TSTP Solution File: SEU212+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU212+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:08:11 EDT 2022
% Result : Theorem 0.61s 0.85s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 60
% Syntax : Number of formulae : 597 ( 342 unt; 25 typ; 0 def)
% Number of atoms : 3762 (1358 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 6201 (1112 ~;1125 |; 90 &;3825 @)
% ( 15 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 12 con; 0-3 aty)
% Number of variables : 1061 ( 0 ^1045 !; 16 ?;1061 :)
% 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_B,type,
sK10_B: $i > $i ).
thf(tp_sK11_D,type,
sK11_D: $i > $i > $i > $i ).
thf(tp_sK12_C,type,
sK12_C: $i > $i > $i ).
thf(tp_sK13_SY46,type,
sK13_SY46: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY42,type,
sK2_SY42: $i ).
thf(tp_sK3_SY44,type,
sK3_SY44: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_A,type,
sK9_A: $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(6,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(7,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(8,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(9,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(10,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(11,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(12,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(13,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(14,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(15,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(16,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(17,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(18,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(19,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(20,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(32,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(33,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/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/sandbox2/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] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(43,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(44,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(45,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(46,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(47,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(48,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(49,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(51,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(53,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(55,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(56,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(57,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(58,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(59,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(60,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(61,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(62,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(63,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(64,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(66,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(67,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(68,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(72,plain,
( ( ! [SY42: $i,SY43: $i] :
( ( ( relation @ SY43 )
& ( function @ SY43 ) )
=> ( ( in @ ( ordered_pair @ sK1_A @ SY42 ) @ SY43 )
<=> ( ( in @ sK1_A @ ( relation_dom @ SY43 ) )
& ( SY42
= ( apply @ SY43 @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[37]) ).
thf(73,plain,
( ( ! [SY44: $i] :
( ( ( relation @ SY44 )
& ( function @ SY44 ) )
=> ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ SY44 )
<=> ( ( in @ sK1_A @ ( relation_dom @ SY44 ) )
& ( sK2_SY42
= ( apply @ SY44 @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[72]) ).
thf(74,plain,
( ( ( ( relation @ sK3_SY44 )
& ( function @ sK3_SY44 ) )
=> ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 )
<=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) )
& ( sK2_SY42
= ( apply @ sK3_SY44 @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[73]) ).
thf(75,plain,
( ( relation @ sK3_SY44 )
= $true ),
inference(standard_cnf,[status(thm)],[74]) ).
thf(76,plain,
( ( function @ sK3_SY44 )
= $true ),
inference(standard_cnf,[status(thm)],[74]) ).
thf(77,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 )
<=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) )
& ( sK2_SY42
= ( apply @ sK3_SY44 @ sK1_A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[74]) ).
thf(78,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 )
=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) )
& ( sK2_SY42
= ( apply @ sK3_SY44 @ sK1_A ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[77]) ).
thf(79,plain,
( ( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) )
& ( sK2_SY42
= ( apply @ sK3_SY44 @ sK1_A ) ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[77]) ).
thf(80,plain,
( ( ~ ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 )
=> ( ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) )
& ( sK2_SY42
= ( apply @ sK3_SY44 @ sK1_A ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[78]) ).
thf(81,plain,
( ( ~ ( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) )
& ( sK2_SY42
= ( apply @ sK3_SY44 @ sK1_A ) ) )
=> ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[79]) ).
thf(82,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 )
& ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(83,plain,
( ( ( sK2_SY42
= ( apply @ sK3_SY44 @ sK1_A ) )
& ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) )
& ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(86,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(88,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(89,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(90,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(91,plain,
( ( ~ ( empty @ sK6_A )
& ( relation @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(92,plain,
( ( empty @ sK7_A )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(93,plain,
( ( ( empty @ sK8_A )
& ( relation @ sK8_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(94,plain,
( ( ( function @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(95,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(96,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(97,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(98,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY45: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ SY45 ) @ A )
| ~ ( in @ ( sK12_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK13_SY46 @ B @ A ) ) @ A )
| ( in @ ( sK12_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK11_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(99,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( C
= ( apply @ A @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( C = empty_set ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C != empty_set )
| ( C
= ( apply @ A @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(100,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(101,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(102,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(104,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(105,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(106,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(107,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( C
= ( apply @ A @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( C = empty_set ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C != empty_set )
| ( C
= ( apply @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(108,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY45: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ SY45 ) @ A )
| ~ ( in @ ( sK12_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK13_SY46 @ B @ A ) ) @ A )
| ( in @ ( sK12_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK11_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(110,plain,
$true = $true,
inference(copy,[status(thm)],[64]) ).
