%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU297+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 : n007.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 10:43:51 AM UTC 2026
% Result : Theorem 2.97s 0.78s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 21
% Syntax : Number of formulae : 468 ( 158 unt; 0 typ; 0 def)
% Number of atoms : 5903 (2064 equ; 0 cnn)
% Maximal formula atoms : 12 ( 12 avg)
% Number of connectives : 13171 (3045 ~;2100 |; 81 &;7891 @)
% ( 12 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 10 con; 0-4 aty)
% Number of variables : 1485 ( 0 ^;1449 !; 36 ?;1485 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_sK10_SY65,type,
sK10_SY65: $i > $i ).
thf(tp_sK11_SY53,type,
sK11_SY53: $i > $i ).
thf(tp_sK12_SY66,type,
sK12_SY66: $i > $i > $i > $i ).
thf(tp_sK13_SY73,type,
sK13_SY73: $i > $i > $i > $i ).
thf(tp_sK14_SY75,type,
sK14_SY75: $i > $i > $i > $i ).
thf(tp_sK15_SY69,type,
sK15_SY69: $i > $i > $i > $i ).
thf(tp_sK16_SY69,type,
sK16_SY69: $i > $i > $i > $i ).
thf(tp_sK17_SY69,type,
sK17_SY69: $i > $i > $i > $i ).
thf(tp_sK18_SY79,type,
sK18_SY79: $i > $i > $i > $i > $i ).
thf(tp_sK19_SY69,type,
sK19_SY69: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY69,type,
sK20_SY69: $i > $i > $i > $i ).
thf(tp_sK21_SY84,type,
sK21_SY84: $i > $i > $i > $i > $i ).
thf(tp_sK22_SY89,type,
sK22_SY89: $i > $i > $i > $i > $i ).
thf(tp_sK23_SY97,type,
sK23_SY97: $i > $i > $i > $i > $i ).
thf(tp_sK24_SY99,type,
sK24_SY99: $i > $i > $i > $i > $i ).
thf(tp_sK2_SY34,type,
sK2_SY34: $i ).
thf(tp_sK3_SY38,type,
sK3_SY38: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SX0,type,
sK7_SX0: $i ).
thf(tp_sK8_SX0,type,
sK8_SX0: $i ).
thf(tp_sK9_SY55,type,
sK9_SY55: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ( relation @ C )
& ( function @ C ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ( in @ ( relation_image @ C @ E ) @ B )
& ( D = F )
& ( in @ ( relation_image @ C @ F ) @ B ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( powerset @ ( relation_dom @ C ) ) )
& ( F = E )
& ( in @ ( relation_image @ C @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_27__finset_1__1) ).
thf(2,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(3,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(4,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(5,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(6,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(7,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(12,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(14,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(15,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(16,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(17,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(18,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(20,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(21,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(30,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(32,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(37,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ( relation @ C )
& ( function @ C ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( powerset @ ( relation_dom @ C ) ) )
& ( in @ ( relation_image @ C @ E ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).
thf(38,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ( relation @ C )
& ( function @ C ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( powerset @ ( relation_dom @ C ) ) )
& ( in @ ( relation_image @ C @ E ) @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[37]) ).
thf(39,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ( relation @ C )
& ( function @ C ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( powerset @ ( relation_dom @ C ) ) )
& ( in @ ( relation_image @ C @ E ) @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ( relation @ C )
& ( function @ C ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ( in @ ( relation_image @ C @ E ) @ B )
& ( D = F )
& ( in @ ( relation_image @ C @ F ) @ B ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( powerset @ ( relation_dom @ C ) ) )
& ( F = E )
& ( in @ ( relation_image @ C @ E ) @ B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(41,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(42,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(43,plain,
$true = $true,
inference(unfold_def,[status(thm)],[4]) ).
thf(44,plain,
$true = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(45,plain,
$true = $true,
inference(unfold_def,[status(thm)],[6]) ).
thf(46,plain,
$true = $true,
inference(unfold_def,[status(thm)],[7]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(48,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(49,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(51,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(52,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(54,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(55,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(57,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(60,plain,
( ( ! [SY34: $i,SY35: $i] :
( ( ( element @ SY34 @ ( powerset @ ( powerset @ sK1_A ) ) )
& ( relation @ SY35 )
& ( function @ SY35 ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ( ( in @ E @ ( powerset @ ( relation_dom @ SY35 ) ) )
& ( in @ ( relation_image @ SY35 @ E ) @ SY34 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(61,plain,
( ( ! [SY38: $i] :
( ( ( element @ sK2_SY34 @ ( powerset @ ( powerset @ sK1_A ) ) )
& ( relation @ SY38 )
& ( function @ SY38 ) )
=> ? [SY39: $i] :
! [SY40: $i] :
( ( in @ SY40 @ SY39 )
<=> ( ( in @ SY40 @ ( powerset @ ( relation_dom @ SY38 ) ) )
& ( in @ ( relation_image @ SY38 @ SY40 ) @ sK2_SY34 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(62,plain,
( ( ( ( element @ sK2_SY34 @ ( powerset @ ( powerset @ sK1_A ) ) )
& ( relation @ sK3_SY38 )
& ( function @ sK3_SY38 ) )
=> ? [SY41: $i] :
! [SY42: $i] :
( ( in @ SY42 @ SY41 )
<=> ( ( in @ SY42 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
& ( in @ ( relation_image @ sK3_SY38 @ SY42 ) @ sK2_SY34 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(63,plain,
( ( element @ sK2_SY34 @ ( powerset @ ( powerset @ sK1_A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[62]) ).
thf(64,plain,
( ( relation @ sK3_SY38 )
= $true ),
inference(standard_cnf,[status(thm)],[62]) ).
thf(65,plain,
( ( function @ sK3_SY38 )
= $true ),
inference(standard_cnf,[status(thm)],[62]) ).
thf(66,plain,
( ( ? [SY41: $i] :
! [SY42: $i] :
( ( in @ SY42 @ SY41 )
<=> ( ( in @ SY42 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
& ( in @ ( relation_image @ sK3_SY38 @ SY42 ) @ sK2_SY34 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[62]) ).
