%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU362+1 : 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 : n017.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 10:44:08 AM UTC 2026
% Result : Theorem 254.47s 42.60s
% Output : CNFRefutation 254.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 27
% Syntax : Number of formulae : 302 ( 166 unt; 0 typ; 0 def)
% Number of atoms : 1911 ( 524 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 3564 ( 762 ~; 519 |; 38 &;2133 @)
% ( 9 <=>; 103 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 10 con; 0-3 aty)
% Number of variables : 548 ( 0 ^; 533 !; 15 ?; 548 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_related,type,
related: $i > $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_sK10_SY81,type,
sK10_SY81: $i ).
thf(tp_sK11_SY83,type,
sK11_SY83: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY51,type,
sK4_SY51: $i > $i ).
thf(tp_sK5_SY73,type,
sK5_SY73: $i ).
thf(tp_sK6_SY53,type,
sK6_SY53: $i > $i ).
thf(tp_sK7_SY52,type,
sK7_SY52: $i > $i ).
thf(tp_sK8_SY64,type,
sK8_SY64: $i > $i ).
thf(tp_sK9_SY78,type,
sK9_SY78: $i ).
thf(tp_subrelstr,type,
subrelstr: $i > $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_the_InternalRel,type,
the_InternalRel: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(11,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(12,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(19,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] : ( subrelstr @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_yellow_0) ).
thf(20,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(23,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(25,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(27,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( rel_str @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(30,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(31,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(32,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(33,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(34,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(35,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(36,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( related @ A @ B @ C )
<=> ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
thf(37,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( subrelstr @ B @ A )
<=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_yellow_0) ).
thf(38,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(42,conjecture,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
=> ( ( ( E = C )
& ( F = D )
& ( related @ B @ E @ F ) )
=> ( related @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_yellow_0) ).
thf(43,negated_conjecture,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
=> ( ( ( E = C )
& ( F = D )
& ( related @ B @ E @ F ) )
=> ( related @ A @ C @ D ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[42]) ).
thf(44,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
=> ( ( ( E = C )
& ( F = D )
& ( related @ B @ E @ F ) )
=> ( related @ A @ C @ D ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[43]) ).
thf(45,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(46,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(50,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(51,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] : ( subrelstr @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(53,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(54,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(55,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(57,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(58,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( rel_str @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(59,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(60,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(61,plain,
$true = $true,
inference(unfold_def,[status(thm)],[30]) ).
thf(62,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(63,plain,
$true = $true,
inference(unfold_def,[status(thm)],[32]) ).
thf(64,plain,
$true = $true,
inference(unfold_def,[status(thm)],[33]) ).
thf(65,plain,
$true = $true,
inference(unfold_def,[status(thm)],[34]) ).
thf(66,plain,
$true = $true,
inference(unfold_def,[status(thm)],[35]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( related @ A @ B @ C )
<=> ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( subrelstr @ B @ A )
<=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(70,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(71,plain,
( ( ( rel_str @ sK1_A )
=> ! [SY44: $i] :
( ( subrelstr @ SY44 @ sK1_A )
=> ! [SY45: $i] :
( ( element @ SY45 @ ( the_carrier @ sK1_A ) )
=> ! [SY46: $i] :
( ( element @ SY46 @ ( the_carrier @ sK1_A ) )
=> ! [SY47: $i] :
( ( element @ SY47 @ ( the_carrier @ SY44 ) )
=> ! [SY48: $i] :
( ( element @ SY48 @ ( the_carrier @ SY44 ) )
=> ( ( ( SY47 = SY45 )
& ( SY48 = SY46 )
& ( related @ SY44 @ SY47 @ SY48 ) )
=> ( related @ sK1_A @ SY45 @ SY46 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(72,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(73,plain,
( ( ! [SY44: $i] :
( ( subrelstr @ SY44 @ sK1_A )
=> ! [SY45: $i] :
( ( element @ SY45 @ ( the_carrier @ sK1_A ) )
=> ! [SY46: $i] :
( ( element @ SY46 @ ( the_carrier @ sK1_A ) )
=> ! [SY47: $i] :
( ( element @ SY47 @ ( the_carrier @ SY44 ) )
=> ! [SY48: $i] :
( ( element @ SY48 @ ( the_carrier @ SY44 ) )
=> ( ( ( SY47 = SY45 )
& ( SY48 = SY46 )
& ( related @ SY44 @ SY47 @ SY48 ) )
=> ( related @ sK1_A @ SY45 @ SY46 ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(74,plain,
( ( ~ ! [SY44: $i] :
( ( subrelstr @ SY44 @ sK1_A )
=> ! [SY45: $i] :
( ( element @ SY45 @ ( the_carrier @ sK1_A ) )
=> ! [SY46: $i] :
( ( element @ SY46 @ ( the_carrier @ sK1_A ) )
=> ! [SY47: $i] :
( ( element @ SY47 @ ( the_carrier @ SY44 ) )
=> ! [SY48: $i] :
( ( element @ SY48 @ ( the_carrier @ SY44 ) )
=> ( ( ( SY47 = SY45 )
& ( SY48 = SY46 )
& ( related @ SY44 @ SY47 @ SY48 ) )
=> ( related @ sK1_A @ SY45 @ SY46 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[73]) ).
thf(75,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(76,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(77,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( subrelstr @ B @ A )
<=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(78,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( related @ A @ B @ C )
<=> ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(79,plain,
$true = $true,
inference(copy,[status(thm)],[66]) ).
thf(80,plain,
$true = $true,
inference(copy,[status(thm)],[65]) ).
thf(81,plain,
$true = $true,
inference(copy,[status(thm)],[64]) ).
thf(82,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(83,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(84,plain,
$true = $true,
inference(copy,[status(thm)],[61]) ).
thf(85,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(86,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(87,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( rel_str @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(89,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(90,plain,
$true = $true,
inference(copy,[status(thm)],[55]) ).
