%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU212+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 10:43:25 AM UTC 2026
% Result : Theorem 0.48s 0.30s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 22
% Syntax : Number of formulae : 481 ( 234 unt; 0 typ; 0 def)
% Number of atoms : 3733 (1392 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 6605 (1682 ~;1160 |; 55 &;3633 @)
% ( 23 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 14 con; 0-3 aty)
% Number of variables : 956 ( 0 ^; 936 !; 20 ?; 956 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_sK10_SY52,type,
sK10_SY52: $i > $i > $i ).
thf(tp_sK11_SY52,type,
sK11_SY52: $i > $i > $i > $i ).
thf(tp_sK12_SX0,type,
sK12_SX0: $i ).
thf(tp_sK13_SX0,type,
sK13_SX0: $i ).
thf(tp_sK14_SX0,type,
sK14_SX0: $i ).
thf(tp_sK15_SX0,type,
sK15_SX0: $i ).
thf(tp_sK16_SY69,type,
sK16_SY69: $i > $i > $i ).
thf(tp_sK17_SY73,type,
sK17_SY73: $i > $i > $i > $i ).
thf(tp_sK18_SY76,type,
sK18_SY76: $i > $i > $i ).
thf(tp_sK19_SY76,type,
sK19_SY76: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY26,type,
sK2_SY26: $i ).
thf(tp_sK3_SY28,type,
sK3_SY28: $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_SY45,type,
sK8_SY45: $i > $i > $i ).
thf(tp_sK9_SY49,type,
sK9_SY49: $i > $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(6,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(8,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(10,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(11,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(12,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(13,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(17,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(29,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(30,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
thf(32,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(33,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(35,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
thf(36,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[35]) ).
thf(37,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(40,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(41,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(42,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(43,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(44,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(45,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(47,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(48,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(49,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(50,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(51,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(52,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(53,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(59,plain,
( ( ! [SY26: $i,SY27: $i] :
( ( ( relation @ SY27 )
& ( function @ SY27 ) )
=> ( ( in @ ( ordered_pair @ sK1_A @ SY26 ) @ SY27 )
<=> ( ( in @ sK1_A @ ( relation_dom @ SY27 ) )
& ( SY26
= ( apply @ SY27 @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(60,plain,
( ( ! [SY28: $i] :
( ( ( relation @ SY28 )
& ( function @ SY28 ) )
=> ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ SY28 )
<=> ( ( in @ sK1_A @ ( relation_dom @ SY28 ) )
& ( sK2_SY26
= ( apply @ SY28 @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[59]) ).
thf(61,plain,
( ( ( ( relation @ sK3_SY28 )
& ( function @ sK3_SY28 ) )
=> ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 )
<=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
& ( sK2_SY26
= ( apply @ sK3_SY28 @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(62,plain,
( ( relation @ sK3_SY28 )
= $true ),
inference(standard_cnf,[status(thm)],[61]) ).
thf(63,plain,
( ( function @ sK3_SY28 )
= $true ),
inference(standard_cnf,[status(thm)],[61]) ).
thf(64,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 )
<=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
& ( sK2_SY26
= ( apply @ sK3_SY28 @ sK1_A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[61]) ).
thf(65,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 )
=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
& ( sK2_SY26
= ( apply @ sK3_SY28 @ sK1_A ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[64]) ).
thf(66,plain,
( ( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
& ( sK2_SY26
= ( apply @ sK3_SY28 @ sK1_A ) ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[64]) ).
thf(67,plain,
( ( ~ ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 )
=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
& ( sK2_SY26
= ( apply @ sK3_SY28 @ sK1_A ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[65]) ).
thf(68,plain,
( ( ~ ( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
& ( sK2_SY26
= ( apply @ sK3_SY28 @ sK1_A ) ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[66]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(71,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(72,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(73,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(74,plain,
$true = $true,
inference(copy,[status(thm)],[53]) ).
thf(75,plain,
$true = $true,
inference(copy,[status(thm)],[52]) ).
thf(76,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(77,plain,
$true = $true,
inference(copy,[status(thm)],[50]) ).
thf(78,plain,
$true = $true,
inference(copy,[status(thm)],[49]) ).
thf(79,plain,
$true = $true,
inference(copy,[status(thm)],[48]) ).
thf(80,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(82,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(83,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(84,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(85,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(86,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(87,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(88,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(89,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(90,plain,
( ( function @ sK3_SY28 )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(91,plain,
( ( relation @ sK3_SY28 )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(92,plain,
( ( ~ ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 )
=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
& ( sK2_SY26
= ( apply @ sK3_SY28 @ sK1_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(93,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(94,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(95,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(96,plain,
( ( ~ ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 )
| ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
| ( sK2_SY26
!= ( apply @ sK3_SY28 @ sK1_A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(97,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( ~ ( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) )
| ~ ( ~ ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( ~ ( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( SX2 = empty_set ) )
| ~ ( ( SX2 != empty_set )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(98,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(99,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(100,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(101,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(102,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(103,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(105,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(106,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(107,plain,
! [SV1: $i] :
( ( ! [SY29: $i] :
~ ( empty @ ( ordered_pair @ SV1 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(108,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV2: $i] :
( ( ! [SY30: $i] :
( ~ ( in @ SV2 @ SY30 )
| ( element @ SV2 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV3: $i] :
( ( ~ ( empty @ SV3 )
| ~ ( ~ ( empty @ ( relation_dom @ SV3 ) )
| ~ ( relation @ ( relation_dom @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(111,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 )
| ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
| ( sK2_SY26
!= ( apply @ sK3_SY28 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ( relation @ SV4 )
| ~ ( function @ SV4 ) )
| ! [SY31: $i,SY32: $i] :
~ ( ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( SY32 = empty_set ) )
| ~ ( ( SY32 != empty_set )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV5: $i] :
( ( ~ ( relation @ SV5 )
| ! [SY33: $i] :
~ ( ~ ( ( SY33
!= ( relation_dom @ SV5 ) )
| ! [SY34: $i] :
~ ( ~ ( ~ ( in @ SY34 @ SY33 )
| ~ ! [SY35: $i] :
~ ( in @ ( ordered_pair @ SY34 @ SY35 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY34 @ SY36 ) @ SV5 )
| ( in @ SY34 @ SY33 ) ) ) )
| ~ ( ~ ! [SY37: $i] :
~ ( ~ ( ~ ( in @ SY37 @ SY33 )
| ~ ! [SY38: $i] :
~ ( in @ ( ordered_pair @ SY37 @ SY38 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ ( ordered_pair @ SY37 @ SY39 ) @ SV5 )
| ( in @ SY37 @ SY33 ) ) )
| ( SY33
= ( relation_dom @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(114,plain,
! [SV6: $i] :
( ( ~ ( empty @ SV6 )
| ( relation @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(115,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(116,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(117,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV7: $i] :
( ( ~ ( empty @ SV7 )
| ( function @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV8: $i] :
( ( ! [SY40: $i] :
( ~ ( in @ SV8 @ SY40 )
| ~ ( in @ SY40 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV9: $i] :
( ( ! [SY41: $i] :
~ ~ ( ~ ( in @ SV9 @ SY41 )
| ~ ( empty @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV10: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV10 )
| ~ ( relation @ SV10 ) )
| ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV11: $i,SV1: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV1 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(123,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[108]) ).