thf(67,plain,
( ( ~ ? [SY41: $i] :
! [SY42: $i] :
( ( in @ SY42 @ SY41 )
<=> ( ( in @ SY42 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
& ( in @ ( relation_image @ sK3_SY38 @ SY42 ) @ sK2_SY34 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[66]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(70,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(71,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(72,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(73,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(74,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(75,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(76,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(77,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(78,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(79,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(81,plain,
$true = $true,
inference(copy,[status(thm)],[46]) ).
thf(82,plain,
$true = $true,
inference(copy,[status(thm)],[45]) ).
thf(83,plain,
$true = $true,
inference(copy,[status(thm)],[44]) ).
thf(84,plain,
$true = $true,
inference(copy,[status(thm)],[43]) ).
thf(85,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(86,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(87,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
& ( relation @ C )
& ( function @ C ) )
=> ( ! [D: $i,E: $i,F: $i] :
( ( ( D = E )
& ( in @ ( relation_image @ C @ E ) @ B )
& ( D = F )
& ( in @ ( relation_image @ C @ F ) @ B ) )
=> ( E = F ) )
=> ? [D: $i] :
! [E: $i] :
( ( in @ E @ D )
<=> ? [F: $i] :
( ( in @ F @ ( powerset @ ( relation_dom @ C ) ) )
& ( F = E )
& ( in @ ( relation_image @ C @ E ) @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(88,plain,
( ( function @ sK3_SY38 )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(89,plain,
( ( relation @ sK3_SY38 )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(90,plain,
( ( element @ sK2_SY34 @ ( powerset @ ( powerset @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(91,plain,
( ( ~ ? [SY41: $i] :
! [SY42: $i] :
( ( in @ SY42 @ SY41 )
<=> ( ( in @ SY42 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
& ( in @ ( relation_image @ sK3_SY38 @ SY42 ) @ sK2_SY34 ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(92,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(93,plain,
( ( ~ ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ SX1 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ SX1 ) @ sK2_SY34 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX1 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ SX1 ) @ sK2_SY34 ) )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(94,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(95,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(96,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(97,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(98,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ ( powerset @ SX0 ) ) )
| ~ ( relation @ SX2 ) )
| ~ ( function @ SX2 ) )
| ~ ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SX3 != SX4 )
| ~ ( in @ ( relation_image @ SX2 @ SX4 ) @ SX1 ) )
| ( SX3 != SX5 ) )
| ~ ( in @ ( relation_image @ SX2 @ SX5 ) @ SX1 ) )
| ( SX4 = SX5 ) )
| ~ ! [SX3: $i] :
~ ! [SX4: $i] :
~ ( ~ ( ~ ( in @ SX4 @ SX3 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX5 @ ( powerset @ ( relation_dom @ SX2 ) ) )
| ( SX5 != SX4 ) )
| ~ ( in @ ( relation_image @ SX2 @ SX4 ) @ SX1 ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX5 @ ( powerset @ ( relation_dom @ SX2 ) ) )
| ( SX5 != SX4 ) )
| ~ ( in @ ( relation_image @ SX2 @ SX4 ) @ SX1 ) )
| ( in @ SX4 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(99,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(100,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(101,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(102,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(103,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(104,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(105,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( finite @ SX1 ) )
| ( finite @ ( relation_image @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(106,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(107,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(108,plain,
! [SV1: $i] :
( ( ~ ( empty @ ( powerset @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(109,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(110,plain,
( ( ~ ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ SX1 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ SX1 ) @ sK2_SY34 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX1 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ SX1 ) @ sK2_SY34 ) )
| ( in @ SX1 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(111,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(112,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( function @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(113,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(114,plain,
! [SV3: $i] :
( ( ~ ( empty @ SV3 )
| ( relation @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(115,plain,
! [SV4: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ~ ~ ( ~ ~ ( ~ ( element @ SY43 @ ( powerset @ ( powerset @ SV4 ) ) )
| ~ ( relation @ SY44 ) )
| ~ ( function @ SY44 ) )
| ~ ! [SX3: $i,SX4: $i,SX5: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SX3 != SX4 )
| ~ ( in @ ( relation_image @ SY44 @ SX4 ) @ SY43 ) )
| ( SX3 != SX5 ) )
| ~ ( in @ ( relation_image @ SY44 @ SX5 ) @ SY43 ) )
| ( SX4 = SX5 ) )
| ~ ! [SX3: $i] :
~ ! [SX4: $i] :
~ ( ~ ( ~ ( in @ SX4 @ SX3 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX5 @ ( powerset @ ( relation_dom @ SY44 ) ) )
| ( SX5 != SX4 ) )
| ~ ( in @ ( relation_image @ SY44 @ SX4 ) @ SY43 ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX5 @ ( powerset @ ( relation_dom @ SY44 ) ) )
| ( SX5 != SX4 ) )
| ~ ( in @ ( relation_image @ SY44 @ SX4 ) @ SY43 ) )
| ( in @ SX4 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(116,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(117,plain,
! [SV5: $i] :
( ( ~ ( finite @ SV5 )
| ! [SY52: $i] :
( ~ ( element @ SY52 @ ( powerset @ SV5 ) )
| ( finite @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(118,plain,
! [SV6: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV6 )
| ~ ( relation @ SV6 ) )
| ~ ( empty @ ( relation_dom @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(119,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(120,plain,
! [SV7: $i] :
( ( ~ ( empty @ SV7 )
| ~ ( ~ ( empty @ ( relation_dom @ SV7 ) )
| ~ ( relation @ ( relation_dom @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(121,plain,
! [SV8: $i] :
( ( ~ ~ ( empty @ SV8 )
| ~ ! [SY53: $i] :
~ ~ ( ~ ( element @ SY53 @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(122,plain,
! [SV9: $i] :
( ( ! [SY54: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) )
| ~ ( finite @ SY54 ) )
| ( finite @ ( relation_image @ SV9 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(123,plain,
! [SV10: $i] :
( ( ~ ! [SY55: $i] :
~ ~ ( ~ ( element @ SY55 @ ( powerset @ SV10 ) )
| ~ ( empty @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(124,plain,
! [SV11: $i] :
( ( ! [SY56: $i] :
( ~ ( in @ SV11 @ SY56 )
| ~ ( in @ SY56 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(125,plain,
! [SV1: $i] :
( ( empty @ ( powerset @ SV1 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(126,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) )
| ~ ( function @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[109]) ).
