%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU167+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 10:43:13 AM UTC 2026
% Result : Theorem 30.11s 5.28s
% Output : CNFRefutation 30.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 31
% Syntax : Number of formulae : 269 ( 168 unt; 0 typ; 0 def)
% Number of atoms : 1325 ( 430 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 2192 ( 430 ~; 287 |; 31 &;1392 @)
% ( 9 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 7 con; 0-2 aty)
% Number of variables : 556 ( 0 ^; 556 !; 0 ?; 556 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY50,type,
sK2_SY50: $i ).
thf(tp_sK3_SY53,type,
sK3_SY53: $i ).
thf(tp_sK4_SY55,type,
sK4_SY55: $i ).
thf(tp_sK5_SY85,type,
sK5_SY85: $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(55,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(60,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(66,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(73,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(76,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(82,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(97,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(98,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[97]) ).
thf(99,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[98]) ).
thf(100,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(101,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(102,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(103,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(104,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(105,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(106,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(107,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(108,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(109,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(110,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(114,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)],[53]) ).
thf(115,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(117,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(119,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(120,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(121,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)],[75]) ).
thf(122,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(123,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(124,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)],[78]) ).
thf(125,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(126,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)],[81]) ).
thf(127,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(128,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(129,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(130,plain,
( ( ! [SY50: $i,SY51: $i,SY52: $i] :
( ( ( subset @ sK1_A @ SY50 )
& ( subset @ SY51 @ SY52 ) )
=> ( subset @ ( cartesian_product2 @ sK1_A @ SY51 ) @ ( cartesian_product2 @ SY50 @ SY52 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[99]) ).
thf(131,plain,
( ( ! [SY53: $i,SY54: $i] :
( ( ( subset @ sK1_A @ sK2_SY50 )
& ( subset @ SY53 @ SY54 ) )
=> ( subset @ ( cartesian_product2 @ sK1_A @ SY53 ) @ ( cartesian_product2 @ sK2_SY50 @ SY54 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[130]) ).
thf(132,plain,
( ( ! [SY55: $i] :
( ( ( subset @ sK1_A @ sK2_SY50 )
& ( subset @ sK3_SY53 @ SY55 ) )
=> ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY53 ) @ ( cartesian_product2 @ sK2_SY50 @ SY55 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[131]) ).
thf(133,plain,
( ( ( ( subset @ sK1_A @ sK2_SY50 )
& ( subset @ sK3_SY53 @ sK4_SY55 ) )
=> ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY53 ) @ ( cartesian_product2 @ sK2_SY50 @ sK4_SY55 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[132]) ).
thf(134,plain,
( ( subset @ sK1_A @ sK2_SY50 )
= $true ),
inference(standard_cnf,[status(thm)],[133]) ).
thf(135,plain,
( ( subset @ sK3_SY53 @ sK4_SY55 )
= $true ),
inference(standard_cnf,[status(thm)],[133]) ).
thf(136,plain,
( ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY53 ) @ ( cartesian_product2 @ sK2_SY50 @ sK4_SY55 ) )
= $false ),
inference(standard_cnf,[status(thm)],[133]) ).
thf(137,plain,
( ( ~ ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY53 ) @ ( cartesian_product2 @ sK2_SY50 @ sK4_SY55 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[136]) ).
thf(138,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(139,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(141,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(142,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(143,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(144,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(145,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(146,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(147,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(148,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(149,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(150,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(151,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(152,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(153,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(154,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(155,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(156,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(157,plain,
$true = $true,
inference(copy,[status(thm)],[110]) ).
thf(158,plain,
$true = $true,
inference(copy,[status(thm)],[109]) ).
thf(159,plain,
$true = $true,
inference(copy,[status(thm)],[108]) ).
thf(160,plain,
$true = $true,
inference(copy,[status(thm)],[107]) ).
thf(161,plain,
$true = $true,
inference(copy,[status(thm)],[106]) ).
thf(162,plain,
$true = $true,
inference(copy,[status(thm)],[105]) ).
thf(163,plain,
$true = $true,
inference(copy,[status(thm)],[104]) ).
thf(164,plain,
$true = $true,
inference(copy,[status(thm)],[103]) ).
thf(165,plain,
$true = $true,
inference(copy,[status(thm)],[102]) ).
thf(166,plain,
$true = $true,
inference(copy,[status(thm)],[101]) ).
thf(167,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(168,plain,
( ( subset @ sK3_SY53 @ sK4_SY55 )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(169,plain,
( ( subset @ sK1_A @ sK2_SY50 )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(170,plain,
( ( ~ ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY53 ) @ ( cartesian_product2 @ sK2_SY50 @ sK4_SY55 ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(171,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( proper_subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(172,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(173,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) )
| ~ ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(174,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(175,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)],[154]) ).