thf(124,plain,
! [SV12: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV12 )
| ( element @ SV2 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(125,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ SV3 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV3 ) )
| ~ ( relation @ ( relation_dom @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(126,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(127,plain,
( ( ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
| ( sK2_SY26
!= ( apply @ sK3_SY28 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(128,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV4 )
| ~ ( function @ SV4 ) ) )
= $true )
| ( ( ! [SY31: $i,SY32: $i] :
~ ( ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( SY32 = empty_set ) )
| ~ ( ( SY32 != empty_set )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(129,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ! [SY33: $i] :
~ ( ~ ( ( SY33
!= ( relation_dom @ SV5 ) )
| ! [SY34: $i] :
~ ( ~ ( ~ ( in @ SY34 @ SY33 )
| ~ ! [SY35: $i] :
~ ( in @ ( ordered_pair @ SY34 @ SY35 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY34 @ SY36 ) @ SV5 )
| ( in @ SY34 @ SY33 ) ) ) )
| ~ ( ~ ! [SY37: $i] :
~ ( ~ ( ~ ( in @ SY37 @ SY33 )
| ~ ! [SY38: $i] :
~ ( in @ ( ordered_pair @ SY37 @ SY38 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ ( ordered_pair @ SY37 @ SY39 ) @ SV5 )
| ( in @ SY37 @ SY33 ) ) )
| ( SY33
= ( relation_dom @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(130,plain,
! [SV6: $i] :
( ( ( ~ ( empty @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(131,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[115]) ).
thf(132,plain,
( ( ~ ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( relation_empty_yielding @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(133,plain,
( ( ~ ~ ( ~ ( empty @ sK7_SX0 )
| ~ ( relation @ sK7_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[117]) ).
thf(134,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $true )
| ( ( function @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(135,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ SV13 )
| ~ ( in @ SV13 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(136,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ~ ( ~ ( in @ SV9 @ SV14 )
| ~ ( empty @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(137,plain,
! [SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV10 )
| ~ ( relation @ SV10 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(138,plain,
! [SV11: $i,SV1: $i] :
( ( empty @ ( ordered_pair @ SV1 @ SV11 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(139,plain,
( ( ~ ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(140,plain,
! [SV12: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV12 ) )
= $true )
| ( ( element @ SV2 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(141,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV3 ) )
| ~ ( relation @ ( relation_dom @ SV3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(142,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(143,plain,
( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
| ( sK2_SY26
!= ( apply @ sK3_SY28 @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(144,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( relation @ SV4 )
| ~ ( function @ SV4 ) ) )
= $false )
| ( ( ! [SY31: $i,SY32: $i] :
~ ( ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( SY32 = empty_set ) )
| ~ ( ( SY32 != empty_set )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(145,plain,
! [SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( ! [SY33: $i] :
~ ( ~ ( ( SY33
!= ( relation_dom @ SV5 ) )
| ! [SY34: $i] :
~ ( ~ ( ~ ( in @ SY34 @ SY33 )
| ~ ! [SY35: $i] :
~ ( in @ ( ordered_pair @ SY34 @ SY35 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY34 @ SY36 ) @ SV5 )
| ( in @ SY34 @ SY33 ) ) ) )
| ~ ( ~ ! [SY37: $i] :
~ ( ~ ( ~ ( in @ SY37 @ SY33 )
| ~ ! [SY38: $i] :
~ ( in @ ( ordered_pair @ SY37 @ SY38 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ ( ordered_pair @ SY37 @ SY39 ) @ SV5 )
| ( in @ SY37 @ SY33 ) ) )
| ( SY33
= ( relation_dom @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(146,plain,
! [SV6: $i] :
( ( ( empty @ SV6 )
= $false )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(147,plain,
( ( ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(148,plain,
( ( ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( relation_empty_yielding @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(149,plain,
( ( ~ ( ~ ( empty @ sK7_SX0 )
| ~ ( relation @ sK7_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(150,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $false )
| ( ( function @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(151,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV13 ) )
= $true )
| ( ( ~ ( in @ SV13 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(152,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( ~ ( in @ SV9 @ SV14 )
| ~ ( empty @ SV14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(153,plain,
! [SV10: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV10 )
| ~ ( relation @ SV10 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(154,plain,
( ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(155,plain,
! [SV12: $i,SV2: $i] :
( ( ( in @ SV2 @ SV12 )
= $false )
| ( ( element @ SV2 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(156,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV3 ) )
| ~ ( relation @ ( relation_dom @ SV3 ) ) )
= $false )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(157,plain,
( ( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) ) )
= $true )
| ( ( sK2_SY26
!= ( apply @ sK3_SY28 @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(158,plain,
! [SV4: $i] :
( ( ( ~ ( relation @ SV4 )
| ~ ( function @ SV4 ) )
= $true )
| ( ( ! [SY31: $i,SY32: $i] :
~ ( ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( SY32 = empty_set ) )
| ~ ( ( SY32 != empty_set )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(159,plain,
! [SV5: $i,SV15: $i] :
( ( ( ~ ( ~ ( ( SV15
!= ( relation_dom @ SV5 ) )
| ! [SY42: $i] :
~ ( ~ ( ~ ( in @ SY42 @ SV15 )
| ~ ! [SY35: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY35 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY36 ) @ SV5 )
| ( in @ SY42 @ SV15 ) ) ) )
| ~ ( ~ ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV15 )
| ~ ! [SY38: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY38 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY39 ) @ SV5 )
| ( in @ SY45 @ SV15 ) ) )
| ( SV15
= ( relation_dom @ SV5 ) ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(160,plain,
( ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(161,plain,
( ( ~ ( relation @ sK6_SX0 )
| ~ ( relation_empty_yielding @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(162,plain,
( ( ~ ( empty @ sK7_SX0 )
| ~ ( relation @ sK7_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(163,plain,
! [SV13: $i,SV8: $i] :
( ( ( in @ SV8 @ SV13 )
= $false )
| ( ( ~ ( in @ SV13 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(164,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ SV14 )
| ~ ( empty @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(165,plain,
! [SV10: $i] :
( ( ( ~ ~ ( empty @ SV10 )
| ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(166,plain,
( ( ~ ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(167,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(168,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV3 ) ) )
= $false )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(169,plain,
! [SV3: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV3 ) ) )
= $false )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(170,plain,
( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
= $false )
| ( ( sK2_SY26
!= ( apply @ sK3_SY28 @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(171,plain,
! [SV4: $i] :
( ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( function @ SV4 ) )
= $true )
| ( ( ! [SY31: $i,SY32: $i] :
~ ( ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( SY32 = empty_set ) )
| ~ ( ( SY32 != empty_set )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(172,plain,
! [SV5: $i,SV15: $i] :
( ( ( ~ ( ( SV15
!= ( relation_dom @ SV5 ) )
| ! [SY42: $i] :
~ ( ~ ( ~ ( in @ SY42 @ SV15 )
| ~ ! [SY35: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY35 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY36 ) @ SV5 )
| ( in @ SY42 @ SV15 ) ) ) )
| ~ ( ~ ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV15 )
| ~ ! [SY38: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY38 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY39 ) @ SV5 )
| ( in @ SY45 @ SV15 ) ) )
| ( SV15
= ( relation_dom @ SV5 ) ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(173,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(174,plain,
( ( ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(175,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(176,plain,
( ( ~ ( relation_empty_yielding @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(177,plain,
( ( ~ ( empty @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(178,plain,
( ( ~ ( relation @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(179,plain,
! [SV8: $i,SV13: $i] :
( ( ( in @ SV13 @ SV8 )
= $false )
| ( ( in @ SV8 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(180,plain,
! [SV14: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV14 ) )
= $true )
| ( ( ~ ( empty @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(181,plain,
! [SV10: $i] :
( ( ( ~ ~ ( empty @ SV10 ) )
= $true )
| ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(182,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(183,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(184,plain,
! [SV3: $i] :
( ( ( empty @ ( relation_dom @ SV3 ) )
= $true )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(185,plain,
! [SV3: $i] :
( ( ( relation @ ( relation_dom @ SV3 ) )
= $true )
| ( ( empty @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(186,plain,
( ( ( sK2_SY26
= ( apply @ sK3_SY28 @ sK1_A ) )
= $false )
| ( ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(187,plain,
! [SV4: $i] :
( ( ( relation @ SV4 )
= $false )
| ( ( ~ ( function @ SV4 ) )
= $true )
| ( ( ! [SY31: $i,SY32: $i] :
~ ( ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( SY32 = empty_set ) )
| ~ ( ( SY32 != empty_set )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(188,plain,
! [SV5: $i,SV15: $i] :
( ( ( ~ ( ( SV15
!= ( relation_dom @ SV5 ) )
| ! [SY42: $i] :
~ ( ~ ( ~ ( in @ SY42 @ SV15 )
| ~ ! [SY35: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY35 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY36 ) @ SV5 )
| ( in @ SY42 @ SV15 ) ) ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(189,plain,
! [SV5: $i,SV15: $i] :
( ( ( ~ ( ~ ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV15 )
| ~ ! [SY38: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY38 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY39 ) @ SV5 )
| ( in @ SY45 @ SV15 ) ) )
| ( SV15
= ( relation_dom @ SV5 ) ) ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(190,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(191,plain,
( ( function @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(192,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(193,plain,
( ( relation_empty_yielding @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[176]) ).
