV73 ) )
= $true )
| ( ( in @ SV97 @ SV89 )
= $true )
| ( ( subset @ SV73 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(533,plain,
! [SV73: $i,SV89: $i] :
( ( ( ~ ( in @ ( sK7_SY129 @ SV89 @ SV73 ) @ SV73 ) )
= $false )
| ( ( subset @ SV73 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[523]) ).
thf(534,plain,
! [SV73: $i,SV89: $i] :
( ( ( in @ ( sK7_SY129 @ SV89 @ SV73 ) @ SV89 )
= $false )
| ( ( subset @ SV73 @ SV89 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[523]) ).
thf(535,plain,
! [SV80: $i,SV61: $i] :
( ( ( subset @ SV61 @ SV80 )
= $true )
| ( ( SV61 = SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(536,plain,
! [SV61: $i,SV80: $i] :
( ( ( subset @ SV80 @ SV61 )
= $true )
| ( ( SV61 = SV80 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(537,plain,
! [SV80: $i,SV61: $i] :
( ( ( subset @ SV61 @ SV80 )
= $false )
| ( ( ~ ( subset @ SV80 @ SV61 ) )
= $true )
| ( ( SV61 = SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(538,plain,
! [SV88: $i,SV70: $i,SV95: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ SV98 @ SV95 )
| ~ ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) )
| ( in @ SV98 @ SV95 ) ) )
= $false )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(539,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
| ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(540,plain,
! [SV89: $i,SV73: $i,SV97: $i] :
( ( ( in @ SV97 @ SV73 )
= $false )
| ( ( in @ SV97 @ SV89 )
= $true )
| ( ( subset @ SV73 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(541,plain,
! [SV73: $i,SV89: $i] :
( ( ( in @ ( sK7_SY129 @ SV89 @ SV73 ) @ SV73 )
= $true )
| ( ( subset @ SV73 @ SV89 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(542,plain,
! [SV61: $i,SV80: $i] :
( ( ( subset @ SV80 @ SV61 )
= $false )
| ( ( subset @ SV61 @ SV80 )
= $false )
| ( ( SV61 = SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(543,plain,
! [SV88: $i,SV70: $i,SV95: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ SV98 @ SV95 )
| ~ ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) ) ) )
= $false )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(544,plain,
! [SV95: $i,SV88: $i,SV70: $i,SV98: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) )
| ( in @ SV98 @ SV95 ) ) )
= $false )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(545,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
| ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(546,plain,
! [SV88: $i,SV70: $i,SV95: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV95 )
| ~ ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(547,plain,
! [SV95: $i,SV88: $i,SV70: $i,SV98: $i] :
( ( ( ~ ~ ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) )
| ( in @ SV98 @ SV95 ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(548,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
| ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(549,plain,
! [SV88: $i,SV70: $i,SV95: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV95 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(550,plain,
! [SV95: $i,SV88: $i,SV70: $i,SV98: $i] :
( ( ( ~ ~ ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) ) )
= $true )
| ( ( in @ SV98 @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(551,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(552,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(553,plain,
! [SV88: $i,SV70: $i,SV95: $i,SV98: $i] :
( ( ( in @ SV98 @ SV95 )
= $false )
| ( ( ~ ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(554,plain,
! [SV95: $i,SV88: $i,SV70: $i,SV98: $i] :
( ( ( ~ ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) ) )
= $false )
| ( ( in @ SV98 @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(555,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(556,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(557,plain,
! [SV95: $i,SV88: $i,SV70: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) )
= $false )
| ( ( in @ SV98 @ SV95 )
= $false )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(558,plain,
! [SV95: $i,SV88: $i,SV70: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV70 )
| ~ ~ ( in @ SV98 @ SV88 ) )
= $true )
| ( ( in @ SV98 @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(559,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(560,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 ) )
= $true )
| ( ( ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(561,plain,
! [SV88: $i,SV95: $i,SV70: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV70 ) )
= $false )
| ( ( in @ SV98 @ SV95 )
= $false )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(562,plain,
! [SV70: $i,SV95: $i,SV88: $i,SV98: $i] :
( ( ( ~ ~ ( in @ SV98 @ SV88 ) )
= $false )
| ( ( in @ SV98 @ SV95 )
= $false )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(563,plain,
! [SV95: $i,SV88: $i,SV70: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV70 ) )
= $true )
| ( ( ~ ~ ( in @ SV98 @ SV88 ) )
= $true )
| ( ( in @ SV98 @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(564,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) ) )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[559]) ).