thf(176,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)],[155]) ).
thf(177,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)],[146]) ).
thf(178,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( proper_subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( proper_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(179,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)],[153]) ).
thf(180,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(181,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(182,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(183,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( disjoint @ SX1 @ SX2 ) )
| ( disjoint @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(184,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)],[143]) ).
thf(185,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)],[141]) ).
thf(186,plain,
! [SV1: $i] :
( ( ! [SY56: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY56 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(187,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(188,plain,
! [SV3: $i] :
( ( ! [SY57: $i] : ( subset @ ( set_difference @ SV3 @ SY57 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(189,plain,
! [SV4: $i] :
( ( ! [SY58: $i] : ( subset @ SV4 @ ( set_union2 @ SV4 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(190,plain,
! [SV5: $i] :
( ( ! [SY59: $i] : ( subset @ SV5 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(191,plain,
( ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY53 ) @ ( cartesian_product2 @ sK2_SY50 @ sK4_SY55 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(192,plain,
! [SV6: $i] :
( ( ! [SY60: $i] :
~ ~ ( ~ ( subset @ SV6 @ SY60 )
| ~ ( proper_subset @ SY60 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(193,plain,
! [SV7: $i] :
( ( ! [SY61: $i] :
( ~ ( subset @ SV7 @ SY61 )
| ( ( set_union2 @ SV7 @ SY61 )
= SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(194,plain,
! [SV8: $i] :
( ( ! [SY62: $i,SY63: $i] :
( ~ ( subset @ SV8 @ SY62 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV8 @ SY63 ) @ ( cartesian_product2 @ SY62 @ SY63 ) )
| ~ ( subset @ ( cartesian_product2 @ SY63 @ SV8 ) @ ( cartesian_product2 @ SY63 @ SY62 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(195,plain,
! [SV9: $i] :
( ( ! [SY64: $i] :
( ~ ( subset @ ( singleton @ SV9 ) @ ( singleton @ SY64 ) )
| ( SV9 = SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(196,plain,
! [SV10: $i] :
( ( ! [SY65: $i] :
~ ( ~ ( ( SV10 != SY65 )
| ~ ( ~ ( subset @ SV10 @ SY65 )
| ~ ( subset @ SY65 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV10 @ SY65 )
| ~ ( subset @ SY65 @ SV10 ) )
| ( SV10 = SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(197,plain,
! [SV11: $i] :
( ( ! [SY66: $i] :
~ ( ~ ( ~ ( subset @ SV11 @ SY66 )
| ! [SY67: $i] :
( ~ ( in @ SY67 @ SV11 )
| ( in @ SY67 @ SY66 ) ) )
| ~ ( ~ ! [SY68: $i] :
( ~ ( in @ SY68 @ SV11 )
| ( in @ SY68 @ SY66 ) )
| ( subset @ SV11 @ SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(198,plain,
! [SV12: $i] :
( ( ! [SY69: $i,SY70: $i] :
( ~ ( subset @ SV12 @ SY69 )
| ( subset @ ( set_difference @ SV12 @ SY70 ) @ ( set_difference @ SY69 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(199,plain,
! [SV13: $i] :
( ( ! [SY71: $i] :
~ ( ~ ( ~ ( proper_subset @ SV13 @ SY71 )
| ~ ( ~ ( subset @ SV13 @ SY71 )
| ~ ( ( SV13 != SY71 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV13 @ SY71 )
| ~ ( ( SV13 != SY71 ) ) )
| ( proper_subset @ SV13 @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(200,plain,
! [SV14: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ~ ~ ( ~ ( subset @ SV14 @ SY72 )
| ~ ( subset @ SY73 @ SY72 ) )
| ( subset @ ( set_union2 @ SV14 @ SY73 ) @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(201,plain,
! [SV15: $i] :
( ( ~ ( subset @ SV15 @ empty_set )
| ( SV15 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(202,plain,
! [SV16: $i] :
( ( ! [SY74: $i] :
( ~ ( subset @ SV16 @ SY74 )
| ( ( set_intersection2 @ SV16 @ SY74 )
= SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(203,plain,
! [SV17: $i] :
( ( ! [SY75: $i,SY76: $i] :
( ~ ~ ( ~ ( subset @ SV17 @ SY75 )
| ~ ( subset @ SY75 @ SY76 ) )