thf(194,plain,
( ( empty @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(195,plain,
( ( relation @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(196,plain,
! [SV14: $i,SV9: $i] :
( ( ( in @ SV9 @ SV14 )
= $false )
| ( ( ~ ( empty @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(197,plain,
! [SV10: $i] :
( ( ( ~ ( empty @ SV10 ) )
= $false )
| ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(198,plain,
( ( empty @ sK4_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(199,plain,
! [SV4: $i] :
( ( ( function @ SV4 )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( ! [SY31: $i,SY32: $i] :
~ ( ~ ( ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY31 @ SY32 ) @ SV4 )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY31 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY32
!= ( apply @ SV4 @ SY31 ) )
| ( SY32 = empty_set ) )
| ~ ( ( SY32 != empty_set )
| ( SY32
= ( apply @ SV4 @ SY31 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(200,plain,
! [SV5: $i,SV15: $i] :
( ( ( ( SV15
!= ( relation_dom @ SV5 ) )
| ! [SY42: $i] :
~ ( ~ ( ~ ( in @ SY42 @ SV15 )
| ~ ! [SY35: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY35 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY36 ) @ SV5 )
| ( in @ SY42 @ SV15 ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(201,plain,
! [SV5: $i,SV15: $i] :
( ( ( ~ ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV15 )
| ~ ! [SY38: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY38 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY39 ) @ SV5 )
| ( in @ SY45 @ SV15 ) ) )
| ( SV15
= ( relation_dom @ SV5 ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(202,plain,
! [SV9: $i,SV14: $i] :
( ( ( empty @ SV14 )
= $false )
| ( ( in @ SV9 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(203,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $true )
| ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(204,plain,
! [SV4: $i,SV16: $i] :
( ( ( ! [SY48: $i] :
~ ( ~ ( ~ ( in @ SV16 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY48
!= ( apply @ SV4 @ SV16 ) )
| ( in @ ( ordered_pair @ SV16 @ SY48 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV16 @ SY48 ) @ SV4 )
| ( SY48
= ( apply @ SV4 @ SV16 ) ) ) ) )
| ~ ( ~ ~ ( in @ SV16 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SY48
!= ( apply @ SV4 @ SV16 ) )
| ( SY48 = empty_set ) )
| ~ ( ( SY48 != empty_set )
| ( SY48
= ( apply @ SV4 @ SV16 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(205,plain,
! [SV5: $i,SV15: $i] :
( ( ( SV15
!= ( relation_dom @ SV5 ) )
= $true )
| ( ( ! [SY42: $i] :
~ ( ~ ( ~ ( in @ SY42 @ SV15 )
| ~ ! [SY35: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY35 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY36 ) @ SV5 )
| ( in @ SY42 @ SV15 ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(206,plain,
! [SV5: $i,SV15: $i] :
( ( ( ~ ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV15 )
| ~ ! [SY38: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY38 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY39 ) @ SV5 )
| ( in @ SY45 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(207,plain,
! [SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( empty @ SV10 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(208,plain,
! [SV17: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV16 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) )
| ~ ( ~ ~ ( in @ SV16 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( SV17 = empty_set ) )
| ~ ( ( SV17 != empty_set )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(209,plain,
! [SV5: $i,SV15: $i] :
( ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( ! [SY42: $i] :
~ ( ~ ( ~ ( in @ SY42 @ SV15 )
| ~ ! [SY35: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY35 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY36: $i] :
~ ( in @ ( ordered_pair @ SY42 @ SY36 ) @ SV5 )
| ( in @ SY42 @ SV15 ) ) ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(210,plain,
! [SV5: $i,SV15: $i] :
( ( ( ! [SY45: $i] :
~ ( ~ ( ~ ( in @ SY45 @ SV15 )
| ~ ! [SY38: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY38 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ( in @ ( ordered_pair @ SY45 @ SY39 ) @ SV5 )
| ( in @ SY45 @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(211,plain,
! [SV10: $i] :
( ( ( empty @ ( relation_dom @ SV10 ) )
= $false )
| ( ( empty @ SV10 )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(212,plain,
! [SV17: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) )
| ~ ( ~ ~ ( in @ SV16 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( SV17 = empty_set ) )
| ~ ( ( SV17 != empty_set )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) ) )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(213,plain,
! [SV5: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV18 @ SV15 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY49 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY50 ) @ SV5 )
| ( in @ SV18 @ SV15 ) ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(214,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
| ~ ! [SY51: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY51 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 )
| ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[210]) ).
thf(215,plain,
! [SV17: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ SV16 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) ) )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(216,plain,
! [SV17: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( in @ SV16 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( SV17 = empty_set ) )
| ~ ( ( SV17 != empty_set )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) ) )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(217,plain,
! [SV5: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ SV18 @ SV15 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY49 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY50 ) @ SV5 )
| ( in @ SV18 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(218,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
| ~ ! [SY51: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY51 ) @ SV5 ) )
| ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 )
| ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(219,plain,
! [SV17: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(220,plain,
! [SV17: $i,SV4: $i,SV16: $i] :
( ( ( ~ ~ ( in @ SV16 @ ( relation_dom @ SV4 ) )
| ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( SV17 = empty_set ) )
| ~ ( ( SV17 != empty_set )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(221,plain,
! [SV5: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( ~ ( in @ SV18 @ SV15 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY49 ) @ SV5 ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(222,plain,
! [SV15: $i,SV5: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY50 ) @ SV5 )
| ( in @ SV18 @ SV15 ) ) )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[217]) ).