thf(91,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(92,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(93,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] : ( subrelstr @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(94,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(95,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(99,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(100,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(101,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(102,plain,
( ( ~ ! [SY44: $i] :
( ( subrelstr @ SY44 @ sK1_A )
=> ! [SY45: $i] :
( ( element @ SY45 @ ( the_carrier @ sK1_A ) )
=> ! [SY46: $i] :
( ( element @ SY46 @ ( the_carrier @ sK1_A ) )
=> ! [SY47: $i] :
( ( element @ SY47 @ ( the_carrier @ SY44 ) )
=> ! [SY48: $i] :
( ( element @ SY48 @ ( the_carrier @ SY44 ) )
=> ( ( ( SY47 = SY45 )
& ( SY48 = SY46 )
& ( related @ SY44 @ SY47 @ SY48 ) )
=> ( related @ sK1_A @ SY45 @ SY46 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(103,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( element @ SX2 @ ( powerset @ ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(104,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(105,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(106,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(107,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ! [SX1: $i] :
~ ( subrelstr @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(108,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(109,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(110,plain,
( ( ~ ! [SX0: $i] :
~ ( rel_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ( relation @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(112,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( subrelstr @ SX1 @ SX0 )
| ( rel_str @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(113,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(114,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(115,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(116,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(117,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( rel_str @ SX1 )
| ~ ( ~ ( ~ ( subrelstr @ SX1 @ SX0 )
| ~ ( ~ ( subset @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) )
| ~ ( subset @ ( the_InternalRel @ SX1 ) @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) )
| ~ ( subset @ ( the_InternalRel @ SX1 ) @ ( the_InternalRel @ SX0 ) ) )
| ( subrelstr @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(118,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( ~ ( ~ ( related @ SX0 @ SX1 @ SX2 )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ ( the_InternalRel @ SX0 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ ( the_InternalRel @ SX0 ) )
| ( related @ SX0 @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(120,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(121,plain,
( ( ~ ! [SX0: $i] :
( ~ ( subrelstr @ SX0 @ sK1_A )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ sK1_A ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ sK1_A ) )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ! [SX4: $i] :
( ~ ( element @ SX4 @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ~ ( ( SX3 != SX1 )
| ( SX4 != SX2 ) )
| ~ ( related @ SX0 @ SX3 @ SX4 ) )
| ( related @ sK1_A @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(122,plain,
! [SV1: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( relation_of2_as_subset @ SY50 @ SV1 @ SY49 )
| ( element @ SY50 @ ( powerset @ ( cartesian_product2 @ SV1 @ SY49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(123,plain,
! [SV2: $i] :
( ( ~ ( rel_str @ SV2 )
| ( one_sorted_str @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(124,plain,
! [SV3: $i] :
( ( ~ ! [SY51: $i] :
~ ( element @ SY51 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(125,plain,
! [SV4: $i] :
( ( ~ ~ ( empty @ SV4 )
| ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY52 @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ SY52 ) )
| ~ ( finite @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(126,plain,
! [SV5: $i] :
( ( ~ ( rel_str @ SV5 )
| ~ ! [SY53: $i] :
~ ( subrelstr @ SY53 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(127,plain,
! [SV6: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ~ ~ ( ~ ( in @ SV6 @ SY54 )
| ~ ( element @ SY54 @ ( powerset @ SY55 ) ) )
| ( element @ SV6 @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(128,plain,
! [SV7: $i] :
( ( ! [SY56: $i] :
( ~ ( element @ SV7 @ SY56 )
| ( empty @ SY56 )
| ( in @ SV7 @ SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(129,plain,
( ( ! [SX0: $i] :
~ ( rel_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(130,plain,
! [SV8: $i] :
( ( ! [SY57: $i,SY58: $i] :
( ~ ( element @ SY58 @ ( powerset @ ( cartesian_product2 @ SV8 @ SY57 ) ) )
| ( relation @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(131,plain,
! [SV9: $i] :
( ( ~ ( rel_str @ SV9 )
| ! [SY59: $i] :
( ~ ( subrelstr @ SY59 @ SV9 )
| ( rel_str @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(132,plain,
! [SV10: $i] :
( ( ! [SY60: $i] :
~ ( ~ ( ~ ( element @ SV10 @ ( powerset @ SY60 ) )
| ( subset @ SV10 @ SY60 ) )
| ~ ( ~ ( subset @ SV10 @ SY60 )
| ( element @ SV10 @ ( powerset @ SY60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(133,plain,
! [SV11: $i] :
( ( ! [SY61: $i,SY62: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV11 @ SY61 )
| ~ ( element @ SY61 @ ( powerset @ SY62 ) ) )
| ~ ( empty @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(134,plain,
! [SV12: $i] :
( ( ~ ( finite @ SV12 )
| ! [SY63: $i] :
( ~ ( element @ SY63 @ ( powerset @ SV12 ) )
| ( finite @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(135,plain,
! [SV13: $i] :
( ( ~ ~ ( empty @ SV13 )
| ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY64 ) )
| ~ ( finite @ SY64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(136,plain,
! [SV14: $i] :
( ( ~ ( rel_str @ SV14 )
| ! [SY65: $i] :
( ~ ( rel_str @ SY65 )
| ~ ( ~ ( ~ ( subrelstr @ SY65 @ SV14 )
| ~ ( ~ ( subset @ ( the_carrier @ SY65 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SY65 ) @ ( the_InternalRel @ SV14 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SY65 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SY65 ) @ ( the_InternalRel @ SV14 ) ) )
| ( subrelstr @ SY65 @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(137,plain,
! [SV15: $i] :
( ( ~ ( rel_str @ SV15 )
| ! [SY66: $i] :
( ~ ( element @ SY66 @ ( the_carrier @ SV15 ) )
| ! [SY67: $i] :
( ~ ( element @ SY67 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( related @ SV15 @ SY66 @ SY67 )
| ( in @ ( ordered_pair @ SY66 @ SY67 ) @ ( the_InternalRel @ SV15 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY66 @ SY67 ) @ ( the_InternalRel @ SV15 ) )
| ( related @ SV15 @ SY66 @ SY67 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(138,plain,
! [SV16: $i] :
( ( ! [SY68: $i] :
( ~ ( in @ SV16 @ SY68 )
| ( element @ SV16 @ SY68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(139,plain,
! [SV17: $i] :
( ( ~ ( rel_str @ SV17 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SV17 ) @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(140,plain,
( ( ! [SX0: $i] :
( ~ ( subrelstr @ SX0 @ sK1_A )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ sK1_A ) )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ sK1_A ) )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ! [SX4: $i] :
( ~ ( element @ SX4 @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ~ ( ( SX3 != SX1 )
| ( SX4 != SX2 ) )
| ~ ( related @ SX0 @ SX3 @ SX4 ) )
| ( related @ sK1_A @ SX1 @ SX2 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(141,plain,
! [SV18: $i,SV1: $i] :
( ( ! [SY69: $i] :
( ~ ( relation_of2_as_subset @ SY69 @ SV1 @ SV18 )
| ( element @ SY69 @ ( powerset @ ( cartesian_product2 @ SV1 @ SV18 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(142,plain,
! [SV2: $i] :
( ( ( ~ ( rel_str @ SV2 ) )
= $true )
| ( ( one_sorted_str @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(143,plain,
! [SV3: $i] :
( ( ! [SY51: $i] :
~ ( element @ SY51 @ SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(144,plain,
! [SV4: $i] :
( ( ( ~ ~ ( empty @ SV4 ) )
= $true )
| ( ( ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY52 @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ SY52 ) )
| ~ ( finite @ SY52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(145,plain,
! [SV5: $i] :
( ( ( ~ ( rel_str @ SV5 ) )
= $true )
| ( ( ~ ! [SY53: $i] :
~ ( subrelstr @ SY53 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(146,plain,
! [SV19: $i,SV6: $i] :
( ( ! [SY70: $i] :
( ~ ~ ( ~ ( in @ SV6 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SY70 ) ) )
| ( element @ SV6 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(147,plain,
! [SV20: $i,SV7: $i] :
( ( ~ ( element @ SV7 @ SV20 )
| ( empty @ SV20 )
| ( in @ SV7 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(148,plain,
( ( ~ ( rel_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[129]) ).