| ( subset @ SV17 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(204,plain,
! [SV18: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ~ ~ ( ~ ( subset @ SV18 @ SY77 )
| ~ ( disjoint @ SY77 @ SY78 ) )
| ( disjoint @ SV18 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(205,plain,
! [SV19: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ~ ( subset @ SV19 @ SY79 )
| ( subset @ ( set_intersection2 @ SV19 @ SY80 ) @ ( set_intersection2 @ SY79 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(206,plain,
! [SV20: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ~ ~ ( ~ ( subset @ SV20 @ SY81 )
| ~ ( subset @ SV20 @ SY82 ) )
| ( subset @ SV20 @ ( set_intersection2 @ SY81 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(207,plain,
! [SV21: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV21 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(208,plain,
! [SV22: $i,SV3: $i] :
( ( subset @ ( set_difference @ SV3 @ SV22 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(209,plain,
! [SV23: $i,SV4: $i] :
( ( subset @ SV4 @ ( set_union2 @ SV4 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(210,plain,
! [SV5: $i] :
( ( subset @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(211,plain,
! [SV25: $i,SV6: $i] :
( ( ~ ~ ( ~ ( subset @ SV6 @ SV25 )
| ~ ( proper_subset @ SV25 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(212,plain,
! [SV26: $i,SV7: $i] :
( ( ~ ( subset @ SV7 @ SV26 )
| ( ( set_union2 @ SV7 @ SV26 )
= SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(213,plain,
! [SV27: $i,SV8: $i] :
( ( ! [SY83: $i] :
( ~ ( subset @ SV8 @ SV27 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV8 @ SY83 ) @ ( cartesian_product2 @ SV27 @ SY83 ) )
| ~ ( subset @ ( cartesian_product2 @ SY83 @ SV8 ) @ ( cartesian_product2 @ SY83 @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(214,plain,
! [SV28: $i,SV9: $i] :
( ( ~ ( subset @ ( singleton @ SV9 ) @ ( singleton @ SV28 ) )
| ( SV9 = SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(215,plain,
! [SV29: $i,SV10: $i] :
( ( ~ ( ~ ( ( SV10 != SV29 )
| ~ ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) )
| ( SV10 = SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(216,plain,
! [SV30: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV11 @ SV30 )
| ! [SY84: $i] :
( ~ ( in @ SY84 @ SV11 )
| ( in @ SY84 @ SV30 ) ) )
| ~ ( ~ ! [SY85: $i] :
( ~ ( in @ SY85 @ SV11 )
| ( in @ SY85 @ SV30 ) )
| ( subset @ SV11 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(217,plain,
! [SV31: $i,SV12: $i] :
( ( ! [SY86: $i] :
( ~ ( subset @ SV12 @ SV31 )
| ( subset @ ( set_difference @ SV12 @ SY86 ) @ ( set_difference @ SV31 @ SY86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(218,plain,
! [SV32: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( proper_subset @ SV13 @ SV32 )
| ~ ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) )
| ( proper_subset @ SV13 @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(219,plain,
! [SV33: $i,SV14: $i] :
( ( ! [SY87: $i] :
( ~ ~ ( ~ ( subset @ SV14 @ SV33 )
| ~ ( subset @ SY87 @ SV33 ) )
| ( subset @ ( set_union2 @ SV14 @ SY87 ) @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(220,plain,
! [SV15: $i] :
( ( ( ~ ( subset @ SV15 @ empty_set ) )
= $true )
| ( ( SV15 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(221,plain,
! [SV34: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV34 )
| ( ( set_intersection2 @ SV16 @ SV34 )
= SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(222,plain,
! [SV35: $i,SV17: $i] :
( ( ! [SY88: $i] :
( ~ ~ ( ~ ( subset @ SV17 @ SV35 )
| ~ ( subset @ SV35 @ SY88 ) )
| ( subset @ SV17 @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(223,plain,
! [SV36: $i,SV18: $i] :
( ( ! [SY89: $i] :
( ~ ~ ( ~ ( subset @ SV18 @ SV36 )
| ~ ( disjoint @ SV36 @ SY89 ) )
| ( disjoint @ SV18 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(224,plain,
! [SV37: $i,SV19: $i] :
( ( ! [SY90: $i] :
( ~ ( subset @ SV19 @ SV37 )
| ( subset @ ( set_intersection2 @ SV19 @ SY90 ) @ ( set_intersection2 @ SV37 @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(225,plain,
! [SV38: $i,SV20: $i] :
( ( ! [SY91: $i] :
( ~ ~ ( ~ ( subset @ SV20 @ SV38 )
| ~ ( subset @ SV20 @ SY91 ) )