thf(111,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(112,plain,
$true = $true,
inference(copy,[status(thm)],[62]) ).
thf(113,plain,
$true = $true,
inference(copy,[status(thm)],[61]) ).
thf(114,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(115,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(116,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(117,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(118,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(119,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(120,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(121,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(122,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(123,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(124,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(125,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(126,plain,
( ( ( function @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(127,plain,
( ( ( empty @ sK8_A )
& ( relation @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(128,plain,
( ( empty @ sK7_A )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(129,plain,
( ( ~ ( empty @ sK6_A )
& ( relation @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(130,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(131,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(132,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(133,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(134,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(135,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(137,plain,
( ( function @ sK3_SY44 )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(138,plain,
( ( relation @ sK3_SY44 )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(139,plain,
( ( ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 )
& ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(140,plain,
( ( ~ ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 )
| ~ ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(141,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(142,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( SX2 = empty_set ) ) )
| ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2 != empty_set )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(143,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(144,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SX1 @ SX0 ) @ ( sK13_SY46 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_dom @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ ( sK11_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(145,plain,
( ( ~ ( ~ ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(146,plain,
( ( ~ ( ~ ( function @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(147,plain,
( ( ~ ( ~ ( empty @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(148,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(149,plain,
( ( ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(150,plain,
! [SV1: $i] :
( ( ! [SY47: $i] :
( ~ ( in @ SV1 @ SY47 )
| ~ ( in @ SY47 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(151,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( function @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(152,plain,
! [SV3: $i] :
( ( ~ ( empty @ SV3 )
| ( relation @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(153,plain,
! [SV4: $i] :
( ( ! [SY48: $i] :
( ( unordered_pair @ SV4 @ SY48 )
= ( unordered_pair @ SY48 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(154,plain,
! [SV5: $i] :
( ( ! [SY49: $i] :
( ( ordered_pair @ SV5 @ SY49 )
= ( unordered_pair @ ( unordered_pair @ SV5 @ SY49 ) @ ( singleton @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(155,plain,
! [SV6: $i] :
( ( element @ ( sK10_B @ SV6 ) @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(156,plain,
! [SV7: $i] :
( ( ! [SY50: $i] :
~ ( empty @ ( ordered_pair @ SV7 @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(157,plain,
! [SV8: $i] :
( ( ~ ( empty @ ( singleton @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(158,plain,
! [SV9: $i] :
( ( ! [SY51: $i] :
~ ( empty @ ( unordered_pair @ SV9 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(159,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
| ~ ( relation @ SV10 )
| ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(160,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(161,plain,
! [SV11: $i] :
( ( ! [SY52: $i] :
( ~ ( in @ SV11 @ SY52 )
| ( element @ SV11 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(162,plain,
! [SV12: $i] :
( ( ! [SY53: $i] :
( ~ ( element @ SV12 @ SY53 )
| ( empty @ SY53 )
| ( in @ SV12 @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(163,plain,
! [SV13: $i] :
( ( ~ ( empty @ SV13 )
| ( SV13 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(164,plain,
! [SV14: $i] :
( ( ! [SY54: $i] :
( ~ ( empty @ SY54 )
| ~ ( in @ SV14 @ SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(165,plain,
! [SV15: $i] :
( ( ! [SY55: $i] :
( ( SV15 = SY55 )
| ~ ( empty @ SV15 )
| ~ ( empty @ SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(166,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 )