thf(149,plain,
! [SV21: $i,SV8: $i] :
( ( ! [SY71: $i] :
( ~ ( element @ SY71 @ ( powerset @ ( cartesian_product2 @ SV8 @ SV21 ) ) )
| ( relation @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(150,plain,
! [SV9: $i] :
( ( ( ~ ( rel_str @ SV9 ) )
= $true )
| ( ( ! [SY59: $i] :
( ~ ( subrelstr @ SY59 @ SV9 )
| ( rel_str @ SY59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(151,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( element @ SV10 @ ( powerset @ SV22 ) )
| ( subset @ SV10 @ SV22 ) )
| ~ ( ~ ( subset @ SV10 @ SV22 )
| ( element @ SV10 @ ( powerset @ SV22 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(152,plain,
! [SV23: $i,SV11: $i] :
( ( ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV11 @ SV23 )
| ~ ( element @ SV23 @ ( powerset @ SY72 ) ) )
| ~ ( empty @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(153,plain,
! [SV12: $i] :
( ( ( ~ ( finite @ SV12 ) )
= $true )
| ( ( ! [SY63: $i] :
( ~ ( element @ SY63 @ ( powerset @ SV12 ) )
| ( finite @ SY63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(154,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty @ SV13 ) )
= $true )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY64 ) )
| ~ ( finite @ SY64 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(155,plain,
! [SV14: $i] :
( ( ( ~ ( rel_str @ SV14 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( rel_str @ SY65 )
| ~ ( ~ ( ~ ( subrelstr @ SY65 @ SV14 )
| ~ ( ~ ( subset @ ( the_carrier @ SY65 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SY65 ) @ ( the_InternalRel @ SV14 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SY65 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SY65 ) @ ( the_InternalRel @ SV14 ) ) )
| ( subrelstr @ SY65 @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV15: $i] :
( ( ( ~ ( rel_str @ SV15 ) )
= $true )
| ( ( ! [SY66: $i] :
( ~ ( element @ SY66 @ ( the_carrier @ SV15 ) )
| ! [SY67: $i] :
( ~ ( element @ SY67 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( related @ SV15 @ SY66 @ SY67 )
| ( in @ ( ordered_pair @ SY66 @ SY67 ) @ ( the_InternalRel @ SV15 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY66 @ SY67 ) @ ( the_InternalRel @ SV15 ) )
| ( related @ SV15 @ SY66 @ SY67 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(157,plain,
! [SV24: $i,SV16: $i] :
( ( ~ ( in @ SV16 @ SV24 )
| ( element @ SV16 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(158,plain,
! [SV17: $i] :
( ( ( ~ ( rel_str @ SV17 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV17 ) @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(159,plain,
( ( ~ ( subrelstr @ sK3_SX0 @ sK1_A )
| ! [SY73: $i] :
( ~ ( element @ SY73 @ ( the_carrier @ sK1_A ) )
| ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ sK1_A ) )
| ! [SY75: $i] :
( ~ ( element @ SY75 @ ( the_carrier @ sK3_SX0 ) )
| ! [SY76: $i] :
( ~ ( element @ SY76 @ ( the_carrier @ sK3_SX0 ) )
| ~ ~ ( ~ ~ ( ( SY75 != SY73 )
| ( SY76 != SY74 ) )
| ~ ( related @ sK3_SX0 @ SY75 @ SY76 ) )
| ( related @ sK1_A @ SY73 @ SY74 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[140]) ).
thf(160,plain,
! [SV18: $i,SV1: $i,SV25: $i] :
( ( ~ ( relation_of2_as_subset @ SV25 @ SV1 @ SV18 )
| ( element @ SV25 @ ( powerset @ ( cartesian_product2 @ SV1 @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(161,plain,
! [SV2: $i] :
( ( ( rel_str @ SV2 )
= $false )
| ( ( one_sorted_str @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(162,plain,
! [SV3: $i] :
( ( ~ ( element @ ( sK4_SY51 @ SV3 ) @ SV3 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[143]) ).