| ( subset @ SV20 @ ( set_intersection2 @ SV38 @ SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(226,plain,
! [SV25: $i,SV6: $i] :
( ( ~ ( ~ ( subset @ SV6 @ SV25 )
| ~ ( proper_subset @ SV25 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(227,plain,
! [SV26: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV26 ) )
= $true )
| ( ( ( set_union2 @ SV7 @ SV26 )
= SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(228,plain,
! [SV39: $i,SV27: $i,SV8: $i] :
( ( ~ ( subset @ SV8 @ SV27 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV8 @ SV39 ) @ ( cartesian_product2 @ SV27 @ SV39 ) )
| ~ ( subset @ ( cartesian_product2 @ SV39 @ SV8 ) @ ( cartesian_product2 @ SV39 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(229,plain,
! [SV28: $i,SV9: $i] :
( ( ( ~ ( subset @ ( singleton @ SV9 ) @ ( singleton @ SV28 ) ) )
= $true )
| ( ( SV9 = SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(230,plain,
! [SV29: $i,SV10: $i] :
( ( ~ ( ( SV10 != SV29 )
| ~ ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) )
| ( SV10 = SV29 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(231,plain,
! [SV30: $i,SV11: $i] :
( ( ~ ( ~ ( subset @ SV11 @ SV30 )
| ! [SY84: $i] :
( ~ ( in @ SY84 @ SV11 )
| ( in @ SY84 @ SV30 ) ) )
| ~ ( ~ ! [SY85: $i] :
( ~ ( in @ SY85 @ SV11 )
| ( in @ SY85 @ SV30 ) )
| ( subset @ SV11 @ SV30 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(232,plain,
! [SV40: $i,SV31: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV31 )
| ( subset @ ( set_difference @ SV12 @ SV40 ) @ ( set_difference @ SV31 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(233,plain,
! [SV32: $i,SV13: $i] :
( ( ~ ( ~ ( proper_subset @ SV13 @ SV32 )
| ~ ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) )
| ( proper_subset @ SV13 @ SV32 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(234,plain,
! [SV41: $i,SV33: $i,SV14: $i] :
( ( ~ ~ ( ~ ( subset @ SV14 @ SV33 )
| ~ ( subset @ SV41 @ SV33 ) )
| ( subset @ ( set_union2 @ SV14 @ SV41 ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(235,plain,
! [SV15: $i] :
( ( ( subset @ SV15 @ empty_set )
= $false )
| ( ( SV15 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(236,plain,
! [SV34: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV34 ) )
= $true )
| ( ( ( set_intersection2 @ SV16 @ SV34 )
= SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(237,plain,
! [SV42: $i,SV35: $i,SV17: $i] :
( ( ~ ~ ( ~ ( subset @ SV17 @ SV35 )
| ~ ( subset @ SV35 @ SV42 ) )
| ( subset @ SV17 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(238,plain,
! [SV43: $i,SV36: $i,SV18: $i] :
( ( ~ ~ ( ~ ( subset @ SV18 @ SV36 )
| ~ ( disjoint @ SV36 @ SV43 ) )
| ( disjoint @ SV18 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(239,plain,
! [SV44: $i,SV37: $i,SV19: $i] :
( ( ~ ( subset @ SV19 @ SV37 )
| ( subset @ ( set_intersection2 @ SV19 @ SV44 ) @ ( set_intersection2 @ SV37 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(240,plain,
! [SV45: $i,SV38: $i,SV20: $i] :
( ( ~ ~ ( ~ ( subset @ SV20 @ SV38 )
| ~ ( subset @ SV20 @ SV45 ) )
| ( subset @ SV20 @ ( set_intersection2 @ SV38 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(241,plain,
! [SV25: $i,SV6: $i] :
( ( ~ ( subset @ SV6 @ SV25 )
| ~ ( proper_subset @ SV25 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(242,plain,
! [SV26: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV26 )
= $false )
| ( ( ( set_union2 @ SV7 @ SV26 )
= SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(243,plain,
! [SV39: $i,SV27: $i,SV8: $i] :
( ( ( ~ ( subset @ SV8 @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( cartesian_product2 @ SV8 @ SV39 ) @ ( cartesian_product2 @ SV27 @ SV39 ) )
| ~ ( subset @ ( cartesian_product2 @ SV39 @ SV8 ) @ ( cartesian_product2 @ SV39 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(244,plain,
! [SV28: $i,SV9: $i] :
( ( ( subset @ ( singleton @ SV9 ) @ ( singleton @ SV28 ) )
= $false )
| ( ( SV9 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(245,plain,
! [SV29: $i,SV10: $i] :
( ( ~ ( ( SV10 != SV29 )
| ~ ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(246,plain,
! [SV29: $i,SV10: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) )
| ( SV10 = SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(247,plain,
! [SV30: $i,SV11: $i] :