| ~ ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(167,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(168,plain,
! [SV16: $i] :
( ( ~ ( function @ SV16 )
| ~ ( relation @ SV16 )
| ~ ( ~ ~ ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ ( relation_dom @ SV16 ) )
| ! [SY57: $i] :
( ( SY57
!= ( apply @ SV16 @ SY56 ) )
| ( in @ ( ordered_pair @ SY56 @ SY57 ) @ SV16 ) ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ ( relation_dom @ SV16 ) )
| ! [SY59: $i] :
( ~ ( in @ ( ordered_pair @ SY58 @ SY59 ) @ SV16 )
| ( SY59
= ( apply @ SV16 @ SY58 ) ) ) ) )
| ~ ~ ( ~ ! [SY60: $i] :
( ( in @ SY60 @ ( relation_dom @ SV16 ) )
| ! [SY61: $i] :
( ( SY61
!= ( apply @ SV16 @ SY60 ) )
| ( SY61 = empty_set ) ) )
| ~ ! [SY62: $i] :
( ( in @ SY62 @ ( relation_dom @ SV16 ) )
| ! [SY63: $i] :
( ( SY63 != empty_set )
| ( SY63
= ( apply @ SV16 @ SY62 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(169,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(170,plain,
! [SV17: $i] :
( ( ~ ( relation @ SV17 )
| ~ ( ~ ! [SY64: $i] :
( ~ ( ~ ( ! [SY65: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SY64 @ SV17 ) @ SY65 ) @ SV17 )
| ~ ( in @ ( sK12_C @ SY64 @ SV17 ) @ SY64 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY64 @ SV17 ) @ ( sK13_SY46 @ SY64 @ SV17 ) ) @ SV17 )
| ( in @ ( sK12_C @ SY64 @ SV17 ) @ SY64 ) ) )
| ( SY64
= ( relation_dom @ SV17 ) ) )
| ~ ! [SY66: $i] :
( ( SY66
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY67: $i] :
( ! [SY68: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY68 ) @ SV17 )
| ( in @ SY67 @ SY66 ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SY66 )
| ( in @ ( ordered_pair @ SY69 @ ( sK11_D @ SY69 @ SY66 @ SV17 ) ) @ SV17 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(171,plain,
( ( ~ ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(172,plain,
( ( ~ ( function @ sK9_A )
| ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(173,plain,
( ( ~ ( empty @ sK8_A )
| ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(174,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(175,plain,
( ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(176,plain,
! [SV18: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV18 )
| ~ ( in @ SV18 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(177,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(178,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ SV3 ) )
= $true )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(179,plain,
! [SV19: $i,SV4: $i] :
( ( ( unordered_pair @ SV4 @ SV19 )
= ( unordered_pair @ SV19 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(180,plain,
! [SV20: $i,SV5: $i] :
( ( ( ordered_pair @ SV5 @ SV20 )
= ( unordered_pair @ ( unordered_pair @ SV5 @ SV20 ) @ ( singleton @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(181,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV7 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(182,plain,
! [SV8: $i] :
( ( empty @ ( singleton @ SV8 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(183,plain,
! [SV22: $i,SV9: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV9 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(184,plain,
! [SV10: $i] :
( ( ( ( empty @ SV10 )
| ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(185,plain,
! [SV23: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ SV23 )
| ( element @ SV11 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(186,plain,
! [SV24: $i,SV12: $i] :
( ( ~ ( element @ SV12 @ SV24 )
| ( empty @ SV24 )
| ( in @ SV12 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(187,plain,
! [SV13: $i] :
( ( ( ~ ( empty @ SV13 ) )
= $true )
| ( ( SV13 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(188,plain,
! [SV14: $i,SV25: $i] :
( ( ~ ( empty @ SV25 )
| ~ ( in @ SV14 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(189,plain,
! [SV26: $i,SV15: $i] :
( ( ( SV15 = SV26 )
| ~ ( empty @ SV15 )
| ~ ( empty @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(190,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(191,plain,
( ( ~ ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(192,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(193,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(194,plain,
! [SV16: $i] :
( ( ( ~ ( function @ SV16 )
| ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ ( relation_dom @ SV16 ) )
| ! [SY57: $i] :
( ( SY57
!= ( apply @ SV16 @ SY56 ) )
| ( in @ ( ordered_pair @ SY56 @ SY57 ) @ SV16 ) ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ ( relation_dom @ SV16 ) )
| ! [SY59: $i] :
( ~ ( in @ ( ordered_pair @ SY58 @ SY59 ) @ SV16 )
| ( SY59
= ( apply @ SV16 @ SY58 ) ) ) ) )
| ~ ~ ( ~ ! [SY60: $i] :
( ( in @ SY60 @ ( relation_dom @ SV16 ) )
| ! [SY61: $i] :
( ( SY61
!= ( apply @ SV16 @ SY60 ) )
| ( SY61 = empty_set ) ) )
| ~ ! [SY62: $i] :
( ( in @ SY62 @ ( relation_dom @ SV16 ) )
| ! [SY63: $i] :
( ( SY63 != empty_set )
| ( SY63
= ( apply @ SV16 @ SY62 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(195,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(196,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[169]) ).