thf(127,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ SX1 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ SX1 ) @ sK2_SY34 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX1 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ SX1 ) @ sK2_SY34 ) )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[110]) ).
thf(128,plain,
( ( ~ ~ ( ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[111]) ).
thf(129,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(130,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[113]) ).
thf(131,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ SV3 ) )
= $true )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(132,plain,
! [SV4: $i,SV12: $i] :
( ( ! [SY57: $i] :
( ~ ~ ( ~ ~ ( ~ ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
| ~ ( relation @ SY57 ) )
| ~ ( function @ SY57 ) )
| ~ ! [SY58: $i,SY59: $i,SY60: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY58 != SY59 )
| ~ ( in @ ( relation_image @ SY57 @ SY59 ) @ SV12 ) )
| ( SY58 != SY60 ) )
| ~ ( in @ ( relation_image @ SY57 @ SY60 ) @ SV12 ) )
| ( SY59 = SY60 ) )
| ~ ! [SY61: $i] :
~ ! [SY62: $i] :
~ ( ~ ( ~ ( in @ SY62 @ SY61 )
| ~ ! [SY63: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY63 @ ( powerset @ ( relation_dom @ SY57 ) ) )
| ( SY63 != SY62 ) )
| ~ ( in @ ( relation_image @ SY57 @ SY62 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY64: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY64 @ ( powerset @ ( relation_dom @ SY57 ) ) )
| ( SY64 != SY62 ) )
| ~ ( in @ ( relation_image @ SY57 @ SY62 ) @ SV12 ) )
| ( in @ SY62 @ SY61 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(133,plain,
( ( ~ ~ ( ~ ( relation @ sK7_SX0 )
| ~ ( function @ sK7_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(134,plain,
! [SV5: $i] :
( ( ( ~ ( finite @ SV5 ) )
= $true )
| ( ( ! [SY52: $i] :
( ~ ( element @ SY52 @ ( powerset @ SV5 ) )
| ( finite @ SY52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(135,plain,
! [SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV6 )
| ~ ( relation @ SV6 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(136,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
| ~ ( one_to_one @ sK8_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[119]) ).
thf(137,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV7 ) )
| ~ ( relation @ ( relation_dom @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(138,plain,
! [SV8: $i] :
( ( ( ~ ~ ( empty @ SV8 ) )
= $true )
| ( ( ~ ! [SY53: $i] :
~ ~ ( ~ ( element @ SY53 @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ SY53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(139,plain,
! [SV13: $i,SV9: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) )
| ~ ( finite @ SV13 ) )
| ( finite @ ( relation_image @ SV9 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(140,plain,
! [SV10: $i] :
( ( ! [SY55: $i] :
~ ~ ( ~ ( element @ SY55 @ ( powerset @ SV10 ) )
| ~ ( empty @ SY55 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(141,plain,
! [SV14: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ SV14 )
| ~ ( in @ SV14 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(142,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) )
| ~ ( function @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(143,plain,
! [SV15: $i] :
( ( ~ ! [SY65: $i] :
~ ( ~ ( ~ ( in @ SY65 @ SV15 )
| ~ ( ~ ( in @ SY65 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ SY65 ) @ sK2_SY34 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY65 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ SY65 ) @ sK2_SY34 ) )
| ( in @ SY65 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(144,plain,
( ( ~ ( ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(145,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(146,plain,
( ( ~ ( ~ ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(147,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(148,plain,
! [SV16: $i,SV4: $i,SV12: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
| ~ ( relation @ SV16 ) )
| ~ ( function @ SV16 ) )
| ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) )
| ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(149,plain,
( ( ~ ( ~ ( relation @ sK7_SX0 )
| ~ ( function @ sK7_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(150,plain,
! [SV5: $i] :
( ( ( finite @ SV5 )
= $false )
| ( ( ! [SY52: $i] :
( ~ ( element @ SY52 @ ( powerset @ SV5 ) )
| ( finite @ SY52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(151,plain,
! [SV6: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV6 )
| ~ ( relation @ SV6 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(152,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
| ~ ( one_to_one @ sK8_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(153,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV7 ) )
| ~ ( relation @ ( relation_dom @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(154,plain,
! [SV8: $i] :
( ( ( ~ ( empty @ SV8 ) )
= $false )
| ( ( ~ ! [SY53: $i] :
~ ~ ( ~ ( element @ SY53 @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ SY53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(155,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) )
| ~ ( finite @ SV13 ) ) )
= $true )
| ( ( finite @ ( relation_image @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ( element @ ( sK9_SY55 @ SV10 ) @ ( powerset @ SV10 ) )
| ~ ( empty @ ( sK9_SY55 @ SV10 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[140]) ).
thf(157,plain,
! [SV14: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV14 ) )
= $true )
| ( ( ~ ( in @ SV14 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(158,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) )
| ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(159,plain,
! [SV15: $i] :
( ( ! [SY65: $i] :
~ ( ~ ( ~ ( in @ SY65 @ SV15 )
| ~ ( ~ ( in @ SY65 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ SY65 ) @ sK2_SY34 ) ) )
| ~ ( ~ ~ ( ~ ( in @ SY65 @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ SY65 ) @ sK2_SY34 ) )
| ( in @ SY65 @ SV15 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(160,plain,
( ( ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(161,plain,
( ( ~ ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(162,plain,
! [SV16: $i,SV4: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
| ~ ( relation @ SV16 ) )
| ~ ( function @ SV16 ) ) )
= $true )
| ( ( ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) )
| ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(163,plain,
( ( ~ ( relation @ sK7_SX0 )
| ~ ( function @ sK7_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(164,plain,
! [SV5: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ ( powerset @ SV5 ) )
| ( finite @ SV17 ) )
= $true )
| ( ( finite @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(165,plain,
! [SV6: $i] :
( ( ( ~ ~ ( empty @ SV6 )
| ~ ( relation @ SV6 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(166,plain,
( ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
| ~ ( one_to_one @ sK8_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(167,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV7 ) )
| ~ ( relation @ ( relation_dom @ SV7 ) ) )
= $false )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(168,plain,
! [SV8: $i] :
( ( ( empty @ SV8 )
= $true )
| ( ( ~ ! [SY53: $i] :
~ ~ ( ~ ( element @ SY53 @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ SY53 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(169,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) )
| ~ ( finite @ SV13 ) ) )
= $false )
| ( ( finite @ ( relation_image @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(170,plain,
! [SV10: $i] :
( ( ~ ( ~ ( element @ ( sK9_SY55 @ SV10 ) @ ( powerset @ SV10 ) )
| ~ ( empty @ ( sK9_SY55 @ SV10 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(171,plain,
! [SV14: $i,SV11: $i] :
( ( ( in @ SV11 @ SV14 )
= $false )
| ( ( ~ ( in @ SV14 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(172,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(173,plain,
( ( ~ ( function @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[158]) ).