( ( ~ ( ~ ( subset @ SV11 @ SV30 )
| ! [SY84: $i] :
( ~ ( in @ SY84 @ SV11 )
| ( in @ SY84 @ SV30 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(248,plain,
! [SV30: $i,SV11: $i] :
( ( ~ ( ~ ! [SY85: $i] :
( ~ ( in @ SY85 @ SV11 )
| ( in @ SY85 @ SV30 ) )
| ( subset @ SV11 @ SV30 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(249,plain,
! [SV40: $i,SV31: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV31 ) )
= $true )
| ( ( subset @ ( set_difference @ SV12 @ SV40 ) @ ( set_difference @ SV31 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(250,plain,
! [SV32: $i,SV13: $i] :
( ( ~ ( ~ ( proper_subset @ SV13 @ SV32 )
| ~ ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(251,plain,
! [SV32: $i,SV13: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) )
| ( proper_subset @ SV13 @ SV32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(252,plain,
! [SV41: $i,SV33: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV14 @ SV33 )
| ~ ( subset @ SV41 @ SV33 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV14 @ SV41 ) @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(253,plain,
! [SV34: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV34 )
= $false )
| ( ( ( set_intersection2 @ SV16 @ SV34 )
= SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(254,plain,
! [SV42: $i,SV35: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV17 @ SV35 )
| ~ ( subset @ SV35 @ SV42 ) ) )
= $true )
| ( ( subset @ SV17 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(255,plain,
! [SV43: $i,SV36: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV18 @ SV36 )
| ~ ( disjoint @ SV36 @ SV43 ) ) )
= $true )
| ( ( disjoint @ SV18 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(256,plain,
! [SV44: $i,SV37: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV37 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV19 @ SV44 ) @ ( set_intersection2 @ SV37 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(257,plain,
! [SV45: $i,SV38: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV20 @ SV38 )
| ~ ( subset @ SV20 @ SV45 ) ) )
= $true )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV38 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(258,plain,
! [SV25: $i,SV6: $i] :
( ( ( ~ ( subset @ SV6 @ SV25 ) )
= $true )
| ( ( ~ ( proper_subset @ SV25 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(259,plain,
! [SV39: $i,SV27: $i,SV8: $i] :
( ( ( subset @ SV8 @ SV27 )
= $false )
| ( ( ~ ( ~ ( subset @ ( cartesian_product2 @ SV8 @ SV39 ) @ ( cartesian_product2 @ SV27 @ SV39 ) )
| ~ ( subset @ ( cartesian_product2 @ SV39 @ SV8 ) @ ( cartesian_product2 @ SV39 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(260,plain,
! [SV29: $i,SV10: $i] :
( ( ( SV10 != SV29 )
| ~ ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(261,plain,
! [SV29: $i,SV10: $i] :
( ( ~ ~ ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) )
| ( SV10 = SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(262,plain,
! [SV30: $i,SV11: $i] :
( ( ~ ( subset @ SV11 @ SV30 )
| ! [SY84: $i] :
( ~ ( in @ SY84 @ SV11 )
| ( in @ SY84 @ SV30 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(263,plain,
! [SV30: $i,SV11: $i] :
( ( ~ ! [SY85: $i] :
( ~ ( in @ SY85 @ SV11 )
| ( in @ SY85 @ SV30 ) )
| ( subset @ SV11 @ SV30 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(264,plain,
! [SV40: $i,SV31: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV31 )
= $false )
| ( ( subset @ ( set_difference @ SV12 @ SV40 ) @ ( set_difference @ SV31 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(265,plain,
! [SV32: $i,SV13: $i] :
( ( ~ ( proper_subset @ SV13 @ SV32 )
| ~ ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(266,plain,
! [SV32: $i,SV13: $i] :
( ( ~ ~ ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) )
| ( proper_subset @ SV13 @ SV32 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(267,plain,
! [SV41: $i,SV33: $i,SV14: $i] :
( ( ( ~ ( ~ ( subset @ SV14 @ SV33 )
| ~ ( subset @ SV41 @ SV33 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV14 @ SV41 ) @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(268,plain,
! [SV42: $i,SV35: $i,SV17: $i] :
( ( ( ~ ( ~ ( subset @ SV17 @ SV35 )
| ~ ( subset @ SV35 @ SV42 ) ) )
= $false )