thf(197,plain,
! [SV17: $i] :
( ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ( ~ ! [SY64: $i] :
( ~ ( ~ ( ! [SY65: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SY64 @ SV17 ) @ SY65 ) @ SV17 )
| ~ ( in @ ( sK12_C @ SY64 @ SV17 ) @ SY64 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY64 @ SV17 ) @ ( sK13_SY46 @ SY64 @ SV17 ) ) @ SV17 )
| ( in @ ( sK12_C @ SY64 @ SV17 ) @ SY64 ) ) )
| ( SY64
= ( relation_dom @ SV17 ) ) )
| ~ ! [SY66: $i] :
( ( SY66
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY67: $i] :
( ! [SY68: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY68 ) @ SV17 )
| ( in @ SY67 @ SY66 ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SY66 )
| ( in @ ( ordered_pair @ SY69 @ ( sK11_D @ SY69 @ SY66 @ SV17 ) ) @ SV17 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(198,plain,
( ( ~ ~ ( empty @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(199,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[171]) ).
thf(200,plain,
( ( ~ ( function @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(201,plain,
( ( ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(202,plain,
( ( ~ ( empty @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(203,plain,
( ( ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(204,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(205,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(206,plain,
( ( ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(207,plain,
( ( ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(208,plain,
! [SV18: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV18 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(209,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( function @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(210,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $false )
| ( ( relation @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(211,plain,
! [SV21: $i,SV7: $i] :
( ( empty @ ( ordered_pair @ SV7 @ SV21 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(212,plain,
! [SV22: $i,SV9: $i] :
( ( empty @ ( unordered_pair @ SV9 @ SV22 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(213,plain,
! [SV10: $i] :
( ( ( empty @ SV10 )
= $true )
| ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(214,plain,
! [SV23: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV23 ) )
= $true )
| ( ( element @ SV11 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(215,plain,
! [SV24: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ SV24 ) )
= $true )
| ( ( ( empty @ SV24 )
| ( in @ SV12 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(216,plain,
! [SV13: $i] :
( ( ( empty @ SV13 )
= $false )
| ( ( SV13 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(217,plain,
! [SV14: $i,SV25: $i] :
( ( ( ~ ( empty @ SV25 ) )
= $true )
| ( ( ~ ( in @ SV14 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(218,plain,
! [SV26: $i,SV15: $i] :
( ( ( ( SV15 = SV26 )
| ~ ( empty @ SV15 ) )
= $true )
| ( ( ~ ( empty @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(219,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(220,plain,
( ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(221,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(222,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(223,plain,
! [SV16: $i] :
( ( ( ~ ( function @ SV16 ) )
= $true )
| ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ ( relation_dom @ SV16 ) )
| ! [SY57: $i] :
( ( SY57
!= ( apply @ SV16 @ SY56 ) )
| ( in @ ( ordered_pair @ SY56 @ SY57 ) @ SV16 ) ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ ( relation_dom @ SV16 ) )
| ! [SY59: $i] :
( ~ ( in @ ( ordered_pair @ SY58 @ SY59 ) @ SV16 )
| ( SY59
= ( apply @ SV16 @ SY58 ) ) ) ) )
| ~ ~ ( ~ ! [SY60: $i] :