thf(565,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[559]) ).
thf(566,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(567,plain,
! [SV88: $i,SV95: $i,SV70: $i,SV98: $i] :
( ( ( in @ SV98 @ SV70 )
= $true )
| ( ( in @ SV98 @ SV95 )
= $false )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(568,plain,
! [SV70: $i,SV95: $i,SV88: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV88 ) )
= $true )
| ( ( in @ SV98 @ SV95 )
= $false )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(569,plain,
! [SV95: $i,SV88: $i,SV70: $i,SV98: $i] :
( ( ( in @ SV98 @ SV70 )
= $false )
| ( ( ~ ~ ( in @ SV98 @ SV88 ) )
= $true )
| ( ( in @ SV98 @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(570,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) ) )
= $true )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[564]) ).
thf(571,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(572,plain,
! [SV70: $i,SV95: $i,SV88: $i,SV98: $i] :
( ( ( in @ SV98 @ SV88 )
= $false )
| ( ( in @ SV98 @ SV95 )
= $false )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(573,plain,
! [SV95: $i,SV70: $i,SV88: $i,SV98: $i] :
( ( ( ~ ( in @ SV98 @ SV88 ) )
= $false )
| ( ( in @ SV98 @ SV70 )
= $false )
| ( ( in @ SV98 @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(574,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(575,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $true )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) ) )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[571]) ).
thf(576,plain,
! [SV95: $i,SV70: $i,SV88: $i,SV98: $i] :
( ( ( in @ SV98 @ SV88 )
= $true )
| ( ( in @ SV98 @ SV70 )
= $false )
| ( ( in @ SV98 @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(577,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 ) )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(578,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(579,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
| ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 ) )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(580,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $true )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[577]) ).
thf(581,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
= $true )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(582,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) ) )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(583,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[579]) ).
thf(584,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV95 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(585,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) ) )
= $true )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(586,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
| ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(587,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 ) )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(588,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[586]) ).
thf(589,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $true )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[587]) ).
thf(590,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( ~ ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 ) )
= $true )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(591,plain,
! [SV95: $i,SV70: $i,SV88: $i] :
( ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV70 )
= $false )
| ( ( in @ ( sK8_SY131 @ SV88 @ SV70 @ SV95 ) @ SV88 )
= $true )
| ( ( SV95
= ( set_difference @ SV70 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(592,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[357,591,589,584,583,580,576,572,567,565,542,541,540,536,535,534,529,528,524,521,520,506,505,504,503,474,466,455,453,446,437,434,421,413,412,411,410,393,392,391,390,386,361,360,359,358]) ).
thf(593,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[592,338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU134+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
% 0.07/0.19 % Computer : n008.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:02:09 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.66/0.48
% 1.66/0.48 No.of.Axioms: 29
% 1.66/0.48
% 1.66/0.48 Length.of.Defs: 0
% 1.66/0.48
% 1.66/0.48 Contains.Choice.Funs: false
% 1.66/0.48 .................
% 1.66/0.48
% 1.66/0.48 ********************************
% 1.66/0.48 * All subproblems solved! *
% 1.66/0.48 ********************************
% 1.66/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:29,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:592,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.66/0.48
% 1.66/0.48 %**** Beginning of derivation protocol ****
% 1.66/0.48 % SZS output start CNFRefutation
% See solution above
% 1.66/0.48
% 1.66/0.48 %**** End of derivation protocol ****
% 1.66/0.48 %**** no. of clauses in derivation: 576 ****
% 1.66/0.48 %**** clause counter: 592 ****
% 1.66/0.48
% 1.66/0.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:29,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:592,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------