| ( ( subset @ SV17 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(269,plain,
! [SV43: $i,SV36: $i,SV18: $i] :
( ( ( ~ ( ~ ( subset @ SV18 @ SV36 )
| ~ ( disjoint @ SV36 @ SV43 ) ) )
= $false )
| ( ( disjoint @ SV18 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(270,plain,
! [SV44: $i,SV37: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV37 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV19 @ SV44 ) @ ( set_intersection2 @ SV37 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(271,plain,
! [SV45: $i,SV38: $i,SV20: $i] :
( ( ( ~ ( ~ ( subset @ SV20 @ SV38 )
| ~ ( subset @ SV20 @ SV45 ) ) )
= $false )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV38 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(272,plain,
! [SV25: $i,SV6: $i] :
( ( ( subset @ SV6 @ SV25 )
= $false )
| ( ( ~ ( proper_subset @ SV25 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(273,plain,
! [SV27: $i,SV39: $i,SV8: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV8 @ SV39 ) @ ( cartesian_product2 @ SV27 @ SV39 ) )
| ~ ( subset @ ( cartesian_product2 @ SV39 @ SV8 ) @ ( cartesian_product2 @ SV39 @ SV27 ) ) )
= $false )
| ( ( subset @ SV8 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(274,plain,
! [SV29: $i,SV10: $i] :
( ( ( SV10 != SV29 )
= $true )
| ( ( ~ ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(275,plain,
! [SV29: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) ) )
= $true )
| ( ( SV10 = SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(276,plain,
! [SV30: $i,SV11: $i] :
( ( ( ~ ( subset @ SV11 @ SV30 ) )
= $true )
| ( ( ! [SY84: $i] :
( ~ ( in @ SY84 @ SV11 )
| ( in @ SY84 @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(277,plain,
! [SV30: $i,SV11: $i] :
( ( ( ~ ! [SY85: $i] :
( ~ ( in @ SY85 @ SV11 )
| ( in @ SY85 @ SV30 ) ) )
= $true )
| ( ( subset @ SV11 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(278,plain,
! [SV32: $i,SV13: $i] :
( ( ( ~ ( proper_subset @ SV13 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(279,plain,
! [SV32: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) ) )
= $true )
| ( ( proper_subset @ SV13 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(280,plain,
! [SV41: $i,SV33: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV33 )
| ~ ( subset @ SV41 @ SV33 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV14 @ SV41 ) @ SV33 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(281,plain,
! [SV42: $i,SV35: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV35 )
| ~ ( subset @ SV35 @ SV42 ) )
= $true )
| ( ( subset @ SV17 @ SV42 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(282,plain,
! [SV43: $i,SV36: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV36 )
| ~ ( disjoint @ SV36 @ SV43 ) )
= $true )
| ( ( disjoint @ SV18 @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(283,plain,
! [SV45: $i,SV38: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV38 )
| ~ ( subset @ SV20 @ SV45 ) )
= $true )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV38 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(284,plain,
! [SV6: $i,SV25: $i] :
( ( ( proper_subset @ SV25 @ SV6 )
= $false )
| ( ( subset @ SV6 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(285,plain,
! [SV27: $i,SV39: $i,SV8: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV8 @ SV39 ) @ ( cartesian_product2 @ SV27 @ SV39 ) ) )
= $false )
| ( ( subset @ SV8 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(286,plain,
! [SV27: $i,SV8: $i,SV39: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV39 @ SV8 ) @ ( cartesian_product2 @ SV39 @ SV27 ) ) )
= $false )
| ( ( subset @ SV8 @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(287,plain,
! [SV29: $i,SV10: $i] :
( ( ( SV10 = SV29 )
= $false )
| ( ( ~ ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(288,plain,
! [SV29: $i,SV10: $i] :
( ( ( ~ ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) ) )
= $false )
| ( ( SV10 = SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(289,plain,
! [SV30: $i,SV11: $i] :
( ( ( subset @ SV11 @ SV30 )
= $false )
| ( ( ! [SY84: $i] :
( ~ ( in @ SY84 @ SV11 )
| ( in @ SY84 @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(290,plain,
! [SV30: $i,SV11: $i] :
( ( ( ! [SY85: $i] :