( ( in @ SY60 @ ( relation_dom @ SV16 ) )
| ! [SY61: $i] :
( ( SY61
!= ( apply @ SV16 @ SY60 ) )
| ( SY61 = empty_set ) ) )
| ~ ! [SY62: $i] :
( ( in @ SY62 @ ( relation_dom @ SV16 ) )
| ! [SY63: $i] :
( ( SY63 != empty_set )
| ( SY63
= ( apply @ SV16 @ SY62 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(224,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(225,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(226,plain,
! [SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( ~ ( ~ ! [SY64: $i] :
( ~ ( ~ ( ! [SY65: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SY64 @ SV17 ) @ SY65 ) @ SV17 )
| ~ ( in @ ( sK12_C @ SY64 @ SV17 ) @ SY64 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY64 @ SV17 ) @ ( sK13_SY46 @ SY64 @ SV17 ) ) @ SV17 )
| ( in @ ( sK12_C @ SY64 @ SV17 ) @ SY64 ) ) )
| ( SY64
= ( relation_dom @ SV17 ) ) )
| ~ ! [SY66: $i] :
( ( SY66
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY67: $i] :
( ! [SY68: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY68 ) @ SV17 )
| ( in @ SY67 @ SY66 ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SY66 )
| ( in @ ( ordered_pair @ SY69 @ ( sK11_D @ SY69 @ SY66 @ SV17 ) ) @ SV17 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(227,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(228,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(229,plain,
( ( function @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(230,plain,
( ( relation @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(231,plain,
( ( empty @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(232,plain,
( ( relation @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(233,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(234,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(235,plain,
( ( relation @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(236,plain,
( ( relation_empty_yielding @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(237,plain,
! [SV18: $i,SV1: $i] :
( ( ( in @ SV1 @ SV18 )
= $false )
| ( ( ~ ( in @ SV18 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(238,plain,
! [SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( empty @ SV10 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(239,plain,
! [SV23: $i,SV11: $i] :
( ( ( in @ SV11 @ SV23 )
= $false )
| ( ( element @ SV11 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(240,plain,
! [SV24: $i,SV12: $i] :
( ( ( element @ SV12 @ SV24 )
= $false )
| ( ( ( empty @ SV24 )
| ( in @ SV12 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(241,plain,
! [SV14: $i,SV25: $i] :
( ( ( empty @ SV25 )
= $false )
| ( ( ~ ( in @ SV14 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(242,plain,
! [SV26: $i,SV15: $i] :
( ( ( SV15 = SV26 )
= $true )
| ( ( ~ ( empty @ SV15 ) )
= $true )
| ( ( ~ ( empty @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(243,plain,
( ( ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) ) )
= $true )
| ( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(244,plain,
! [SV16: $i] :
( ( ( function @ SV16 )
= $false )
| ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ ( relation_dom @ SV16 ) )
| ! [SY57: $i] :
( ( SY57
!= ( apply @ SV16 @ SY56 ) )
| ( in @ ( ordered_pair @ SY56 @ SY57 ) @ SV16 ) ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ ( relation_dom @ SV16 ) )
| ! [SY59: $i] :
( ~ ( in @ ( ordered_pair @ SY58 @ SY59 ) @ SV16 )
| ( SY59
= ( apply @ SV16 @ SY58 ) ) ) ) )
| ~ ~ ( ~ ! [SY60: $i] :
( ( in @ SY60 @ ( relation_dom @ SV16 ) )
| ! [SY61: $i] :
( ( SY61
!= ( apply @ SV16 @ SY60 ) )
| ( SY61 = empty_set ) ) )
| ~ ! [SY62: $i] :
( ( in @ SY62 @ ( relation_dom @ SV16 ) )
| ! [SY63: $i] :
( ( SY63 != empty_set )
| ( SY63
= ( apply @ SV16 @ SY62 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(245,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(246,plain,