thf(174,plain,
! [SV15: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
| ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[159]) ).
thf(175,plain,
( ( ~ ( empty @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(176,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(177,plain,
( ( ~ ~ ( empty @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(178,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(179,plain,
! [SV16: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
| ~ ( relation @ SV16 ) )
| ~ ( function @ SV16 ) ) )
= $false )
| ( ( ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) )
| ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(180,plain,
( ( ~ ( relation @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(181,plain,
( ( ~ ( function @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(182,plain,
! [SV5: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ ( powerset @ SV5 ) ) )
= $true )
| ( ( finite @ SV17 )
= $true )
| ( ( finite @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(183,plain,
! [SV6: $i] :
( ( ( ~ ~ ( empty @ SV6 ) )
= $true )
| ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(184,plain,
( ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(185,plain,
( ( ~ ( one_to_one @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(186,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $false )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(187,plain,
! [SV7: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV7 ) ) )
= $false )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(188,plain,
! [SV8: $i] :
( ( ( ! [SY53: $i] :
~ ~ ( ~ ( element @ SY53 @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ SY53 ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(189,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) )
| ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(190,plain,
! [SV10: $i] :
( ( ~ ( element @ ( sK9_SY55 @ SV10 ) @ ( powerset @ SV10 ) )
| ~ ( empty @ ( sK9_SY55 @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(191,plain,
! [SV11: $i,SV14: $i] :
( ( ( in @ SV14 @ SV11 )
= $false )
| ( ( in @ SV11 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(192,plain,
( ( ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(193,plain,
( ( function @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(194,plain,
! [SV15: $i] :
( ( ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
| ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) ) )
| ~ ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(195,plain,
( ( empty @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(196,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(197,plain,
( ( ~ ( empty @ sK6_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(198,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(199,plain,
! [SV16: $i,SV4: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
| ~ ( relation @ SV16 ) )
| ~ ( function @ SV16 ) )
= $true )
| ( ( ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) )
| ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(200,plain,
( ( relation @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(201,plain,
( ( function @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(202,plain,
! [SV5: $i,SV17: $i] :
( ( ( element @ SV17 @ ( powerset @ SV5 ) )
= $false )
| ( ( finite @ SV17 )
= $true )
| ( ( finite @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(203,plain,
! [SV6: $i] :
( ( ( ~ ( empty @ SV6 ) )
= $false )
| ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(204,plain,
( ( ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(205,plain,
( ( one_to_one @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(206,plain,
! [SV7: $i] :
( ( ( empty @ ( relation_dom @ SV7 ) )
= $true )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(207,plain,
! [SV7: $i] :
( ( ( relation @ ( relation_dom @ SV7 ) )
= $true )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(208,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK11_SY53 @ SV8 ) @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ ( sK11_SY53 @ SV8 ) ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[188]) ).
thf(209,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) ) )
= $true )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(210,plain,
! [SV10: $i] :
( ( ~ ( element @ ( sK9_SY55 @ SV10 ) @ ( powerset @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(211,plain,
! [SV10: $i] :
( ( ~ ( empty @ ( sK9_SY55 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(212,plain,
( ( ~ ( relation @ sK4_SX0 )
| ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(213,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
| ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(214,plain,
( ( empty @ sK6_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(215,plain,
! [SV16: $i,SV4: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
| ~ ( relation @ SV16 ) ) )
= $true )
| ( ( ~ ( function @ SV16 ) )
= $true )
| ( ( ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) )
| ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(216,plain,
! [SV6: $i] :
( ( ( empty @ SV6 )
= $true )
| ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(217,plain,
( ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(218,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_SY53 @ SV8 ) @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ ( sK11_SY53 @ SV8 ) ) ) )
= $true )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(219,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) ) )
= $false )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(220,plain,
! [SV10: $i] :
( ( element @ ( sK9_SY55 @ SV10 ) @ ( powerset @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(221,plain,
! [SV10: $i] :
( ( empty @ ( sK9_SY55 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(222,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(223,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(224,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
| ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(225,plain,
! [SV16: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( ~ ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
| ~ ( relation @ SV16 ) ) )
= $false )
| ( ( ~ ( function @ SV16 ) )
= $true )
| ( ( ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) )
| ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(226,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( empty @ SV6 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(227,plain,
( ( ~ ( relation @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(228,plain,
( ( ~ ( function @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(229,plain,
! [SV8: $i] :
( ( ( ~ ( element @ ( sK11_SY53 @ SV8 ) @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ ( sK11_SY53 @ SV8 ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(230,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(231,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(232,plain,
( ( empty @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(233,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(234,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(235,plain,
! [SV16: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
| ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( function @ SV16 ) )
= $true )
| ( ( ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) )
| ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(236,plain,
! [SV6: $i] :
( ( ( empty @ ( relation_dom @ SV6 ) )
= $false )
| ( ( empty @ SV6 )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(237,plain,
( ( relation @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(238,plain,
( ( function @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(239,plain,
! [SV8: $i] :
( ( ( ~ ( element @ ( sK11_SY53 @ SV8 ) @ ( powerset @ SV8 ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(240,plain,
! [SV8: $i] :
( ( ( ~ ~ ( empty @ ( sK11_SY53 @ SV8 ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(241,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(242,plain,
! [SV15: $i] :
( ( ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(243,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(244,plain,
! [SV16: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) ) )
= $true )
| ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( function @ SV16 ) )
= $true )
| ( ( ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) )
| ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(245,plain,
! [SV8: $i] :
( ( ( element @ ( sK11_SY53 @ SV8 ) @ ( powerset @ SV8 ) )
= $true )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(246,plain,
! [SV8: $i] :
( ( ( ~ ( empty @ ( sK11_SY53 @ SV8 ) ) )
= $true )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[240]) ).