thf(163,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ SV4 ) )
= $false )
| ( ( ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY52 @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ SY52 ) )
| ~ ( finite @ SY52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(164,plain,
! [SV5: $i] :
( ( ( rel_str @ SV5 )
= $false )
| ( ( ~ ! [SY53: $i] :
~ ( subrelstr @ SY53 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(165,plain,
! [SV26: $i,SV19: $i,SV6: $i] :
( ( ~ ~ ( ~ ( in @ SV6 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV26 ) ) )
| ( element @ SV6 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(166,plain,
! [SV20: $i,SV7: $i] :
( ( ( ~ ( element @ SV7 @ SV20 ) )
= $true )
| ( ( ( empty @ SV20 )
| ( in @ SV7 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(167,plain,
( ( rel_str @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(168,plain,
! [SV21: $i,SV8: $i,SV27: $i] :
( ( ~ ( element @ SV27 @ ( powerset @ ( cartesian_product2 @ SV8 @ SV21 ) ) )
| ( relation @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(169,plain,
! [SV9: $i] :
( ( ( rel_str @ SV9 )
= $false )
| ( ( ! [SY59: $i] :
( ~ ( subrelstr @ SY59 @ SV9 )
| ( rel_str @ SY59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(170,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( ~ ( element @ SV10 @ ( powerset @ SV22 ) )
| ( subset @ SV10 @ SV22 ) )
| ~ ( ~ ( subset @ SV10 @ SV22 )
| ( element @ SV10 @ ( powerset @ SV22 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(171,plain,
! [SV28: $i,SV23: $i,SV11: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV11 @ SV23 )
| ~ ( element @ SV23 @ ( powerset @ SV28 ) ) )
| ~ ( empty @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(172,plain,
! [SV12: $i] :
( ( ( finite @ SV12 )
= $false )
| ( ( ! [SY63: $i] :
( ~ ( element @ SY63 @ ( powerset @ SV12 ) )
| ( finite @ SY63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(173,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ SV13 ) )
= $false )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY64 ) )
| ~ ( finite @ SY64 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(174,plain,
! [SV14: $i] :
( ( ( rel_str @ SV14 )
= $false )
| ( ( ! [SY65: $i] :
( ~ ( rel_str @ SY65 )
| ~ ( ~ ( ~ ( subrelstr @ SY65 @ SV14 )
| ~ ( ~ ( subset @ ( the_carrier @ SY65 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SY65 ) @ ( the_InternalRel @ SV14 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SY65 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SY65 ) @ ( the_InternalRel @ SV14 ) ) )
| ( subrelstr @ SY65 @ SV14 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(175,plain,
! [SV15: $i] :
( ( ( rel_str @ SV15 )
= $false )
| ( ( ! [SY66: $i] :
( ~ ( element @ SY66 @ ( the_carrier @ SV15 ) )
| ! [SY67: $i] :
( ~ ( element @ SY67 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( related @ SV15 @ SY66 @ SY67 )
| ( in @ ( ordered_pair @ SY66 @ SY67 ) @ ( the_InternalRel @ SV15 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY66 @ SY67 ) @ ( the_InternalRel @ SV15 ) )
| ( related @ SV15 @ SY66 @ SY67 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(176,plain,
! [SV24: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ SV24 ) )
= $true )
| ( ( element @ SV16 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(177,plain,
! [SV17: $i] :
( ( ( rel_str @ SV17 )
= $false )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV17 ) @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(178,plain,
( ( ~ ( subrelstr @ sK3_SX0 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(179,plain,
( ( ! [SY73: $i] :
( ~ ( element @ SY73 @ ( the_carrier @ sK1_A ) )
| ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ sK1_A ) )
| ! [SY75: $i] :
( ~ ( element @ SY75 @ ( the_carrier @ sK3_SX0 ) )
| ! [SY76: $i] :
( ~ ( element @ SY76 @ ( the_carrier @ sK3_SX0 ) )
| ~ ~ ( ~ ~ ( ( SY75 != SY73 )
| ( SY76 != SY74 ) )
| ~ ( related @ sK3_SX0 @ SY75 @ SY76 ) )
| ( related @ sK1_A @ SY73 @ SY74 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[159]) ).
thf(180,plain,
! [SV18: $i,SV1: $i,SV25: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV25 @ SV1 @ SV18 ) )
= $true )
| ( ( element @ SV25 @ ( powerset @ ( cartesian_product2 @ SV1 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[160]) ).
thf(181,plain,
! [SV3: $i] :
( ( element @ ( sK4_SY51 @ SV3 ) @ SV3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(182,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $true )
| ( ( ~ ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY52 @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ SY52 ) )
| ~ ( finite @ SY52 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(183,plain,
! [SV5: $i] :
( ( ( ! [SY53: $i] :
~ ( subrelstr @ SY53 @ SV5 ) )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(184,plain,
! [SV26: $i,SV19: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( in @ SV6 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV26 ) ) ) )
= $true )
| ( ( element @ SV6 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(185,plain,
! [SV20: $i,SV7: $i] :
( ( ( element @ SV7 @ SV20 )
= $false )
| ( ( ( empty @ SV20 )
| ( in @ SV7 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(186,plain,
! [SV21: $i,SV8: $i,SV27: $i] :
( ( ( ~ ( element @ SV27 @ ( powerset @ ( cartesian_product2 @ SV8 @ SV21 ) ) ) )
= $true )
| ( ( relation @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(187,plain,
! [SV9: $i,SV29: $i] :
( ( ( ~ ( subrelstr @ SV29 @ SV9 )
| ( rel_str @ SV29 ) )
= $true )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(188,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( ~ ( element @ SV10 @ ( powerset @ SV22 ) )
| ( subset @ SV10 @ SV22 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(189,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( ~ ( subset @ SV10 @ SV22 )
| ( element @ SV10 @ ( powerset @ SV22 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(190,plain,
! [SV28: $i,SV23: $i,SV11: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV11 @ SV23 )
| ~ ( element @ SV23 @ ( powerset @ SV28 ) ) )
| ~ ( empty @ SV28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(191,plain,
! [SV12: $i,SV30: $i] :
( ( ( ~ ( element @ SV30 @ ( powerset @ SV12 ) )
| ( finite @ SV30 ) )
= $true )
| ( ( finite @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(192,plain,
! [SV13: $i] :
( ( ( empty @ SV13 )
= $true )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY64 ) )
| ~ ( finite @ SY64 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(193,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( rel_str @ SV31 )
| ~ ( ~ ( ~ ( subrelstr @ SV31 @ SV14 )
| ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) )
| ( subrelstr @ SV31 @ SV14 ) ) ) )
= $true )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(194,plain,
! [SV15: $i,SV32: $i] :
( ( ( ~ ( element @ SV32 @ ( the_carrier @ SV15 ) )
| ! [SY77: $i] :
( ~ ( element @ SY77 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( related @ SV15 @ SV32 @ SY77 )
| ( in @ ( ordered_pair @ SV32 @ SY77 ) @ ( the_InternalRel @ SV15 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV32 @ SY77 ) @ ( the_InternalRel @ SV15 ) )
| ( related @ SV15 @ SV32 @ SY77 ) ) ) ) )
= $true )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(195,plain,
! [SV24: $i,SV16: $i] :
( ( ( in @ SV16 @ SV24 )
= $false )
| ( ( element @ SV16 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(196,plain,
( ( subrelstr @ sK3_SX0 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(197,plain,
( ( ~ ( element @ sK5_SY73 @ ( the_carrier @ sK1_A ) )
| ! [SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ sK1_A ) )
| ! [SY79: $i] :
( ~ ( element @ SY79 @ ( the_carrier @ sK3_SX0 ) )
| ! [SY80: $i] :
( ~ ( element @ SY80 @ ( the_carrier @ sK3_SX0 ) )
| ~ ~ ( ~ ~ ( ( SY79 != sK5_SY73 )
| ( SY80 != SY78 ) )
| ~ ( related @ sK3_SX0 @ SY79 @ SY80 ) )
| ( related @ sK1_A @ sK5_SY73 @ SY78 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[179]) ).