( ~ ( in @ SY85 @ SV11 )
| ( in @ SY85 @ SV30 ) ) )
= $false )
| ( ( subset @ SV11 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(291,plain,
! [SV32: $i,SV13: $i] :
( ( ( proper_subset @ SV13 @ SV32 )
= $false )
| ( ( ~ ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(292,plain,
! [SV32: $i,SV13: $i] :
( ( ( ~ ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) ) )
= $false )
| ( ( proper_subset @ SV13 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(293,plain,
! [SV41: $i,SV33: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV33 ) )
= $true )
| ( ( ~ ( subset @ SV41 @ SV33 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV14 @ SV41 ) @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(294,plain,
! [SV42: $i,SV35: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV35 ) )
= $true )
| ( ( ~ ( subset @ SV35 @ SV42 ) )
= $true )
| ( ( subset @ SV17 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(295,plain,
! [SV43: $i,SV36: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV36 ) )
= $true )
| ( ( ~ ( disjoint @ SV36 @ SV43 ) )
= $true )
| ( ( disjoint @ SV18 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(296,plain,
! [SV45: $i,SV38: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV38 ) )
= $true )
| ( ( ~ ( subset @ SV20 @ SV45 ) )
= $true )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV38 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(297,plain,
! [SV27: $i,SV39: $i,SV8: $i] :
( ( ( subset @ ( cartesian_product2 @ SV8 @ SV39 ) @ ( cartesian_product2 @ SV27 @ SV39 ) )
= $true )
| ( ( subset @ SV8 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(298,plain,
! [SV27: $i,SV8: $i,SV39: $i] :
( ( ( subset @ ( cartesian_product2 @ SV39 @ SV8 ) @ ( cartesian_product2 @ SV39 @ SV27 ) )
= $true )
| ( ( subset @ SV8 @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(299,plain,
! [SV29: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) )
= $false )
| ( ( SV10 = SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(300,plain,
! [SV29: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV29 )
| ~ ( subset @ SV29 @ SV10 ) )
= $true )
| ( ( SV10 = SV29 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(301,plain,
! [SV30: $i,SV11: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ SV11 )
| ( in @ SV46 @ SV30 ) )
= $true )
| ( ( subset @ SV11 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(302,plain,
! [SV11: $i,SV30: $i] :
( ( ( ~ ( in @ ( sK5_SY85 @ SV30 @ SV11 ) @ SV11 )
| ( in @ ( sK5_SY85 @ SV30 @ SV11 ) @ SV30 ) )
= $false )
| ( ( subset @ SV11 @ SV30 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[290]) ).
thf(303,plain,
! [SV32: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) )
= $false )
| ( ( proper_subset @ SV13 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(304,plain,
! [SV32: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV32 )
| ~ ( ( SV13 != SV32 ) ) )
= $true )
| ( ( proper_subset @ SV13 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(305,plain,
! [SV41: $i,SV33: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV33 )
= $false )
| ( ( ~ ( subset @ SV41 @ SV33 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV14 @ SV41 ) @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(306,plain,
! [SV42: $i,SV35: $i,SV17: $i] :
( ( ( subset @ SV17 @ SV35 )
= $false )
| ( ( ~ ( subset @ SV35 @ SV42 ) )
= $true )
| ( ( subset @ SV17 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(307,plain,
! [SV43: $i,SV36: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV36 )
= $false )
| ( ( ~ ( disjoint @ SV36 @ SV43 ) )
= $true )
| ( ( disjoint @ SV18 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(308,plain,
! [SV45: $i,SV38: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV38 )
= $false )
| ( ( ~ ( subset @ SV20 @ SV45 ) )
= $true )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV38 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(309,plain,
! [SV29: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV29 ) )
= $false )
| ( ( SV10 = SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(310,plain,
! [SV10: $i,SV29: $i] :
( ( ( ~ ( subset @ SV29 @ SV10 ) )
= $false )
| ( ( SV10 = SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[299]) ).