thf(247,plain,
! [SV13: $i,SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(248,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(249,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) ) )
= $true )
| ( ( ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(250,plain,
! [SV16: $i,SV4: $i,SV12: $i] :
( ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( function @ SV16 ) )
= $true )
| ( ( ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) )
| ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(251,plain,
! [SV8: $i] :
( ( ( empty @ ( sK11_SY53 @ SV8 ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(252,plain,
! [SV13: $i,SV9: $i] :
( ( ( function @ SV9 )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( relation_image @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(253,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) ) )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(254,plain,
! [SV15: $i] :
( ( ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(255,plain,
! [SV15: $i] :
( ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $false )
| ( ( ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(256,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( ~ ( function @ SV16 ) )
= $true )
| ( ( ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) )
| ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(257,plain,
! [SV9: $i,SV13: $i] :
( ( ( finite @ SV13 )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false )
| ( ( finite @ ( relation_image @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(258,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) ) )
= $true )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[253]) ).
thf(259,plain,
! [SV15: $i] :
( ( ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(260,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( function @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) )
| ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(261,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(262,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
| ( in @ ( sK10_SY65 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $false )
| ( ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(263,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( ~ ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) ) )
= $true )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(264,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) ) )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(265,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(266,plain,
! [SV15: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) ) )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $false )
| ( ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(267,plain,
! [SV15: $i] :
( ( ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $false )
| ( ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(268,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( ! [SY66: $i,SY67: $i,SY68: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( SY66 != SY67 )
| ~ ( in @ ( relation_image @ SV16 @ SY67 ) @ SV12 ) )
| ( SY66 != SY68 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY68 ) @ SV12 ) )
| ( SY67 = SY68 ) ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(269,plain,
! [SV15: $i] :
( ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $true )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(270,plain,
! [SV15: $i] :
( ( ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 )
= $true )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(271,plain,
! [SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) ) )
= $true )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $false )
| ( ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(272,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ! [SY73: $i,SY74: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= SY73 )
| ~ ( in @ ( relation_image @ SV16 @ SY73 ) @ SV12 ) )
| ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= SY74 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY74 ) @ SV12 ) )
| ( SY73 = SY74 ) ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[268]) ).
thf(273,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
| ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $false )
| ( ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(274,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ! [SY75: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
| ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= SY75 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY75 ) @ SV12 ) )
| ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= SY75 ) ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[272]) ).
thf(275,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) ) )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $false )
| ( ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(276,plain,
! [SV15: $i] :
( ( ( ~ ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 ) )
= $false )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $false )
| ( ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[273]) ).
thf(277,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
| ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
| ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[274]) ).
thf(278,plain,
! [SV15: $i] :
( ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $true )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $false )
| ( ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(279,plain,
! [SV15: $i] :
( ( ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 )
= $true )
| ( ( in @ ( sK10_SY65 @ SV15 ) @ ( powerset @ ( relation_dom @ sK3_SY38 ) ) )
= $false )
| ( ( in @ ( relation_image @ sK3_SY38 @ ( sK10_SY65 @ SV15 ) ) @ sK2_SY34 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(280,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
| ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(281,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(282,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
| ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) ) )
= $true )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(283,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(284,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
| ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(285,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ! [SY76: $i] :
~ ( ~ ( ~ ( in @ SY76 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY76 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY76 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY76 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY76 ) @ SV12 ) )
| ( in @ SY76 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[283]) ).
thf(286,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
| ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(287,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( ~ ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(288,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ! [SY76: $i] :
~ ( ~ ( ~ ( in @ SY76 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY76 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY76 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY76 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY76 ) @ SV12 ) )
| ( in @ SY76 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(289,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
| ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) ) )
= $true )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(290,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(291,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV18: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY79 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY80 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
| ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(292,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
| ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(293,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(294,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY79 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY80 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
| ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) ) ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(295,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(296,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[292]) ).
thf(297,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ! [SY81: $i] :
~ ( ~ ( ~ ( in @ SY81 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY81 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY81 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY81 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY81 ) @ SV12 ) )
| ( in @ SY81 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[293]) ).
thf(298,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY79 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(299,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY80 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
| ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) ) ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(300,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) ) )
= $true )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(301,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(302,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ! [SY81: $i] :
~ ( ~ ( ~ ( in @ SY81 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY81 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY81 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY81 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY81 ) @ SV12 ) )
| ( in @ SY81 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(303,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY79 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(304,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i] :
( ( ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY80 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
| ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(305,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
| ~ ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(306,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(307,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV19: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY84 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY84 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY85 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY85 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
| ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(308,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) ) )
= $true )
| ( ( ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY79 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(309,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i] :
( ( ( ~ ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY80 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(310,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
!= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(311,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( ~ ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 ) )
= $false )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(312,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY86 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY86 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY86 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY86 ) @ SV12 ) )
| ( in @ SY86 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[306]) ).
thf(313,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY84 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY84 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY85 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY85 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
| ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) ) ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(314,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV18: $i] :
( ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ~ ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY79 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(315,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i] :
( ( ( ~ ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY80 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(316,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(317,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( ~ ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(318,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ! [SY86: $i] :
~ ( ~ ( ~ ( in @ SY86 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY86 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY86 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY86 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY86 ) @ SV12 ) )
| ( in @ SY86 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(319,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV19: $i] :
( ( ( ~ ( ~ ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY84 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY84 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(320,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY85 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY85 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
| ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) ) ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(321,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i] :
( ( ( ! [SY79: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY79 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY79 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(322,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i] :
( ( ( ! [SY80: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY80 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY80 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(323,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(324,plain,
! [SV4: $i,SV12: $i,SV16: $i] :
( ( ( ! [SY69: $i] :
~ ! [SY70: $i] :
~ ( ~ ( ~ ( in @ SY70 @ SY69 )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY70 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY70 ) @ SV12 ) )
| ( in @ SY70 @ SY69 ) ) ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(325,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV20: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY89 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY90 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY90 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
| ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(326,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY84 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY84 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(327,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i] :
( ( ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY85 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY85 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
| ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(328,plain,
! [SV16: $i,SV18: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 )
!= SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[321]) ).