! [SV17: $i] :
( ( ( ~ ! [SY64: $i] :
( ~ ( ~ ( ! [SY65: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SY64 @ SV17 ) @ SY65 ) @ SV17 )
| ~ ( in @ ( sK12_C @ SY64 @ SV17 ) @ SY64 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY64 @ SV17 ) @ ( sK13_SY46 @ SY64 @ SV17 ) ) @ SV17 )
| ( in @ ( sK12_C @ SY64 @ SV17 ) @ SY64 ) ) )
| ( SY64
= ( relation_dom @ SV17 ) ) )
| ~ ! [SY66: $i] :
( ( SY66
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY67: $i] :
( ! [SY68: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY68 ) @ SV17 )
| ( in @ SY67 @ SY66 ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SY66 )
| ( in @ ( ordered_pair @ SY69 @ ( sK11_D @ SY69 @ SY66 @ SV17 ) ) @ SV17 ) ) ) ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(247,plain,
( ( empty @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(248,plain,
! [SV27: $i] :
( ( ~ ( empty @ SV27 )
| ( empty @ ( relation_dom @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(249,plain,
! [SV28: $i] :
( ( ~ ( empty @ SV28 )
| ( relation @ ( relation_dom @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(250,plain,
! [SV1: $i,SV18: $i] :
( ( ( in @ SV18 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(251,plain,
! [SV10: $i] :
( ( ( empty @ ( relation_dom @ SV10 ) )
= $false )
| ( ( empty @ SV10 )
= $true )
| ( ( relation @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(252,plain,
! [SV12: $i,SV24: $i] :
( ( ( empty @ SV24 )
= $true )
| ( ( in @ SV12 @ SV24 )
= $true )
| ( ( element @ SV12 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(253,plain,
! [SV25: $i,SV14: $i] :
( ( ( in @ SV14 @ SV25 )
= $false )
| ( ( empty @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(254,plain,
! [SV26: $i,SV15: $i] :
( ( ( empty @ SV15 )
= $false )
| ( ( SV15 = SV26 )
= $true )
| ( ( ~ ( empty @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(255,plain,
( ( ( sK2_SY42
= ( apply @ sK3_SY44 @ sK1_A ) )
= $false )
| ( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(256,plain,
! [SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ ( relation_dom @ SV16 ) )
| ! [SY57: $i] :
( ( SY57
!= ( apply @ SV16 @ SY56 ) )
| ( in @ ( ordered_pair @ SY56 @ SY57 ) @ SV16 ) ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ ( relation_dom @ SV16 ) )
| ! [SY59: $i] :
( ~ ( in @ ( ordered_pair @ SY58 @ SY59 ) @ SV16 )
| ( SY59
= ( apply @ SV16 @ SY58 ) ) ) ) )
| ~ ~ ( ~ ! [SY60: $i] :
( ( in @ SY60 @ ( relation_dom @ SV16 ) )
| ! [SY61: $i] :
( ( SY61
!= ( apply @ SV16 @ SY60 ) )
| ( SY61 = empty_set ) ) )
| ~ ! [SY62: $i] :
( ( in @ SY62 @ ( relation_dom @ SV16 ) )
| ! [SY63: $i] :
( ( SY63 != empty_set )
| ( SY63
= ( apply @ SV16 @ SY62 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(257,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(258,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(259,plain,
! [SV17: $i] :
( ( ( ~ ! [SY64: $i] :
( ~ ( ~ ( ! [SY65: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SY64 @ SV17 ) @ SY65 ) @ SV17 )
| ~ ( in @ ( sK12_C @ SY64 @ SV17 ) @ SY64 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY64 @ SV17 ) @ ( sK13_SY46 @ SY64 @ SV17 ) ) @ SV17 )
| ( in @ ( sK12_C @ SY64 @ SV17 ) @ SY64 ) ) )
| ( SY64
= ( relation_dom @ SV17 ) ) ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(260,plain,
! [SV17: $i] :
( ( ( ~ ! [SY66: $i] :
( ( SY66
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY67: $i] :
( ! [SY68: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY68 ) @ SV17 )
| ( in @ SY67 @ SY66 ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SY66 )
| ( in @ ( ordered_pair @ SY69 @ ( sK11_D @ SY69 @ SY66 @ SV17 ) ) @ SV17 ) ) ) ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(261,plain,
! [SV27: $i] :