thf(311,plain,
! [SV29: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV29 ) )
= $true )
| ( ( ~ ( subset @ SV29 @ SV10 ) )
= $true )
| ( ( SV10 = SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(312,plain,
! [SV30: $i,SV11: $i,SV46: $i] :
( ( ( ~ ( in @ SV46 @ SV11 ) )
= $true )
| ( ( in @ SV46 @ SV30 )
= $true )
| ( ( subset @ SV11 @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(313,plain,
! [SV11: $i,SV30: $i] :
( ( ( ~ ( in @ ( sK5_SY85 @ SV30 @ SV11 ) @ SV11 ) )
= $false )
| ( ( subset @ SV11 @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(314,plain,
! [SV11: $i,SV30: $i] :
( ( ( in @ ( sK5_SY85 @ SV30 @ SV11 ) @ SV30 )
= $false )
| ( ( subset @ SV11 @ SV30 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(315,plain,
! [SV32: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV32 ) )
= $false )
| ( ( proper_subset @ SV13 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(316,plain,
! [SV32: $i,SV13: $i] :
( ( ( ~ ( ( SV13 != SV32 ) ) )
= $false )
| ( ( proper_subset @ SV13 @ SV32 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(317,plain,
! [SV32: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV32 ) )
= $true )
| ( ( ~ ( ( SV13 != SV32 ) ) )
= $true )
| ( ( proper_subset @ SV13 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(318,plain,
! [SV14: $i,SV33: $i,SV41: $i] :
( ( ( subset @ SV41 @ SV33 )
= $false )
| ( ( subset @ SV14 @ SV33 )
= $false )
| ( ( subset @ ( set_union2 @ SV14 @ SV41 ) @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(319,plain,
! [SV17: $i,SV42: $i,SV35: $i] :
( ( ( subset @ SV35 @ SV42 )
= $false )
| ( ( subset @ SV17 @ SV35 )
= $false )
| ( ( subset @ SV17 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(320,plain,
! [SV18: $i,SV43: $i,SV36: $i] :
( ( ( disjoint @ SV36 @ SV43 )
= $false )
| ( ( subset @ SV18 @ SV36 )
= $false )
| ( ( disjoint @ SV18 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(321,plain,
! [SV38: $i,SV45: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV45 )
= $false )
| ( ( subset @ SV20 @ SV38 )
= $false )
| ( ( subset @ SV20 @ ( set_intersection2 @ SV38 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(322,plain,
! [SV29: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV29 )
= $true )
| ( ( SV10 = SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(323,plain,
! [SV10: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV10 )
= $true )
| ( ( SV10 = SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(324,plain,
! [SV29: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV29 )
= $false )
| ( ( ~ ( subset @ SV29 @ SV10 ) )
= $true )
| ( ( SV10 = SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(325,plain,
! [SV30: $i,SV11: $i,SV46: $i] :
( ( ( in @ SV46 @ SV11 )
= $false )
| ( ( in @ SV46 @ SV30 )
= $true )
| ( ( subset @ SV11 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(326,plain,
! [SV11: $i,SV30: $i] :
( ( ( in @ ( sK5_SY85 @ SV30 @ SV11 ) @ SV11 )
= $true )
| ( ( subset @ SV11 @ SV30 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(327,plain,
! [SV32: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV32 )
= $true )
| ( ( proper_subset @ SV13 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(328,plain,
! [SV32: $i,SV13: $i] :
( ( ( SV13 != SV32 )
= $true )
| ( ( proper_subset @ SV13 @ SV32 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(329,plain,
! [SV32: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV32 )
= $false )
| ( ( ~ ( ( SV13 != SV32 ) ) )
= $true )
| ( ( proper_subset @ SV13 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(330,plain,
! [SV10: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV10 )
= $false )
| ( ( subset @ SV10 @ SV29 )
= $false )
| ( ( SV10 = SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(331,plain,
! [SV32: $i,SV13: $i] :
( ( ( SV13 = SV32 )
= $false )
| ( ( proper_subset @ SV13 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(332,plain,
! [SV32: $i,SV13: $i] :
( ( ( SV13 != SV32 )
= $false )
| ( ( subset @ SV13 @ SV32 )
= $false )
| ( ( proper_subset @ SV13 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(333,plain,
! [SV32: $i,SV13: $i] :
( ( ( SV13 = SV32 )
= $true )
| ( ( subset @ SV13 @ SV32 )
= $false )
| ( ( proper_subset @ SV13 @ SV32 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(334,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[157,333,331,330,327,326,325,323,322,321,320,319,318,314,298,297,284,270,264,253,244,242,235,210,209,208,207,191,187,169,168,166,165,164,163,162,161,160,159,158]) ).
thf(335,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU167+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n018.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 15:05:06 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.11/5.28
% 30.11/5.28 No.of.Axioms: 30
% 30.11/5.28
% 30.11/5.28 Length.of.Defs: 0
% 30.11/5.28
% 30.11/5.28 Contains.Choice.Funs: false
% 30.11/5.28 .......
% 30.11/5.28
% 30.11/5.28 ********************************
% 30.11/5.28 * All subproblems solved! *
% 30.11/5.28 ********************************
% 30.11/5.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:32,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:334,loop_count:0,foatp_calls:1,translation:fof_full)
% 30.11/5.28
% 30.11/5.28 %**** Beginning of derivation protocol ****
% 30.11/5.28 % SZS output start CNFRefutation
% See solution above
% 30.11/5.28
% 30.11/5.28 %**** End of derivation protocol ****
% 30.11/5.28 %**** no. of clauses in derivation: 269 ****
% 30.11/5.28 %**** clause counter: 334 ****
% 30.11/5.28
% 30.11/5.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:32,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:334,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------