thf(329,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV21 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV21 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(330,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ! [SY91: $i] :
~ ( ~ ( ~ ( in @ SY91 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY91 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY91 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY91 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY91 ) @ SV12 ) )
| ( in @ SY91 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[323]) ).
thf(331,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ~ ! [SY94: $i] :
~ ( ~ ( ~ ( in @ SY94 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY94 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY94 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY94 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY94 ) @ SV12 ) )
| ( in @ SY94 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[324]) ).
thf(332,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY89 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY90 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY90 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
| ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) ) ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(333,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) ) )
= $true )
| ( ( ~ ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY84 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY84 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(334,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i] :
( ( ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY85 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY85 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(335,plain,
! [SV16: $i,SV18: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 )
!= SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(336,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i,SV21: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV21 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV21 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(337,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ! [SY91: $i] :
~ ( ~ ( ~ ( in @ SY91 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY91 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY91 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY91 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY91 ) @ SV12 ) )
| ( in @ SY91 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[330]) ).
thf(338,plain,
! [SV16: $i,SV12: $i,SV4: $i] :
( ( ( ! [SY94: $i] :
~ ( ~ ( ~ ( in @ SY94 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY71: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY71 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY71 != SY94 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY94 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY72: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY72 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY72 != SY94 ) )
| ~ ( in @ ( relation_image @ SV16 @ SY94 ) @ SV12 ) )
| ( in @ SY94 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(339,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV20: $i] :
( ( ( ~ ( ~ ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY89 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[332]) ).
thf(340,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY90 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY90 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
| ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) ) ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[332]) ).
thf(341,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV19: $i] :
( ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ~ ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY84 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY84 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(342,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i] :
( ( ( ~ ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY85 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY85 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(343,plain,
! [SV16: $i,SV18: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 )
!= SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
= $false )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(344,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( in @ SV21 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV21 != SV18 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(345,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV22: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY97 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY98 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY98 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
| ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(346,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY99 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY99 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY100 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY100 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
| ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) ) ) ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(347,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY89 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(348,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i] :
( ( ( ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY90 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY90 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
| ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(349,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i] :
( ( ( ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY84 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY84 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(350,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i] :
( ( ( ! [SY85: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY85 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY85 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(351,plain,
! [SV16: $i,SV18: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 )
!= SV18 ) ) )
= $false )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(352,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i] :
( ( ( ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
= $false )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[343]) ).
thf(353,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( in @ SV21 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV21 != SV18 ) ) )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(354,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY97 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY98 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY98 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
| ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) ) ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(355,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( ~ ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY99 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY99 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
| ~ ( ~ ~ ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY100 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY100 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
| ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) ) ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(356,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) ) )
= $true )
| ( ( ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY89 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(357,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i] :
( ( ( ~ ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY90 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY90 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(358,plain,
! [SV16: $i,SV19: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 )
!= SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[349]) ).
thf(359,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV24 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV24 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(360,plain,
! [SV16: $i,SV18: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 )
!= SV18 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(361,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i] :
( ( ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(362,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i,SV21: $i] :
( ( ( ~ ( ~ ( in @ SV21 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV21 != SV18 ) ) )
= $false )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(363,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY97 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(364,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY98 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY98 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
| ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) ) ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(365,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( ~ ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY99 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY99 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(366,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY100 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY100 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
| ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) ) ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(367,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV20: $i] :
( ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ~ ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY89 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(368,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i] :
( ( ( ~ ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY90 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY90 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(369,plain,
! [SV16: $i,SV19: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 )
!= SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[358]) ).
thf(370,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV24 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV24 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(371,plain,
! [SV16: $i,SV18: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 )
!= SV18 ) )
= $false )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(372,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV21 != SV18 ) )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(373,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY97 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(374,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i] :
( ( ( ~ ~ ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY98 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY98 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
| ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(375,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
| ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY99 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY99 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(376,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i] :
( ( ( ~ ~ ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY100 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY100 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
| ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(377,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i] :
( ( ( ! [SY89: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY89 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY89 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(378,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i] :
( ( ( ! [SY90: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY90 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY90 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(379,plain,
! [SV16: $i,SV19: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 )
!= SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
= $false )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(380,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( in @ SV24 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV24 != SV19 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(381,plain,
! [SV16: $i,SV18: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) ) )
= $false )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(382,plain,
! [SV16: $i,SV18: $i,SV12: $i,SV4: $i] :
( ( ( ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 )
!= SV18 )
= $false )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(383,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i,SV21: $i] :
( ( ( ~ ( in @ SV21 @ ( powerset @ ( relation_dom @ SV16 ) ) ) )
= $true )
| ( ( SV21 != SV18 )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(384,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) ) )
= $true )
| ( ( ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY97 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(385,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i] :
( ( ( ~ ~ ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY98 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY98 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(386,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) ) )
= $true )
| ( ( ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY99 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY99 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(387,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i] :
( ( ( ~ ~ ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY100 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY100 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(388,plain,
! [SV16: $i,SV20: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 )
!= SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[377]) ).