thf(198,plain,
! [SV18: $i,SV1: $i,SV25: $i] :
( ( ( relation_of2_as_subset @ SV25 @ SV1 @ SV18 )
= $false )
| ( ( element @ SV25 @ ( powerset @ ( cartesian_product2 @ SV1 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(199,plain,
! [SV4: $i] :
( ( ( ! [SY52: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY52 @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ SY52 ) )
| ~ ( finite @ SY52 ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(200,plain,
! [SV5: $i] :
( ( ( ~ ( subrelstr @ ( sK6_SY53 @ SV5 ) @ SV5 ) )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[183]) ).
thf(201,plain,
! [SV26: $i,SV19: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ SV6 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV26 ) ) ) )
= $false )
| ( ( element @ SV6 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(202,plain,
! [SV7: $i,SV20: $i] :
( ( ( empty @ SV20 )
= $true )
| ( ( in @ SV7 @ SV20 )
= $true )
| ( ( element @ SV7 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(203,plain,
! [SV21: $i,SV8: $i,SV27: $i] :
( ( ( element @ SV27 @ ( powerset @ ( cartesian_product2 @ SV8 @ SV21 ) ) )
= $false )
| ( ( relation @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(204,plain,
! [SV9: $i,SV29: $i] :
( ( ( ~ ( subrelstr @ SV29 @ SV9 ) )
= $true )
| ( ( rel_str @ SV29 )
= $true )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(205,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( element @ SV10 @ ( powerset @ SV22 ) )
| ( subset @ SV10 @ SV22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(206,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( subset @ SV10 @ SV22 )
| ( element @ SV10 @ ( powerset @ SV22 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(207,plain,
! [SV28: $i,SV23: $i,SV11: $i] :
( ( ~ ~ ( ~ ( in @ SV11 @ SV23 )
| ~ ( element @ SV23 @ ( powerset @ SV28 ) ) )
| ~ ( empty @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(208,plain,
! [SV12: $i,SV30: $i] :
( ( ( ~ ( element @ SV30 @ ( powerset @ SV12 ) ) )
= $true )
| ( ( finite @ SV30 )
= $true )
| ( ( finite @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(209,plain,
! [SV13: $i] :
( ( ( ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY64 @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ SY64 ) )
| ~ ( finite @ SY64 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(210,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( rel_str @ SV31 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subrelstr @ SV31 @ SV14 )
| ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) )
| ( subrelstr @ SV31 @ SV14 ) ) ) )
= $true )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(211,plain,
! [SV15: $i,SV32: $i] :
( ( ( ~ ( element @ SV32 @ ( the_carrier @ SV15 ) ) )
= $true )
| ( ( ! [SY77: $i] :
( ~ ( element @ SY77 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( related @ SV15 @ SV32 @ SY77 )
| ( in @ ( ordered_pair @ SV32 @ SY77 ) @ ( the_InternalRel @ SV15 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV32 @ SY77 ) @ ( the_InternalRel @ SV15 ) )
| ( related @ SV15 @ SV32 @ SY77 ) ) ) ) )
= $true )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(212,plain,
( ( ~ ( element @ sK5_SY73 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(213,plain,
( ( ! [SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ sK1_A ) )
| ! [SY79: $i] :
( ~ ( element @ SY79 @ ( the_carrier @ sK3_SX0 ) )
| ! [SY80: $i] :
( ~ ( element @ SY80 @ ( the_carrier @ sK3_SX0 ) )
| ~ ~ ( ~ ~ ( ( SY79 != sK5_SY73 )
| ( SY80 != SY78 ) )
| ~ ( related @ sK3_SX0 @ SY79 @ SY80 ) )
| ( related @ sK1_A @ sK5_SY73 @ SY78 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(214,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK7_SY52 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ ( sK7_SY52 @ SV4 ) ) )
| ~ ( finite @ ( sK7_SY52 @ SV4 ) ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[199]) ).
thf(215,plain,
! [SV5: $i] :
( ( ( subrelstr @ ( sK6_SY53 @ SV5 ) @ SV5 )
= $true )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(216,plain,
! [SV26: $i,SV19: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV26 ) ) )
= $true )
| ( ( element @ SV6 @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(217,plain,
! [SV9: $i,SV29: $i] :
( ( ( subrelstr @ SV29 @ SV9 )
= $false )
| ( ( rel_str @ SV29 )
= $true )
| ( ( rel_str @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(218,plain,
! [SV22: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( powerset @ SV22 ) ) )
= $true )
| ( ( subset @ SV10 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(219,plain,
! [SV22: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV22 ) )
= $true )
| ( ( element @ SV10 @ ( powerset @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(220,plain,
! [SV28: $i,SV23: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( in @ SV11 @ SV23 )
| ~ ( element @ SV23 @ ( powerset @ SV28 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(221,plain,
! [SV12: $i,SV30: $i] :
( ( ( element @ SV30 @ ( powerset @ SV12 ) )
= $false )
| ( ( finite @ SV30 )
= $true )
| ( ( finite @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(222,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK8_SY64 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK8_SY64 @ SV13 ) ) )
| ~ ( finite @ ( sK8_SY64 @ SV13 ) ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[209]) ).