thf(223,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
| ~ ! [SY51: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY51 ) @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 )
| ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(224,plain,
! [SV17: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ ( relation_dom @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(225,plain,
! [SV17: $i,SV4: $i,SV16: $i] :
( ( ( ~ ~ ( in @ SV16 @ ( relation_dom @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( SV17 = empty_set ) )
| ~ ( ( SV17 != empty_set )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(226,plain,
! [SV5: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV15 )
| ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY49 ) @ SV5 ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(227,plain,
! [SV15: $i,SV5: $i,SV18: $i] :
( ( ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY50 ) @ SV5 )
| ( in @ SV18 @ SV15 ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(228,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
| ~ ! [SY51: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY51 ) @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 )
| ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(229,plain,
! [SV17: $i,SV4: $i,SV16: $i] :
( ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(230,plain,
! [SV17: $i,SV4: $i,SV16: $i] :
( ( ( ~ ( in @ SV16 @ ( relation_dom @ SV4 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( SV17 = empty_set ) )
| ~ ( ( SV17 != empty_set )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(231,plain,
! [SV5: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ SV18 @ SV15 ) )
= $true )
| ( ( ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY49 ) @ SV5 ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(232,plain,
! [SV15: $i,SV5: $i,SV18: $i] :
( ( ( ~ ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY50 ) @ SV5 ) )
= $true )
| ( ( in @ SV18 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(233,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 )
| ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(234,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ! [SY51: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY51 ) @ SV5 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 )
| ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(235,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(236,plain,
! [SV17: $i,SV4: $i,SV16: $i] :
( ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( SV17 = empty_set ) )
| ~ ( ( SV17 != empty_set )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(237,plain,
! [SV5: $i,SV15: $i,SV18: $i] :
( ( ( in @ SV18 @ SV15 )
= $false )
| ( ( ~ ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY49 ) @ SV5 ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(238,plain,
! [SV15: $i,SV5: $i,SV18: $i] :
( ( ( ~ ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY50 ) @ SV5 ) )
= $false )
| ( ( in @ SV18 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(239,plain,
! [SV15: $i,SV5: $i] :
( ( ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 )
| ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(240,plain,
! [SV15: $i,SV5: $i] :
( ( ( ! [SY51: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY51 ) @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 )
| ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(241,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 ) ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(242,plain,
! [SV4: $i,SV17: $i,SV16: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(243,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( SV17 = empty_set ) )
| ~ ( ( SV17 != empty_set )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(244,plain,
! [SV15: $i,SV5: $i,SV18: $i] :
( ( ( ! [SY49: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY49 ) @ SV5 ) )
= $false )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(245,plain,
! [SV15: $i,SV5: $i,SV18: $i] :
( ( ( ! [SY50: $i] :
~ ( in @ ( ordered_pair @ SV18 @ SY50 ) @ SV5 ) )
= $true )
| ( ( in @ SV18 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[238]) ).
thf(246,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 )
| ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(247,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV19 ) @ SV5 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 )
| ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(248,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 ) )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(249,plain,
! [SV4: $i,SV17: $i,SV16: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(250,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( ~ ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( SV17 = empty_set ) ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(251,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( ~ ( ( SV17 != empty_set )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) ) )
= $false )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(252,plain,
! [SV5: $i,SV15: $i,SV18: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV18 @ ( sK9_SY49 @ SV15 @ SV5 @ SV18 ) ) @ SV5 ) )
= $false )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[244]) ).
thf(253,plain,
! [SV15: $i,SV5: $i,SV20: $i,SV18: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV18 @ SV20 ) @ SV5 ) )
= $true )
| ( ( in @ SV18 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(254,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(255,plain,
! [SV15: $i,SV5: $i] :
( ( ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(256,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV19 ) @ SV5 )
= $false )
| ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 )
| ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) ) )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(257,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(258,plain,
! [SV4: $i,SV17: $i,SV16: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 ) )
= $true )
| ( ( SV17
= ( apply @ SV4 @ SV16 ) )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(259,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
| ( SV17 = empty_set ) )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(260,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( ( SV17 != empty_set )
| ( SV17
= ( apply @ SV4 @ SV16 ) ) )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(261,plain,
! [SV5: $i,SV15: $i,SV18: $i] :
( ( ( in @ ( ordered_pair @ SV18 @ ( sK9_SY49 @ SV15 @ SV5 @ SV18 ) ) @ SV5 )
= $true )
| ( ( in @ SV18 @ SV15 )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(262,plain,
! [SV15: $i,SV5: $i,SV20: $i,SV18: $i] :
( ( ( in @ ( ordered_pair @ SV18 @ SV20 ) @ SV5 )
= $false )
| ( ( in @ SV18 @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $false )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(263,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 ) )
= $true )
| ( ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(264,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 )
| ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV19 ) @ SV5 )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(265,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( SV17
= ( apply @ SV4 @ SV16 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(266,plain,
! [SV4: $i,SV17: $i,SV16: $i] :
( ( ( in @ ( ordered_pair @ SV16 @ SV17 ) @ SV4 )
= $false )
| ( ( SV17
= ( apply @ SV4 @ SV16 ) )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(267,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( SV17
!= ( apply @ SV4 @ SV16 ) )
= $true )
| ( ( SV17 = empty_set )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(268,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( SV17 != empty_set )
= $true )
| ( ( SV17
= ( apply @ SV4 @ SV16 ) )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(269,plain,
! [SV15: $i,SV5: $i] :
( ( ( ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(270,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( ~ ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV19 ) @ SV5 )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(271,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV19 ) @ SV5 )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(272,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( SV17
= ( apply @ SV4 @ SV16 ) )
= $false )
| ( ( SV17 = empty_set )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(273,plain,
! [SV16: $i,SV4: $i,SV17: $i] :
( ( ( SV17 = empty_set )
= $false )
| ( ( SV17
= ( apply @ SV4 @ SV16 ) )
= $true )
| ( ( in @ SV16 @ ( relation_dom @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(274,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ ( sK10_SY52 @ SV15 @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[269]) ).
thf(275,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( ~ ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV19 ) @ SV5 )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(276,plain,
! [SV15: $i,SV5: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ ( sK10_SY52 @ SV15 @ SV5 ) ) @ SV5 )
= $true )
| ( ( in @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV15 )
= $true )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(277,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( ! [SY52: $i] :
~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SY52 ) @ SV5 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV19 ) @ SV5 )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(278,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ ( sK11_SY52 @ SV19 @ SV15 @ SV5 ) ) @ SV5 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV19 ) @ SV5 )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[277]) ).
thf(279,plain,
! [SV19: $i,SV15: $i,SV5: $i] :
( ( ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ ( sK11_SY52 @ SV19 @ SV15 @ SV5 ) ) @ SV5 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK8_SY45 @ SV5 @ SV15 ) @ SV19 ) @ SV5 )
= $false )
| ( ( SV15
= ( relation_dom @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(280,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[74,279,276,273,272,271,266,265,262,261,255,211,202,198,195,194,193,192,191,190,186,185,184,183,179,155,150,146,142,138,91,90,80,79,78,77,76,75]) ).
thf(281,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(282,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(283,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(284,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(285,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(286,plain,
$true = $true,
inference(copy,[status(thm)],[53]) ).
thf(287,plain,
$true = $true,
inference(copy,[status(thm)],[52]) ).
thf(288,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(289,plain,
$true = $true,
inference(copy,[status(thm)],[50]) ).
thf(290,plain,
$true = $true,
inference(copy,[status(thm)],[49]) ).
thf(291,plain,
$true = $true,
inference(copy,[status(thm)],[48]) ).