thf(389,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV25 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV25 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(390,plain,
! [SV16: $i,SV19: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 )
!= SV19 ) ) )
= $false )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(391,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i] :
( ( ( ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
= $false )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(392,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( in @ SV24 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV24 != SV19 ) ) )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(393,plain,
! [SV16: $i,SV18: $i,SV12: $i,SV4: $i] :
( ( ( in @ ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(394,plain,
! [SV16: $i,SV18: $i,SV12: $i,SV4: $i] :
( ( ( ( sK18_SY79 @ SV4 @ SV12 @ SV18 @ SV16 )
= SV18 )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(395,plain,
! [SV4: $i,SV12: $i,SV18: $i,SV16: $i,SV21: $i] :
( ( ( in @ SV21 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( SV21 != SV18 )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(396,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV22: $i] :
( ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ~ ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY97 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(397,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i] :
( ( ( ~ ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY98 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY98 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(398,plain,
! [SV16: $i,SV12: $i,SV4: $i,SV23: $i] :
( ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ~ ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY99 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY99 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(399,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i] :
( ( ( ~ ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY100 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY100 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(400,plain,
! [SV16: $i,SV20: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 )
!= SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(401,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i,SV25: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV25 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV25 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(402,plain,
! [SV16: $i,SV19: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 )
!= SV19 ) ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(403,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i] :
( ( ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(404,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i,SV24: $i] :
( ( ( ~ ( ~ ( in @ SV24 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV24 != SV19 ) ) )
= $false )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(405,plain,
! [SV4: $i,SV12: $i,SV16: $i,SV18: $i,SV21: $i] :
( ( ( SV21 = SV18 )
= $false )
| ( ( in @ SV21 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 ) )
= $true )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(406,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i] :
( ( ( ! [SY97: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY97 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY97 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(407,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i] :
( ( ( ! [SY98: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY98 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY98 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[397]) ).
thf(408,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i] :
( ( ( ! [SY99: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY99 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY99 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(409,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i] :
( ( ( ! [SY100: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY100 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SY100 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(410,plain,
! [SV16: $i,SV20: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 )
!= SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
= $false )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(411,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( in @ SV25 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV25 != SV20 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(412,plain,
! [SV16: $i,SV19: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 )
!= SV19 ) )
= $false )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(413,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV24 != SV19 ) )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(414,plain,
! [SV4: $i,SV21: $i,SV12: $i,SV18: $i,SV16: $i] :
( ( ( in @ ( relation_image @ SV16 @ SV18 ) @ SV12 )
= $false )
| ( ( in @ SV21 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( SV21 = SV18 )
= $false )
| ( ( in @ SV18 @ ( sK15_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK13_SY73 @ SV16 @ SV12 @ SV4 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(415,plain,
! [SV16: $i,SV22: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 )
!= SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[406]) ).
thf(416,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV26 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV26 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(417,plain,
! [SV16: $i,SV23: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 )
!= SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[408]) ).
thf(418,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV27 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV27 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(419,plain,
! [SV16: $i,SV20: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 )
!= SV20 ) ) )
= $false )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(420,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i] :
( ( ( ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
= $false )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(421,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( in @ SV25 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV25 != SV20 ) ) )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(422,plain,
! [SV16: $i,SV19: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) ) )
= $false )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(423,plain,
! [SV16: $i,SV19: $i,SV12: $i,SV4: $i] :
( ( ( ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 )
!= SV19 )
= $false )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(424,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( powerset @ ( relation_dom @ SV16 ) ) ) )
= $true )
| ( ( SV24 != SV19 )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(425,plain,
! [SV16: $i,SV22: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 )
!= SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(426,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i,SV26: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV26 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV26 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(427,plain,
! [SV16: $i,SV23: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 )
!= SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(428,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i,SV27: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV27 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV27 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(429,plain,
! [SV16: $i,SV20: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 )
!= SV20 ) ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(430,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i] :
( ( ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(431,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i,SV25: $i] :
( ( ( ~ ( ~ ( in @ SV25 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV25 != SV20 ) ) )
= $false )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(432,plain,
! [SV16: $i,SV19: $i,SV12: $i,SV4: $i] :
( ( ( in @ ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(433,plain,
! [SV16: $i,SV19: $i,SV12: $i,SV4: $i] :
( ( ( ( sK21_SY84 @ SV4 @ SV12 @ SV19 @ SV16 )
= SV19 )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(434,plain,
! [SV4: $i,SV12: $i,SV19: $i,SV16: $i,SV24: $i] :
( ( ( in @ SV24 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( SV24 != SV19 )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(435,plain,
! [SV16: $i,SV22: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 )
!= SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
= $false )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(436,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ SV26 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV26 != SV22 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(437,plain,
! [SV16: $i,SV23: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 )
!= SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
= $false )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(438,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ SV27 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV27 != SV23 ) )
| ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(439,plain,
! [SV16: $i,SV20: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 )
!= SV20 ) )
= $false )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(440,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV25 != SV20 ) )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(441,plain,
! [SV4: $i,SV12: $i,SV16: $i,SV19: $i,SV24: $i] :
( ( ( SV24 = SV19 )
= $false )