( ( ( ~ ( empty @ SV27 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(262,plain,
! [SV28: $i] :
( ( ( ~ ( empty @ SV28 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(263,plain,
! [SV15: $i,SV26: $i] :
( ( ( empty @ SV26 )
= $false )
| ( ( SV15 = SV26 )
= $true )
| ( ( empty @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(264,plain,
( ( ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) )
= $false )
| ( ( sK2_SY42
= ( apply @ sK3_SY44 @ sK1_A ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(265,plain,
! [SV16: $i] :
( ( ( ~ ~ ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ ( relation_dom @ SV16 ) )
| ! [SY57: $i] :
( ( SY57
!= ( apply @ SV16 @ SY56 ) )
| ( in @ ( ordered_pair @ SY56 @ SY57 ) @ SV16 ) ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ ( relation_dom @ SV16 ) )
| ! [SY59: $i] :
( ~ ( in @ ( ordered_pair @ SY58 @ SY59 ) @ SV16 )
| ( SY59
= ( apply @ SV16 @ SY58 ) ) ) ) )
| ~ ~ ( ~ ! [SY60: $i] :
( ( in @ SY60 @ ( relation_dom @ SV16 ) )
| ! [SY61: $i] :
( ( SY61
!= ( apply @ SV16 @ SY60 ) )
| ( SY61 = empty_set ) ) )
| ~ ! [SY62: $i] :
( ( in @ SY62 @ ( relation_dom @ SV16 ) )
| ! [SY63: $i] :
( ( SY63 != empty_set )
| ( SY63
= ( apply @ SV16 @ SY62 ) ) ) ) ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(266,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(267,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(268,plain,
! [SV17: $i] :
( ( ( ! [SY64: $i] :
( ~ ( ~ ( ! [SY65: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SY64 @ SV17 ) @ SY65 ) @ SV17 )
| ~ ( in @ ( sK12_C @ SY64 @ SV17 ) @ SY64 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY64 @ SV17 ) @ ( sK13_SY46 @ SY64 @ SV17 ) ) @ SV17 )
| ( in @ ( sK12_C @ SY64 @ SV17 ) @ SY64 ) ) )
| ( SY64
= ( relation_dom @ SV17 ) ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(269,plain,
! [SV17: $i] :
( ( ( ! [SY66: $i] :
( ( SY66
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY67: $i] :
( ! [SY68: $i] :
~ ( in @ ( ordered_pair @ SY67 @ SY68 ) @ SV17 )
| ( in @ SY67 @ SY66 ) )
| ~ ! [SY69: $i] :
( ~ ( in @ SY69 @ SY66 )
| ( in @ ( ordered_pair @ SY69 @ ( sK11_D @ SY69 @ SY66 @ SV17 ) ) @ SV17 ) ) ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(270,plain,
! [SV27: $i] :
( ( ( empty @ SV27 )
= $false )
| ( ( empty @ ( relation_dom @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(271,plain,
! [SV28: $i] :
( ( ( empty @ SV28 )
= $false )
| ( ( relation @ ( relation_dom @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(272,plain,
! [SV16: $i] :
( ( ( ~ ~ ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ ( relation_dom @ SV16 ) )
| ! [SY57: $i] :
( ( SY57
!= ( apply @ SV16 @ SY56 ) )
| ( in @ ( ordered_pair @ SY56 @ SY57 ) @ SV16 ) ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ ( relation_dom @ SV16 ) )
| ! [SY59: $i] :
( ~ ( in @ ( ordered_pair @ SY58 @ SY59 ) @ SV16 )
| ( SY59
= ( apply @ SV16 @ SY58 ) ) ) ) ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(273,plain,
! [SV16: $i] :
( ( ( ~ ~ ( ~ ! [SY60: $i] :
( ( in @ SY60 @ ( relation_dom @ SV16 ) )
| ! [SY61: $i] :
( ( SY61
!= ( apply @ SV16 @ SY60 ) )
| ( SY61 = empty_set ) ) )
| ~ ! [SY62: $i] :
( ( in @ SY62 @ ( relation_dom @ SV16 ) )
| ! [SY63: $i] :
( ( SY63 != empty_set )
| ( SY63
= ( apply @ SV16 @ SY62 ) ) ) ) ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(274,plain,
! [SV17: $i,SV29: $i] :
( ( ( ~ ( ~ ( ! [SY70: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ SY70 ) @ SV17 )
| ~ ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ ( sK13_SY46 @ SV29 @ SV17 ) ) @ SV17 )
| ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) ) )
| ( SV29
= ( relation_dom @ SV17 ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(275,plain,
! [SV17: $i,SV30: $i] :
( ( ( ( SV30
!= ( relation_dom @ SV17 ) )