thf(292,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(293,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(294,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(295,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(296,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(297,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(298,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(299,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(301,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(302,plain,
( ( function @ sK3_SY28 )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(303,plain,
( ( relation @ sK3_SY28 )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(304,plain,
( ( ~ ( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
& ( sK2_SY26
= ( apply @ sK3_SY28 @ sK1_A ) ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(305,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(306,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(307,plain,
( ( ~ ( ~ ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
| ( sK2_SY26
!= ( apply @ sK3_SY28 @ sK1_A ) ) )
| ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(308,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(309,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ! [SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( ~ ( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) )
| ~ ( ~ ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ~ ( ~ ( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( SX2 = empty_set ) )
| ~ ( ( SX2 != empty_set )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(310,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(311,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(312,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(313,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(314,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(315,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
~ ( ~ ( ( SX1
!= ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(316,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(317,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(318,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(319,plain,
! [SV21: $i] :
( ( ! [SY53: $i] :
~ ( empty @ ( ordered_pair @ SV21 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(320,plain,
! [SV22: $i] :
( ( ~ ( empty @ SV22 )
| ( function @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(321,plain,
! [SV23: $i] :
( ( ! [SY54: $i] :
( ~ ( in @ SV23 @ SY54 )
| ( element @ SV23 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(322,plain,
( ( ~ ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
| ( sK2_SY26
!= ( apply @ sK3_SY28 @ sK1_A ) ) )
| ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(323,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(324,plain,
! [SV24: $i] :
( ( ~ ~ ( ~ ( relation @ SV24 )
| ~ ( function @ SV24 ) )
| ! [SY55: $i,SY56: $i] :
~ ( ~ ( ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( SY56 = empty_set ) )
| ~ ( ( SY56 != empty_set )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(325,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(326,plain,
! [SV25: $i] :
( ( ! [SY57: $i] :
( ~ ( in @ SV25 @ SY57 )
| ~ ( in @ SY57 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(327,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(328,plain,
! [SV26: $i] :
( ( ! [SY58: $i] :
~ ~ ( ~ ( in @ SV26 @ SY58 )
| ~ ( empty @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(329,plain,
! [SV27: $i] :
( ( ~ ( empty @ SV27 )
| ( relation @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(330,plain,
! [SV28: $i] :
( ( ~ ( relation @ SV28 )
| ! [SY59: $i] :
~ ( ~ ( ( SY59
!= ( relation_dom @ SV28 ) )
| ! [SY60: $i] :
~ ( ~ ( ~ ( in @ SY60 @ SY59 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY60 @ SY62 ) @ SV28 )
| ( in @ SY60 @ SY59 ) ) ) )
| ~ ( ~ ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SY59 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY63 @ SY64 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY63 @ SY65 ) @ SV28 )
| ( in @ SY63 @ SY59 ) ) )
| ( SY59
= ( relation_dom @ SV28 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(331,plain,
! [SV29: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV29 )
| ~ ( relation @ SV29 ) )
| ~ ( empty @ ( relation_dom @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(332,plain,
! [SV30: $i] :
( ( ~ ( empty @ SV30 )
| ~ ( ~ ( empty @ ( relation_dom @ SV30 ) )
| ~ ( relation @ ( relation_dom @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(333,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(334,plain,
! [SV31: $i,SV21: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV21 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(335,plain,
! [SV22: $i] :
( ( ( ~ ( empty @ SV22 ) )
= $true )
| ( ( function @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(336,plain,
! [SV32: $i,SV23: $i] :
( ( ~ ( in @ SV23 @ SV32 )
| ( element @ SV23 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(337,plain,
( ( ~ ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
| ( sK2_SY26
!= ( apply @ sK3_SY28 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(338,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY26 ) @ sK3_SY28 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(339,plain,
( ( ~ ~ ( ~ ( relation @ sK12_SX0 )
| ~ ( relation_empty_yielding @ sK12_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[323]) ).
thf(340,plain,
! [SV24: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV24 )
| ~ ( function @ SV24 ) ) )
= $true )
| ( ( ! [SY55: $i,SY56: $i] :
~ ( ~ ( ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( SY56 = empty_set ) )
| ~ ( ( SY56 != empty_set )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(341,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK13_SX0 )
| ~ ( relation @ sK13_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[325]) ).
thf(342,plain,
! [SV33: $i,SV25: $i] :
( ( ~ ( in @ SV25 @ SV33 )
| ~ ( in @ SV33 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(343,plain,
( ( ~ ~ ( ~ ( relation @ sK14_SX0 )
| ~ ( function @ sK14_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[327]) ).
thf(344,plain,
! [SV34: $i,SV26: $i] :
( ( ~ ~ ( ~ ( in @ SV26 @ SV34 )
| ~ ( empty @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(345,plain,
! [SV27: $i] :
( ( ( ~ ( empty @ SV27 ) )
= $true )
| ( ( relation @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(346,plain,
! [SV28: $i] :
( ( ( ~ ( relation @ SV28 ) )
= $true )
| ( ( ! [SY59: $i] :
~ ( ~ ( ( SY59
!= ( relation_dom @ SV28 ) )
| ! [SY60: $i] :
~ ( ~ ( ~ ( in @ SY60 @ SY59 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY60 @ SY62 ) @ SV28 )
| ( in @ SY60 @ SY59 ) ) ) )
| ~ ( ~ ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SY59 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY63 @ SY64 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY63 @ SY65 ) @ SV28 )
| ( in @ SY63 @ SY59 ) ) )
| ( SY59
= ( relation_dom @ SV28 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(347,plain,
! [SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV29 )
| ~ ( relation @ SV29 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(348,plain,
! [SV30: $i] :
( ( ( ~ ( empty @ SV30 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV30 ) )
| ~ ( relation @ ( relation_dom @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(349,plain,
( ( ~ ~ ( ~ ( empty @ sK15_SX0 )
| ~ ( relation @ sK15_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[333]) ).
thf(350,plain,
! [SV31: $i,SV21: $i] :
( ( empty @ ( ordered_pair @ SV21 @ SV31 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(351,plain,
! [SV22: $i] :
( ( ( empty @ SV22 )
= $false )
| ( ( function @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(352,plain,
! [SV32: $i,SV23: $i] :
( ( ( ~ ( in @ SV23 @ SV32 ) )
= $true )
| ( ( element @ SV23 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(353,plain,
( ( ~ ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
| ( sK2_SY26
!= ( apply @ sK3_SY28 @ sK1_A ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(354,plain,
( ( ~ ( ~ ( relation @ sK12_SX0 )
| ~ ( relation_empty_yielding @ sK12_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(355,plain,
! [SV24: $i] :
( ( ( ~ ( ~ ( relation @ SV24 )
| ~ ( function @ SV24 ) ) )
= $false )
| ( ( ! [SY55: $i,SY56: $i] :
~ ( ~ ( ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( SY56 = empty_set ) )
| ~ ( ( SY56 != empty_set )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(356,plain,
( ( ~ ( ~ ~ ( empty @ sK13_SX0 )
| ~ ( relation @ sK13_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(357,plain,
! [SV33: $i,SV25: $i] :
( ( ( ~ ( in @ SV25 @ SV33 ) )
= $true )
| ( ( ~ ( in @ SV33 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(358,plain,
( ( ~ ( ~ ( relation @ sK14_SX0 )
| ~ ( function @ sK14_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[343]) ).