| ( ( in @ SV24 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 ) )
= $true )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(442,plain,
! [SV16: $i,SV22: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 )
!= SV22 ) ) )
= $false )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(443,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i] :
( ( ( ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
= $false )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(444,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ SV26 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV26 != SV22 ) ) )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(445,plain,
! [SV16: $i,SV23: $i,SV12: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 )
!= SV23 ) ) )
= $false )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(446,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i] :
( ( ( ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
= $false )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(447,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( in @ SV27 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV27 != SV23 ) ) )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(448,plain,
! [SV16: $i,SV20: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) ) )
= $false )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(449,plain,
! [SV16: $i,SV20: $i,SV12: $i,SV4: $i] :
( ( ( ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 )
!= SV20 )
= $false )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(450,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ ( powerset @ ( relation_dom @ SV16 ) ) ) )
= $true )
| ( ( SV25 != SV20 )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(451,plain,
! [SV4: $i,SV24: $i,SV12: $i,SV19: $i,SV16: $i] :
( ( ( in @ ( relation_image @ SV16 @ SV19 ) @ SV12 )
= $false )
| ( ( in @ SV24 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( SV24 = SV19 )
= $false )
| ( ( in @ SV19 @ ( sK16_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(452,plain,
! [SV16: $i,SV22: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 )
!= SV22 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(453,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i] :
( ( ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(454,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ SV26 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV26 != SV22 ) ) )
= $false )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(455,plain,
! [SV16: $i,SV23: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 )
!= SV23 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(456,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i] :
( ( ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(457,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i,SV27: $i] :
( ( ( ~ ( ~ ( in @ SV27 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV27 != SV23 ) ) )
= $false )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(458,plain,
! [SV16: $i,SV20: $i,SV12: $i,SV4: $i] :
( ( ( in @ ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(459,plain,
! [SV16: $i,SV20: $i,SV12: $i,SV4: $i] :
( ( ( ( sK22_SY89 @ SV4 @ SV12 @ SV20 @ SV16 )
= SV20 )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(460,plain,
! [SV4: $i,SV12: $i,SV20: $i,SV16: $i,SV25: $i] :
( ( ( in @ SV25 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( SV25 != SV20 )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(461,plain,
! [SV16: $i,SV22: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 )
!= SV22 ) )
= $false )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(462,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV26 != SV22 ) )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(463,plain,
! [SV16: $i,SV23: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 )
!= SV23 ) )
= $false )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(464,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ ( powerset @ ( relation_dom @ SV16 ) ) )
| ( SV27 != SV23 ) )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(465,plain,
! [SV4: $i,SV12: $i,SV16: $i,SV20: $i,SV25: $i] :
( ( ( SV25 = SV20 )
= $false )
| ( ( in @ SV25 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 ) )
= $true )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(466,plain,
! [SV16: $i,SV22: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) ) )
= $false )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(467,plain,
! [SV16: $i,SV22: $i,SV12: $i,SV4: $i] :
( ( ( ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 )
!= SV22 )
= $false )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(468,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ ( powerset @ ( relation_dom @ SV16 ) ) ) )
= $true )
| ( ( SV26 != SV22 )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(469,plain,
! [SV16: $i,SV23: $i,SV12: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) ) )
= $false )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(470,plain,
! [SV16: $i,SV23: $i,SV12: $i,SV4: $i] :
( ( ( ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 )
!= SV23 )
= $false )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(471,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i,SV27: $i] :
( ( ( ~ ( in @ SV27 @ ( powerset @ ( relation_dom @ SV16 ) ) ) )
= $true )
| ( ( SV27 != SV23 )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(472,plain,
! [SV4: $i,SV25: $i,SV12: $i,SV20: $i,SV16: $i] :
( ( ( in @ ( relation_image @ SV16 @ SV20 ) @ SV12 )
= $false )
| ( ( in @ SV25 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( SV25 = SV20 )
= $false )
| ( ( in @ SV20 @ ( sK17_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK14_SY75 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(473,plain,
! [SV16: $i,SV22: $i,SV12: $i,SV4: $i] :
( ( ( in @ ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(474,plain,
! [SV16: $i,SV22: $i,SV12: $i,SV4: $i] :
( ( ( ( sK23_SY97 @ SV4 @ SV12 @ SV22 @ SV16 )
= SV22 )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(475,plain,
! [SV4: $i,SV12: $i,SV22: $i,SV16: $i,SV26: $i] :
( ( ( in @ SV26 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( SV26 != SV22 )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(476,plain,
! [SV16: $i,SV23: $i,SV12: $i,SV4: $i] :
( ( ( in @ ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 ) @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(477,plain,
! [SV16: $i,SV23: $i,SV12: $i,SV4: $i] :
( ( ( ( sK24_SY99 @ SV4 @ SV12 @ SV23 @ SV16 )
= SV23 )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $false )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(478,plain,
! [SV4: $i,SV12: $i,SV23: $i,SV16: $i,SV27: $i] :
( ( ( in @ SV27 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( SV27 != SV23 )
= $true )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(479,plain,
! [SV4: $i,SV12: $i,SV16: $i,SV22: $i,SV26: $i] :
( ( ( SV26 = SV22 )
= $false )
| ( ( in @ SV26 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 ) )
= $true )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(480,plain,
! [SV4: $i,SV12: $i,SV16: $i,SV23: $i,SV27: $i] :
( ( ( SV27 = SV23 )
= $false )
| ( ( in @ SV27 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( ~ ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 ) )
= $true )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(481,plain,
! [SV4: $i,SV26: $i,SV12: $i,SV22: $i,SV16: $i] :
( ( ( in @ ( relation_image @ SV16 @ SV22 ) @ SV12 )
= $false )
| ( ( in @ SV26 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( SV26 = SV22 )
= $false )
| ( ( in @ SV22 @ ( sK19_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( ( sK12_SY66 @ SV4 @ SV12 @ SV16 )
= ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(482,plain,
! [SV4: $i,SV27: $i,SV12: $i,SV23: $i,SV16: $i] :
( ( ( in @ ( relation_image @ SV16 @ SV23 ) @ SV12 )
= $false )
| ( ( in @ SV27 @ ( powerset @ ( relation_dom @ SV16 ) ) )
= $false )
| ( ( SV27 = SV23 )
= $false )
| ( ( in @ SV23 @ ( sK20_SY69 @ SV4 @ SV12 @ SV16 ) )
= $true )
| ( ( in @ ( relation_image @ SV16 @ ( sK13_SY73 @ SV16 @ SV12 @ SV4 ) ) @ SV12 )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( element @ SV12 @ ( powerset @ ( powerset @ SV4 ) ) )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(483,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[81,482,481,477,476,474,473,472,459,458,456,453,451,433,432,430,414,403,394,393,361,279,278,270,269,267,257,254,251,245,238,237,236,232,231,221,220,214,207,206,205,202,201,200,198,196,195,193,191,147,145,125,90,89,88,84,83,82]) ).
thf(484,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[483]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU297+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
% 0.13/0.19 % Computer : n007.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Tue Oct 6 15:11:03 UTC 2026
% 0.13/0.19 % CPUTime :
% 0.13/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.97/0.78
% 2.97/0.78 No.of.Axioms: 20
% 2.97/0.78
% 2.97/0.78 Length.of.Defs: 0
% 2.97/0.78
% 2.97/0.78 Contains.Choice.Funs: false
% 2.97/0.78 ..............
% 2.97/0.78
% 2.97/0.78 ********************************
% 2.97/0.78 * All subproblems solved! *
% 2.97/0.78 ********************************
% 2.97/0.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:23,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:483,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.97/0.78
% 2.97/0.78 %**** Beginning of derivation protocol ****
% 2.97/0.78 % SZS output start CNFRefutation
% See solution above
% 2.97/0.78
% 2.97/0.78 %**** End of derivation protocol ****
% 2.97/0.78 %**** no. of clauses in derivation: 468 ****
% 2.97/0.78 %**** clause counter: 483 ****
% 2.97/0.78
% 2.97/0.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:23,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:483,loop_count:0,foatp_calls:1,translation:fof_full)
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