thf(223,plain,
! [SV14: $i,SV31: $i] :
( ( ( rel_str @ SV31 )
= $false )
| ( ( ~ ( ~ ( ~ ( subrelstr @ SV31 @ SV14 )
| ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) )
| ( subrelstr @ SV31 @ SV14 ) ) ) )
= $true )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(224,plain,
! [SV15: $i,SV32: $i] :
( ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( ! [SY77: $i] :
( ~ ( element @ SY77 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( related @ SV15 @ SV32 @ SY77 )
| ( in @ ( ordered_pair @ SV32 @ SY77 ) @ ( the_InternalRel @ SV15 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV32 @ SY77 ) @ ( the_InternalRel @ SV15 ) )
| ( related @ SV15 @ SV32 @ SY77 ) ) ) ) )
= $true )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(225,plain,
( ( element @ sK5_SY73 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(226,plain,
( ( ~ ( element @ sK9_SY78 @ ( the_carrier @ sK1_A ) )
| ! [SY81: $i] :
( ~ ( element @ SY81 @ ( the_carrier @ sK3_SX0 ) )
| ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ sK3_SX0 ) )
| ~ ~ ( ~ ~ ( ( SY81 != sK5_SY73 )
| ( SY82 != sK9_SY78 ) )
| ~ ( related @ sK3_SX0 @ SY81 @ SY82 ) )
| ( related @ sK1_A @ sK5_SY73 @ sK9_SY78 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[213]) ).
thf(227,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK7_SY52 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ ( sK7_SY52 @ SV4 ) ) )
| ~ ( finite @ ( sK7_SY52 @ SV4 ) ) ) )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(228,plain,
! [SV26: $i,SV19: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV19 ) )
= $true )
| ( ( ~ ( element @ SV19 @ ( powerset @ SV26 ) ) )
= $true )
| ( ( element @ SV6 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(229,plain,
! [SV22: $i,SV10: $i] :
( ( ( element @ SV10 @ ( powerset @ SV22 ) )
= $false )
| ( ( subset @ SV10 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(230,plain,
! [SV22: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV22 )
= $false )
| ( ( element @ SV10 @ ( powerset @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(231,plain,
! [SV28: $i,SV23: $i,SV11: $i] :
( ( ( ~ ( ~ ( in @ SV11 @ SV23 )
| ~ ( element @ SV23 @ ( powerset @ SV28 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(232,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK8_SY64 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK8_SY64 @ SV13 ) ) )
| ~ ( finite @ ( sK8_SY64 @ SV13 ) ) ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(233,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( ~ ( subrelstr @ SV31 @ SV14 )
| ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) )
| ( subrelstr @ SV31 @ SV14 ) ) )
= $false )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(234,plain,
! [SV32: $i,SV15: $i,SV33: $i] :
( ( ( ~ ( element @ SV33 @ ( the_carrier @ SV15 ) )
| ~ ( ~ ( ~ ( related @ SV15 @ SV32 @ SV33 )
| ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) )
| ( related @ SV15 @ SV32 @ SV33 ) ) ) )
= $true )
| ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(235,plain,
( ( ~ ( element @ sK9_SY78 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(236,plain,
( ( ! [SY81: $i] :
( ~ ( element @ SY81 @ ( the_carrier @ sK3_SX0 ) )
| ! [SY82: $i] :
( ~ ( element @ SY82 @ ( the_carrier @ sK3_SX0 ) )
| ~ ~ ( ~ ~ ( ( SY81 != sK5_SY73 )
| ( SY82 != sK9_SY78 ) )
| ~ ( related @ sK3_SX0 @ SY81 @ SY82 ) )
| ( related @ sK1_A @ sK5_SY73 @ sK9_SY78 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(237,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_SY52 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ ( sK7_SY52 @ SV4 ) ) )
| ~ ( finite @ ( sK7_SY52 @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(238,plain,
! [SV26: $i,SV19: $i,SV6: $i] :
( ( ( in @ SV6 @ SV19 )
= $false )
| ( ( ~ ( element @ SV19 @ ( powerset @ SV26 ) ) )
= $true )
| ( ( element @ SV6 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(239,plain,
! [SV28: $i,SV23: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV23 )
| ~ ( element @ SV23 @ ( powerset @ SV28 ) ) )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(240,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK8_SY64 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK8_SY64 @ SV13 ) ) )
| ~ ( finite @ ( sK8_SY64 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(241,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( ~ ( subrelstr @ SV31 @ SV14 )
| ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) ) ) )
= $false )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(242,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) )
| ( subrelstr @ SV31 @ SV14 ) ) )
= $false )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(243,plain,
! [SV32: $i,SV15: $i,SV33: $i] :
( ( ( ~ ( element @ SV33 @ ( the_carrier @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( related @ SV15 @ SV32 @ SV33 )
| ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) )
| ( related @ SV15 @ SV32 @ SV33 ) ) ) )
= $true )
| ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(244,plain,
( ( element @ sK9_SY78 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(245,plain,
( ( ~ ( element @ sK10_SY81 @ ( the_carrier @ sK3_SX0 ) )
| ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ sK3_SX0 ) )
| ~ ~ ( ~ ~ ( ( sK10_SY81 != sK5_SY73 )
| ( SY83 != sK9_SY78 ) )
| ~ ( related @ sK3_SX0 @ sK10_SY81 @ SY83 ) )
| ( related @ sK1_A @ sK5_SY73 @ sK9_SY78 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[236]) ).