thf(359,plain,
! [SV34: $i,SV26: $i] :
( ( ~ ( ~ ( in @ SV26 @ SV34 )
| ~ ( empty @ SV34 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(360,plain,
! [SV27: $i] :
( ( ( empty @ SV27 )
= $false )
| ( ( relation @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(361,plain,
! [SV28: $i] :
( ( ( relation @ SV28 )
= $false )
| ( ( ! [SY59: $i] :
~ ( ~ ( ( SY59
!= ( relation_dom @ SV28 ) )
| ! [SY60: $i] :
~ ( ~ ( ~ ( in @ SY60 @ SY59 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY60 @ SY61 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY60 @ SY62 ) @ SV28 )
| ( in @ SY60 @ SY59 ) ) ) )
| ~ ( ~ ! [SY63: $i] :
~ ( ~ ( ~ ( in @ SY63 @ SY59 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY63 @ SY64 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY63 @ SY65 ) @ SV28 )
| ( in @ SY63 @ SY59 ) ) )
| ( SY59
= ( relation_dom @ SV28 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(362,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV29 )
| ~ ( relation @ SV29 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(363,plain,
! [SV30: $i] :
( ( ( empty @ SV30 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV30 ) )
| ~ ( relation @ ( relation_dom @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(364,plain,
( ( ~ ( ~ ( empty @ sK15_SX0 )
| ~ ( relation @ sK15_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(365,plain,
! [SV32: $i,SV23: $i] :
( ( ( in @ SV23 @ SV32 )
= $false )
| ( ( element @ SV23 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(366,plain,
( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
| ( sK2_SY26
!= ( apply @ sK3_SY28 @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(367,plain,
( ( ~ ( relation @ sK12_SX0 )
| ~ ( relation_empty_yielding @ sK12_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(368,plain,
! [SV24: $i] :
( ( ( ~ ( relation @ SV24 )
| ~ ( function @ SV24 ) )
= $true )
| ( ( ! [SY55: $i,SY56: $i] :
~ ( ~ ( ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( SY56 = empty_set ) )
| ~ ( ( SY56 != empty_set )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(369,plain,
( ( ~ ~ ( empty @ sK13_SX0 )
| ~ ( relation @ sK13_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(370,plain,
! [SV33: $i,SV25: $i] :
( ( ( in @ SV25 @ SV33 )
= $false )
| ( ( ~ ( in @ SV33 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(371,plain,
( ( ~ ( relation @ sK14_SX0 )
| ~ ( function @ sK14_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(372,plain,
! [SV34: $i,SV26: $i] :
( ( ~ ( in @ SV26 @ SV34 )
| ~ ( empty @ SV34 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(373,plain,
! [SV28: $i,SV35: $i] :
( ( ( ~ ( ~ ( ( SV35
!= ( relation_dom @ SV28 ) )
| ! [SY66: $i] :
~ ( ~ ( ~ ( in @ SY66 @ SV35 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY66 @ SY61 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY66 @ SY62 ) @ SV28 )
| ( in @ SY66 @ SV35 ) ) ) )
| ~ ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ SV35 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY69 @ SY64 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY69 @ SY65 ) @ SV28 )
| ( in @ SY69 @ SV35 ) ) )
| ( SV35
= ( relation_dom @ SV28 ) ) ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(374,plain,
! [SV29: $i] :
( ( ( ~ ~ ( empty @ SV29 )
| ~ ( relation @ SV29 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(375,plain,
! [SV30: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV30 ) )
| ~ ( relation @ ( relation_dom @ SV30 ) ) )
= $false )
| ( ( empty @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(376,plain,
( ( ~ ( empty @ sK15_SX0 )
| ~ ( relation @ sK15_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(377,plain,
( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(378,plain,
( ( sK2_SY26
!= ( apply @ sK3_SY28 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(379,plain,
( ( ~ ( relation @ sK12_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[367]) ).
thf(380,plain,
( ( ~ ( relation_empty_yielding @ sK12_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[367]) ).
thf(381,plain,
! [SV24: $i] :
( ( ( ~ ( relation @ SV24 ) )
= $true )
| ( ( ~ ( function @ SV24 ) )
= $true )
| ( ( ! [SY55: $i,SY56: $i] :
~ ( ~ ( ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( SY56 = empty_set ) )
| ~ ( ( SY56 != empty_set )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(382,plain,
( ( ~ ~ ( empty @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(383,plain,
( ( ~ ( relation @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[369]) ).
thf(384,plain,
! [SV25: $i,SV33: $i] :
( ( ( in @ SV33 @ SV25 )
= $false )
| ( ( in @ SV25 @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(385,plain,
( ( ~ ( relation @ sK14_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(386,plain,
( ( ~ ( function @ sK14_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[371]) ).
thf(387,plain,
! [SV34: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV34 ) )
= $true )
| ( ( ~ ( empty @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(388,plain,
! [SV28: $i,SV35: $i] :
( ( ( ~ ( ( SV35
!= ( relation_dom @ SV28 ) )
| ! [SY66: $i] :
~ ( ~ ( ~ ( in @ SY66 @ SV35 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY66 @ SY61 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY66 @ SY62 ) @ SV28 )
| ( in @ SY66 @ SV35 ) ) ) )
| ~ ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ SV35 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY69 @ SY64 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY69 @ SY65 ) @ SV28 )
| ( in @ SY69 @ SV35 ) ) )
| ( SV35
= ( relation_dom @ SV28 ) ) ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(389,plain,
! [SV29: $i] :
( ( ( ~ ~ ( empty @ SV29 ) )
= $true )
| ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(390,plain,
! [SV30: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV30 ) ) )
= $false )
| ( ( empty @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(391,plain,
! [SV30: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV30 ) ) )
= $false )
| ( ( empty @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(392,plain,
( ( ~ ( empty @ sK15_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(393,plain,
( ( ~ ( relation @ sK15_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(394,plain,
( ( in @ sK1_A @ ( relation_dom @ sK3_SY28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(395,plain,
( ( sK2_SY26
= ( apply @ sK3_SY28 @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[378]) ).
thf(396,plain,
( ( relation @ sK12_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(397,plain,
( ( relation_empty_yielding @ sK12_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(398,plain,
! [SV24: $i] :
( ( ( relation @ SV24 )
= $false )
| ( ( ~ ( function @ SV24 ) )
= $true )
| ( ( ! [SY55: $i,SY56: $i] :
~ ( ~ ( ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( SY56 = empty_set ) )
| ~ ( ( SY56 != empty_set )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(399,plain,
( ( ~ ( empty @ sK13_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[382]) ).
thf(400,plain,
( ( relation @ sK13_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(401,plain,
( ( relation @ sK14_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(402,plain,
( ( function @ sK14_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(403,plain,
! [SV34: $i,SV26: $i] :
( ( ( in @ SV26 @ SV34 )
= $false )
| ( ( ~ ( empty @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(404,plain,
! [SV28: $i,SV35: $i] :
( ( ( ~ ( ( SV35
!= ( relation_dom @ SV28 ) )
| ! [SY66: $i] :
~ ( ~ ( ~ ( in @ SY66 @ SV35 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY66 @ SY61 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY66 @ SY62 ) @ SV28 )
| ( in @ SY66 @ SV35 ) ) ) ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(405,plain,
! [SV28: $i,SV35: $i] :
( ( ( ~ ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ SV35 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY69 @ SY64 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY69 @ SY65 ) @ SV28 )
| ( in @ SY69 @ SV35 ) ) )
| ( SV35
= ( relation_dom @ SV28 ) ) ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(406,plain,
! [SV29: $i] :
( ( ( ~ ( empty @ SV29 ) )
= $false )
| ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(407,plain,
! [SV30: $i] :
( ( ( empty @ ( relation_dom @ SV30 ) )
= $true )
| ( ( empty @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(408,plain,
! [SV30: $i] :
( ( ( relation @ ( relation_dom @ SV30 ) )
= $true )
| ( ( empty @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(409,plain,
( ( empty @ sK15_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(410,plain,
( ( relation @ sK15_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(411,plain,
! [SV24: $i] :
( ( ( function @ SV24 )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( ! [SY55: $i,SY56: $i] :
~ ( ~ ( ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SY55 @ SY56 ) @ SV24 )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) )
| ~ ( ~ ~ ( in @ SY55 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY56
!= ( apply @ SV24 @ SY55 ) )
| ( SY56 = empty_set ) )
| ~ ( ( SY56 != empty_set )
| ( SY56
= ( apply @ SV24 @ SY55 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(412,plain,
( ( empty @ sK13_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(413,plain,
! [SV26: $i,SV34: $i] :
( ( ( empty @ SV34 )
= $false )
| ( ( in @ SV26 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(414,plain,
! [SV28: $i,SV35: $i] :
( ( ( ( SV35
!= ( relation_dom @ SV28 ) )
| ! [SY66: $i] :
~ ( ~ ( ~ ( in @ SY66 @ SV35 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY66 @ SY61 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY66 @ SY62 ) @ SV28 )
| ( in @ SY66 @ SV35 ) ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(415,plain,
! [SV28: $i,SV35: $i] :
( ( ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ SV35 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY69 @ SY64 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY69 @ SY65 ) @ SV28 )
| ( in @ SY69 @ SV35 ) ) )
| ( SV35
= ( relation_dom @ SV28 ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(416,plain,
! [SV29: $i] :
( ( ( empty @ SV29 )
= $true )
| ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(417,plain,
! [SV24: $i,SV36: $i] :
( ( ( ! [SY72: $i] :
~ ( ~ ( ~ ( in @ SV36 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY72
!= ( apply @ SV24 @ SV36 ) )
| ( in @ ( ordered_pair @ SV36 @ SY72 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV36 @ SY72 ) @ SV24 )
| ( SY72
= ( apply @ SV24 @ SV36 ) ) ) ) )
| ~ ( ~ ~ ( in @ SV36 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SY72
!= ( apply @ SV24 @ SV36 ) )
| ( SY72 = empty_set ) )
| ~ ( ( SY72 != empty_set )
| ( SY72
= ( apply @ SV24 @ SV36 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(418,plain,
! [SV28: $i,SV35: $i] :
( ( ( SV35
!= ( relation_dom @ SV28 ) )
= $true )
| ( ( ! [SY66: $i] :
~ ( ~ ( ~ ( in @ SY66 @ SV35 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY66 @ SY61 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY66 @ SY62 ) @ SV28 )
| ( in @ SY66 @ SV35 ) ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(419,plain,
! [SV28: $i,SV35: $i] :
( ( ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ SV35 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY69 @ SY64 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY69 @ SY65 ) @ SV28 )
| ( in @ SY69 @ SV35 ) ) ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(420,plain,
! [SV29: $i] :
( ( ( relation @ SV29 )
= $false )
| ( ( empty @ SV29 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(421,plain,
! [SV37: $i,SV24: $i,SV36: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV36 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) )
| ~ ( ~ ~ ( in @ SV36 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( SV37 = empty_set ) )
| ~ ( ( SV37 != empty_set )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(422,plain,
! [SV28: $i,SV35: $i] :
( ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( ! [SY66: $i] :
~ ( ~ ( ~ ( in @ SY66 @ SV35 )
| ~ ! [SY61: $i] :
~ ( in @ ( ordered_pair @ SY66 @ SY61 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY62: $i] :
~ ( in @ ( ordered_pair @ SY66 @ SY62 ) @ SV28 )
| ( in @ SY66 @ SV35 ) ) ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(423,plain,
! [SV28: $i,SV35: $i] :
( ( ( ! [SY69: $i] :
~ ( ~ ( ~ ( in @ SY69 @ SV35 )
| ~ ! [SY64: $i] :
~ ( in @ ( ordered_pair @ SY69 @ SY64 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY65: $i] :
~ ( in @ ( ordered_pair @ SY69 @ SY65 ) @ SV28 )
| ( in @ SY69 @ SV35 ) ) ) )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(424,plain,
! [SV29: $i] :
( ( ( empty @ ( relation_dom @ SV29 ) )
= $false )
| ( ( empty @ SV29 )
= $true )
| ( ( relation @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(425,plain,
! [SV37: $i,SV24: $i,SV36: $i] :
( ( ( ~ ( ~ ( in @ SV36 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) )
| ~ ( ~ ~ ( in @ SV36 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( SV37 = empty_set ) )
| ~ ( ( SV37 != empty_set )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(426,plain,
! [SV28: $i,SV35: $i,SV38: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV38 @ SV35 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY73 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY74 ) @ SV28 )
| ( in @ SV38 @ SV35 ) ) ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(427,plain,
! [SV35: $i,SV28: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
| ~ ! [SY75: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY75 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 )
| ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) ) ) )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[423]) ).
thf(428,plain,
! [SV37: $i,SV24: $i,SV36: $i] :
( ( ( ~ ( ~ ( in @ SV36 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(429,plain,
! [SV37: $i,SV24: $i,SV36: $i] :
( ( ( ~ ( ~ ~ ( in @ SV36 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( SV37 = empty_set ) )
| ~ ( ( SV37 != empty_set )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(430,plain,
! [SV28: $i,SV35: $i,SV38: $i] :
( ( ( ~ ( ~ ( in @ SV38 @ SV35 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY73 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY74 ) @ SV28 )
| ( in @ SV38 @ SV35 ) ) )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(431,plain,
! [SV35: $i,SV28: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
| ~ ! [SY75: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY75 ) @ SV28 ) )
| ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 )
| ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(432,plain,
! [SV37: $i,SV24: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(433,plain,
! [SV37: $i,SV24: $i,SV36: $i] :
( ( ( ~ ~ ( in @ SV36 @ ( relation_dom @ SV24 ) )
| ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( SV37 = empty_set ) )
| ~ ( ( SV37 != empty_set )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(434,plain,
! [SV28: $i,SV35: $i,SV38: $i] :
( ( ( ~ ( ~ ( in @ SV38 @ SV35 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY73 ) @ SV28 ) ) )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(435,plain,
! [SV35: $i,SV28: $i,SV38: $i] :
( ( ( ~ ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY74 ) @ SV28 )
| ( in @ SV38 @ SV35 ) ) )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(436,plain,
! [SV35: $i,SV28: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
| ~ ! [SY75: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY75 ) @ SV28 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 )
| ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(437,plain,
! [SV37: $i,SV24: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ ( relation_dom @ SV24 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(438,plain,
! [SV37: $i,SV24: $i,SV36: $i] :
( ( ( ~ ~ ( in @ SV36 @ ( relation_dom @ SV24 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( SV37 = empty_set ) )
| ~ ( ( SV37 != empty_set )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(439,plain,
! [SV28: $i,SV35: $i,SV38: $i] :
( ( ( ~ ( in @ SV38 @ SV35 )
| ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY73 ) @ SV28 ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(440,plain,
! [SV35: $i,SV28: $i,SV38: $i] :
( ( ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY74 ) @ SV28 )
| ( in @ SV38 @ SV35 ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(441,plain,
! [SV35: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
| ~ ! [SY75: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY75 ) @ SV28 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 )
| ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(442,plain,
! [SV37: $i,SV24: $i,SV36: $i] :
( ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $false )
| ( ( ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(443,plain,
! [SV37: $i,SV24: $i,SV36: $i] :
( ( ( ~ ( in @ SV36 @ ( relation_dom @ SV24 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( SV37 = empty_set ) )
| ~ ( ( SV37 != empty_set )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(444,plain,
! [SV28: $i,SV35: $i,SV38: $i] :
( ( ( ~ ( in @ SV38 @ SV35 ) )
= $true )
| ( ( ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY73 ) @ SV28 ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(445,plain,
! [SV35: $i,SV28: $i,SV38: $i] :
( ( ( ~ ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY74 ) @ SV28 ) )
= $true )
| ( ( in @ SV38 @ SV35 )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(446,plain,
! [SV35: $i,SV28: $i] :
( ( ( ~ ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 )
| ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(447,plain,
! [SV35: $i,SV28: $i] :
( ( ( ~ ! [SY75: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY75 ) @ SV28 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 )
| ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(448,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) )
= $false )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(449,plain,
! [SV37: $i,SV24: $i,SV36: $i] :
( ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $true )
| ( ( ~ ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( SV37 = empty_set ) )
| ~ ( ( SV37 != empty_set )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(450,plain,
! [SV28: $i,SV35: $i,SV38: $i] :
( ( ( in @ SV38 @ SV35 )
= $false )
| ( ( ~ ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY73 ) @ SV28 ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(451,plain,
! [SV35: $i,SV28: $i,SV38: $i] :
( ( ( ~ ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY74 ) @ SV28 ) )
= $false )
| ( ( in @ SV38 @ SV35 )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(452,plain,
! [SV35: $i,SV28: $i] :
( ( ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
= $true )
| ( ( ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 )
| ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(453,plain,
! [SV35: $i,SV28: $i] :
( ( ( ! [SY75: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY75 ) @ SV28 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 )
| ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(454,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 ) ) )
= $false )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(455,plain,
! [SV24: $i,SV37: $i,SV36: $i] :
( ( ( ~ ( ~ ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) )
= $false )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[448]) ).