thf(246,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_SY52 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ ( sK7_SY52 @ SV4 ) ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(247,plain,
! [SV4: $i] :
( ( ( ~ ( finite @ ( sK7_SY52 @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(248,plain,
! [SV6: $i,SV26: $i,SV19: $i] :
( ( ( element @ SV19 @ ( powerset @ SV26 ) )
= $false )
| ( ( in @ SV6 @ SV19 )
= $false )
| ( ( element @ SV6 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV28: $i,SV23: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV23 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( powerset @ SV28 ) ) )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(250,plain,
! [SV13: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK8_SY64 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK8_SY64 @ SV13 ) ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(251,plain,
! [SV13: $i] :
( ( ( ~ ( finite @ ( sK8_SY64 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(252,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( subrelstr @ SV31 @ SV14 )
| ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) ) )
= $true )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(253,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) )
| ( subrelstr @ SV31 @ SV14 ) )
= $true )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(254,plain,
! [SV32: $i,SV15: $i,SV33: $i] :
( ( ( element @ SV33 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( related @ SV15 @ SV32 @ SV33 )
| ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) )
| ( related @ SV15 @ SV32 @ SV33 ) ) ) )
= $true )
| ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(255,plain,
( ( ~ ( element @ sK10_SY81 @ ( the_carrier @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(256,plain,
( ( ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ sK3_SX0 ) )
| ~ ~ ( ~ ~ ( ( sK10_SY81 != sK5_SY73 )
| ( SY83 != sK9_SY78 ) )
| ~ ( related @ sK3_SX0 @ sK10_SY81 @ SY83 ) )
| ( related @ sK1_A @ sK5_SY73 @ sK9_SY78 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(257,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_SY52 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ ( sK7_SY52 @ SV4 ) ) ) )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(258,plain,
! [SV4: $i] :
( ( ( finite @ ( sK7_SY52 @ SV4 ) )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(259,plain,
! [SV28: $i,SV23: $i,SV11: $i] :
( ( ( in @ SV11 @ SV23 )
= $false )
| ( ( ~ ( element @ SV23 @ ( powerset @ SV28 ) ) )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(260,plain,
! [SV13: $i] :
( ( ( ~ ( ~ ( element @ ( sK8_SY64 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK8_SY64 @ SV13 ) ) ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(261,plain,
! [SV13: $i] :
( ( ( finite @ ( sK8_SY64 @ SV13 ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(262,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( subrelstr @ SV31 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) ) )
= $true )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(263,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) ) )
= $true )
| ( ( subrelstr @ SV31 @ SV14 )
= $true )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(264,plain,
! [SV33: $i,SV32: $i,SV15: $i] :
( ( ( ~ ( ~ ( related @ SV15 @ SV32 @ SV33 )
| ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) )
| ( related @ SV15 @ SV32 @ SV33 ) ) )
= $false )
| ( ( element @ SV33 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(265,plain,
( ( element @ sK10_SY81 @ ( the_carrier @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(266,plain,
( ( ~ ( element @ sK11_SY83 @ ( the_carrier @ sK3_SX0 ) )
| ~ ~ ( ~ ~ ( ( sK10_SY81 != sK5_SY73 )
| ( sK11_SY83 != sK9_SY78 ) )
| ~ ( related @ sK3_SX0 @ sK10_SY81 @ sK11_SY83 ) )
| ( related @ sK1_A @ sK5_SY73 @ sK9_SY78 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[256]) ).
thf(267,plain,
! [SV4: $i] :
( ( ( ~ ( element @ ( sK7_SY52 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ ( sK7_SY52 @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(268,plain,
! [SV11: $i,SV28: $i,SV23: $i] :
( ( ( element @ SV23 @ ( powerset @ SV28 ) )
= $false )
| ( ( in @ SV11 @ SV23 )
= $false )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(269,plain,
! [SV13: $i] :
( ( ( ~ ( element @ ( sK8_SY64 @ SV13 ) @ ( powerset @ SV13 ) )
| ~ ~ ( empty @ ( sK8_SY64 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(270,plain,
! [SV14: $i,SV31: $i] :
( ( ( subrelstr @ SV31 @ SV14 )
= $false )
| ( ( ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) ) )
= $true )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(271,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) ) )
= $false )
| ( ( subrelstr @ SV31 @ SV14 )
= $true )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(272,plain,
! [SV33: $i,SV32: $i,SV15: $i] :
( ( ( ~ ( ~ ( related @ SV15 @ SV32 @ SV33 )
| ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) ) ) )
= $false )
| ( ( element @ SV33 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(273,plain,
! [SV15: $i,SV33: $i,SV32: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) )
| ( related @ SV15 @ SV32 @ SV33 ) ) )
= $false )
| ( ( element @ SV33 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(274,plain,
( ( ~ ( element @ sK11_SY83 @ ( the_carrier @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(275,plain,
( ( ~ ~ ( ~ ~ ( ( sK10_SY81 != sK5_SY73 )
| ( sK11_SY83 != sK9_SY78 ) )
| ~ ( related @ sK3_SX0 @ sK10_SY81 @ sK11_SY83 ) )
| ( related @ sK1_A @ sK5_SY73 @ sK9_SY78 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[266]) ).
thf(276,plain,
! [SV4: $i] :
( ( ( ~ ( element @ ( sK7_SY52 @ SV4 ) @ ( powerset @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(277,plain,
! [SV4: $i] :
( ( ( ~ ~ ( empty @ ( sK7_SY52 @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(278,plain,
! [SV23: $i,SV11: $i,SV28: $i] :
( ( ( empty @ SV28 )
= $false )
| ( ( in @ SV11 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( powerset @ SV28 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(279,plain,
! [SV13: $i] :
( ( ( ~ ( element @ ( sK8_SY64 @ SV13 ) @ ( powerset @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(280,plain,
! [SV13: $i] :
( ( ( ~ ~ ( empty @ ( sK8_SY64 @ SV13 ) ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(281,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) )
= $false )
| ( ( subrelstr @ SV31 @ SV14 )
= $false )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(282,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
| ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) )
= $true )
| ( ( subrelstr @ SV31 @ SV14 )
= $true )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(283,plain,
! [SV33: $i,SV32: $i,SV15: $i] :
( ( ( ~ ( related @ SV15 @ SV32 @ SV33 )
| ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) ) )
= $true )
| ( ( element @ SV33 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(284,plain,
! [SV15: $i,SV33: $i,SV32: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) )
| ( related @ SV15 @ SV32 @ SV33 ) )
= $true )
| ( ( element @ SV33 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(285,plain,
( ( element @ sK11_SY83 @ ( the_carrier @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(286,plain,
( ( ~ ~ ( ~ ~ ( ( sK10_SY81 != sK5_SY73 )
| ( sK11_SY83 != sK9_SY78 ) )
| ~ ( related @ sK3_SX0 @ sK10_SY81 @ sK11_SY83 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(287,plain,
( ( related @ sK1_A @ sK5_SY73 @ sK9_SY78 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(288,plain,
! [SV4: $i] :
( ( ( element @ ( sK7_SY52 @ SV4 ) @ ( powerset @ SV4 ) )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(289,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ ( sK7_SY52 @ SV4 ) ) )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(290,plain,
! [SV13: $i] :
( ( ( element @ ( sK8_SY64 @ SV13 ) @ ( powerset @ SV13 ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(291,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ ( sK8_SY64 @ SV13 ) ) )
= $true )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(292,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) ) )
= $false )
| ( ( subrelstr @ SV31 @ SV14 )
= $false )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(293,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) )
= $false )
| ( ( subrelstr @ SV31 @ SV14 )
= $false )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(294,plain,
! [SV14: $i,SV31: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) )
= $true )
| ( ( subrelstr @ SV31 @ SV14 )
= $true )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(295,plain,
! [SV33: $i,SV32: $i,SV15: $i] :
( ( ( ~ ( related @ SV15 @ SV32 @ SV33 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) )
= $true )
| ( ( element @ SV33 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(296,plain,
! [SV15: $i,SV33: $i,SV32: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) ) )
= $true )
| ( ( related @ SV15 @ SV32 @ SV33 )
= $true )
| ( ( element @ SV33 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(297,plain,
( ( ~ ( ~ ~ ( ( sK10_SY81 != sK5_SY73 )
| ( sK11_SY83 != sK9_SY78 ) )
| ~ ( related @ sK3_SX0 @ sK10_SY81 @ sK11_SY83 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(298,plain,
! [SV4: $i] :
( ( ( empty @ ( sK7_SY52 @ SV4 ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(299,plain,
! [SV13: $i] :
( ( ( empty @ ( sK8_SY64 @ SV13 ) )
= $false )
| ( ( empty @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(300,plain,
! [SV14: $i,SV31: $i] :
( ( ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
= $true )
| ( ( subrelstr @ SV31 @ SV14 )
= $false )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(301,plain,
! [SV14: $i,SV31: $i] :
( ( ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) )
= $true )
| ( ( subrelstr @ SV31 @ SV14 )
= $false )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(302,plain,
! [SV14: $i,SV31: $i] :
( ( ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
= $false )
| ( ( ~ ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) ) )
= $true )
| ( ( subrelstr @ SV31 @ SV14 )
= $true )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(303,plain,
! [SV33: $i,SV32: $i,SV15: $i] :
( ( ( related @ SV15 @ SV32 @ SV33 )
= $false )
| ( ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) )
= $true )
| ( ( element @ SV33 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(304,plain,
! [SV15: $i,SV33: $i,SV32: $i] :
( ( ( in @ ( ordered_pair @ SV32 @ SV33 ) @ ( the_InternalRel @ SV15 ) )
= $false )
| ( ( related @ SV15 @ SV32 @ SV33 )
= $true )
| ( ( element @ SV33 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( element @ SV32 @ ( the_carrier @ SV15 ) )
= $false )
| ( ( rel_str @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(305,plain,
( ( ~ ~ ( ( sK10_SY81 != sK5_SY73 )
| ( sK11_SY83 != sK9_SY78 ) )
| ~ ( related @ sK3_SX0 @ sK10_SY81 @ sK11_SY83 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(306,plain,
! [SV14: $i,SV31: $i] :
( ( ( subset @ ( the_InternalRel @ SV31 ) @ ( the_InternalRel @ SV14 ) )
= $false )
| ( ( subset @ ( the_carrier @ SV31 ) @ ( the_carrier @ SV14 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV14 )
= $true )
| ( ( rel_str @ SV31 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(307,plain,
( ( ~ ~ ( ( sK10_SY81 != sK5_SY73 )
| ( sK11_SY83 != sK9_SY78 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(308,plain,
( ( ~ ( related @ sK3_SX0 @ sK10_SY81 @ sK11_SY83 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(309,plain,
( ( ~ ( ( sK10_SY81 != sK5_SY73 )
| ( sK11_SY83 != sK9_SY78 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(310,plain,
( ( related @ sK3_SX0 @ sK10_SY81 @ sK11_SY83 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(311,plain,
( ( ( sK10_SY81 != sK5_SY73 )
| ( sK11_SY83 != sK9_SY78 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(312,plain,
( ( sK10_SY81 != sK5_SY73 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(313,plain,
( ( sK11_SY83 != sK9_SY78 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(314,plain,
( ( sK10_SY81 = sK5_SY73 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(315,plain,
( ( sK11_SY83 = sK9_SY78 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[313]) ).
thf(316,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[79,315,314,310,306,304,303,301,300,299,298,290,288,287,285,278,265,261,258,248,244,230,229,225,221,217,215,203,202,198,196,195,181,177,167,161,101,90,86,85,84,82,81,80]) ).
thf(317,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[316]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU362+1 : 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
% 0.09/0.18 % Computer : n017.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 15:13:11 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 254.47/42.60
% 254.47/42.60 No.of.Axioms: 26
% 254.47/42.60
% 254.47/42.60 Length.of.Defs: 0
% 254.47/42.60
% 254.47/42.60 Contains.Choice.Funs: false
% 254.47/42.60 ........
% 254.47/42.60
% 254.47/42.60 ********************************
% 254.47/42.60 * All subproblems solved! *
% 254.47/42.60 ********************************
% 254.47/42.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:27,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:316,loop_count:0,foatp_calls:1,translation:fof_full)
% 254.47/42.60
% 254.47/42.60 %**** Beginning of derivation protocol ****
% 254.47/42.60 % SZS output start CNFRefutation
% See solution above
% 254.47/42.61
% 254.47/42.61 %**** End of derivation protocol ****
% 254.47/42.61 %**** no. of clauses in derivation: 302 ****
% 254.47/42.61 %**** clause counter: 316 ****
% 254.47/42.61
% 254.47/42.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:27,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:316,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------