thf(456,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( SV37 = empty_set ) )
| ~ ( ( SV37 != empty_set )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) )
= $false )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(457,plain,
! [SV35: $i,SV28: $i,SV38: $i] :
( ( ( ! [SY73: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY73 ) @ SV28 ) )
= $false )
| ( ( in @ SV38 @ SV35 )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(458,plain,
! [SV35: $i,SV28: $i,SV38: $i] :
( ( ( ! [SY74: $i] :
~ ( in @ ( ordered_pair @ SV38 @ SY74 ) @ SV28 ) )
= $true )
| ( ( in @ SV38 @ SV35 )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(459,plain,
! [SV35: $i,SV28: $i] :
( ( ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 )
| ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) )
= $false )
| ( ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(460,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV39 ) @ SV28 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 )
| ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(461,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 ) )
= $true )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(462,plain,
! [SV24: $i,SV37: $i,SV36: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) )
= $true )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[455]) ).
thf(463,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( SV37 = empty_set ) ) )
= $false )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(464,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( ~ ( ( SV37 != empty_set )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) ) )
= $false )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[456]) ).
thf(465,plain,
! [SV28: $i,SV35: $i,SV38: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV38 @ ( sK17_SY73 @ SV35 @ SV28 @ SV38 ) ) @ SV28 ) )
= $false )
| ( ( in @ SV38 @ SV35 )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[457]) ).
thf(466,plain,
! [SV35: $i,SV28: $i,SV40: $i,SV38: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV38 @ SV40 ) @ SV28 ) )
= $true )
| ( ( in @ SV38 @ SV35 )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(467,plain,
! [SV35: $i,SV28: $i] :
( ( ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 ) )
= $false )
| ( ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(468,plain,
! [SV35: $i,SV28: $i] :
( ( ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
= $false )
| ( ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(469,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV39 ) @ SV28 )
= $false )
| ( ( ~ ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 )
| ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) ) )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(470,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 )
= $true )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(471,plain,
! [SV24: $i,SV37: $i,SV36: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 ) )
= $true )
| ( ( SV37
= ( apply @ SV24 @ SV36 ) )
= $true )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(472,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
| ( SV37 = empty_set ) )
= $true )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(473,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( ( SV37 != empty_set )
| ( SV37
= ( apply @ SV24 @ SV36 ) ) )
= $true )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(474,plain,
! [SV28: $i,SV35: $i,SV38: $i] :
( ( ( in @ ( ordered_pair @ SV38 @ ( sK17_SY73 @ SV35 @ SV28 @ SV38 ) ) @ SV28 )
= $true )
| ( ( in @ SV38 @ SV35 )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(475,plain,
! [SV35: $i,SV28: $i,SV40: $i,SV38: $i] :
( ( ( in @ ( ordered_pair @ SV38 @ SV40 ) @ SV28 )
= $false )
| ( ( in @ SV38 @ SV35 )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $false )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(476,plain,
! [SV35: $i,SV28: $i] :
( ( ( ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 ) )
= $true )
| ( ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(477,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 )
| ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV39 ) @ SV28 )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(478,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( SV37
= ( apply @ SV24 @ SV36 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 )
= $true )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(479,plain,
! [SV24: $i,SV37: $i,SV36: $i] :
( ( ( in @ ( ordered_pair @ SV36 @ SV37 ) @ SV24 )
= $false )
| ( ( SV37
= ( apply @ SV24 @ SV36 ) )
= $true )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $false )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(480,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( SV37
!= ( apply @ SV24 @ SV36 ) )
= $true )
| ( ( SV37 = empty_set )
= $true )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(481,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( SV37 != empty_set )
= $true )
| ( ( SV37
= ( apply @ SV24 @ SV36 ) )
= $true )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(482,plain,
! [SV35: $i,SV28: $i] :
( ( ( ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 ) )
= $false )
| ( ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(483,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( ~ ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV39 ) @ SV28 )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(484,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV39 ) @ SV28 )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(485,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( SV37
= ( apply @ SV24 @ SV36 ) )
= $false )
| ( ( SV37 = empty_set )
= $true )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(486,plain,
! [SV36: $i,SV24: $i,SV37: $i] :
( ( ( SV37 = empty_set )
= $false )
| ( ( SV37
= ( apply @ SV24 @ SV36 ) )
= $true )
| ( ( in @ SV36 @ ( relation_dom @ SV24 ) )
= $true )
| ( ( relation @ SV24 )
= $false )
| ( ( function @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(487,plain,
! [SV35: $i,SV28: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ ( sK18_SY76 @ SV35 @ SV28 ) ) @ SV28 ) )
= $false )
| ( ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[482]) ).
thf(488,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( ~ ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 ) )
= $true )
| ( ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV39 ) @ SV28 )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(489,plain,
! [SV35: $i,SV28: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ ( sK18_SY76 @ SV35 @ SV28 ) ) @ SV28 )
= $true )
| ( ( in @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV35 )
= $true )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(490,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( ! [SY76: $i] :
~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SY76 ) @ SV28 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV39 ) @ SV28 )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(491,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ ( sK19_SY76 @ SV39 @ SV35 @ SV28 ) ) @ SV28 ) )
= $false )
| ( ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV39 ) @ SV28 )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[490]) ).
thf(492,plain,
! [SV39: $i,SV35: $i,SV28: $i] :
( ( ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ ( sK19_SY76 @ SV39 @ SV35 @ SV28 ) ) @ SV28 )
= $true )
| ( ( in @ ( ordered_pair @ ( sK16_SY69 @ SV28 @ SV35 ) @ SV39 ) @ SV28 )
= $false )
| ( ( SV35
= ( relation_dom @ SV28 ) )
= $true )
| ( ( relation @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(493,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[286,492,489,486,485,484,479,478,475,474,468,424,413,412,410,409,408,407,402,401,400,397,396,395,394,384,365,360,351,350,338,303,302,292,291,290,289,288,287]) ).
thf(494,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[493,280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU212+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 15:04:46 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.30
% 0.48/0.30 No.of.Axioms: 21
% 0.48/0.30
% 0.48/0.30 Length.of.Defs: 0
% 0.48/0.30
% 0.48/0.30 Contains.Choice.Funs: false
% 0.48/0.30 .............
% 0.48/0.30
% 0.48/0.30 ********************************
% 0.48/0.30 * All subproblems solved! *
% 0.48/0.30 ********************************
% 0.48/0.30 % SZS status Theorem for /export/starexec/sandbox/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:493,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.48/0.30
% 0.48/0.30 %**** Beginning of derivation protocol ****
% 0.48/0.30 % SZS output start CNFRefutation
% See solution above
% 0.48/0.30
% 0.48/0.30 %**** End of derivation protocol ****
% 0.48/0.30 %**** no. of clauses in derivation: 481 ****
% 0.48/0.30 %**** clause counter: 493 ****
% 0.48/0.30
% 0.48/0.30 % SZS status Theorem for /export/starexec/sandbox/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:493,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------