| ~ ( ~ ! [SY71: $i] :
( ! [SY68: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY68 ) @ SV17 )
| ( in @ SY71 @ SV30 ) )
| ~ ! [SY73: $i] :
( ~ ( in @ SY73 @ SV30 )
| ( in @ ( ordered_pair @ SY73 @ ( sK11_D @ SY73 @ SV30 @ SV17 ) ) @ SV17 ) ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(276,plain,
! [SV16: $i] :
( ( ( ~ ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ ( relation_dom @ SV16 ) )
| ! [SY57: $i] :
( ( SY57
!= ( apply @ SV16 @ SY56 ) )
| ( in @ ( ordered_pair @ SY56 @ SY57 ) @ SV16 ) ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ ( relation_dom @ SV16 ) )
| ! [SY59: $i] :
( ~ ( in @ ( ordered_pair @ SY58 @ SY59 ) @ SV16 )
| ( SY59
= ( apply @ SV16 @ SY58 ) ) ) ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(277,plain,
! [SV16: $i] :
( ( ( ~ ( ~ ! [SY60: $i] :
( ( in @ SY60 @ ( relation_dom @ SV16 ) )
| ! [SY61: $i] :
( ( SY61
!= ( apply @ SV16 @ SY60 ) )
| ( SY61 = empty_set ) ) )
| ~ ! [SY62: $i] :
( ( in @ SY62 @ ( relation_dom @ SV16 ) )
| ! [SY63: $i] :
( ( SY63 != empty_set )
| ( SY63
= ( apply @ SV16 @ SY62 ) ) ) ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(278,plain,
! [SV17: $i,SV29: $i] :
( ( ( ~ ( ~ ( ! [SY70: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ SY70 ) @ SV17 )
| ~ ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ ( sK13_SY46 @ SV29 @ SV17 ) ) @ SV17 )
| ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) ) ) )
= $true )
| ( ( SV29
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(279,plain,
! [SV17: $i,SV30: $i] :
( ( ( ( SV30
!= ( relation_dom @ SV17 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY71: $i] :
( ! [SY68: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY68 ) @ SV17 )
| ( in @ SY71 @ SV30 ) )
| ~ ! [SY73: $i] :
( ~ ( in @ SY73 @ SV30 )
| ( in @ ( ordered_pair @ SY73 @ ( sK11_D @ SY73 @ SV30 @ SV17 ) ) @ SV17 ) ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(280,plain,
! [SV16: $i] :
( ( ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ ( relation_dom @ SV16 ) )
| ! [SY57: $i] :
( ( SY57
!= ( apply @ SV16 @ SY56 ) )
| ( in @ ( ordered_pair @ SY56 @ SY57 ) @ SV16 ) ) )
| ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ ( relation_dom @ SV16 ) )
| ! [SY59: $i] :
( ~ ( in @ ( ordered_pair @ SY58 @ SY59 ) @ SV16 )
| ( SY59
= ( apply @ SV16 @ SY58 ) ) ) ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(281,plain,
! [SV16: $i] :
( ( ( ~ ! [SY60: $i] :
( ( in @ SY60 @ ( relation_dom @ SV16 ) )
| ! [SY61: $i] :
( ( SY61
!= ( apply @ SV16 @ SY60 ) )
| ( SY61 = empty_set ) ) )
| ~ ! [SY62: $i] :
( ( in @ SY62 @ ( relation_dom @ SV16 ) )
| ! [SY63: $i] :
( ( SY63 != empty_set )
| ( SY63
= ( apply @ SV16 @ SY62 ) ) ) ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(282,plain,
! [SV17: $i,SV29: $i] :
( ( ( ~ ( ! [SY70: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ SY70 ) @ SV17 )
| ~ ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ ( sK13_SY46 @ SV29 @ SV17 ) ) @ SV17 )
| ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) ) )
= $false )
| ( ( SV29
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(283,plain,
! [SV17: $i,SV30: $i] :
( ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( ~ ( ~ ! [SY71: $i] :
( ! [SY68: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY68 ) @ SV17 )
| ( in @ SY71 @ SV30 ) )
| ~ ! [SY73: $i] :
( ~ ( in @ SY73 @ SV30 )
| ( in @ ( ordered_pair @ SY73 @ ( sK11_D @ SY73 @ SV30 @ SV17 ) ) @ SV17 ) ) ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(284,plain,
! [SV16: $i] :
( ( ( ~ ! [SY56: $i] :
( ~ ( in @ SY56 @ ( relation_dom @ SV16 ) )
| ! [SY57: $i] :
( ( SY57
!= ( apply @ SV16 @ SY56 ) )
| ( in @ ( ordered_pair @ SY56 @ SY57 ) @ SV16 ) ) ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(285,plain,
! [SV16: $i] :
( ( ( ~ ! [SY58: $i] :
( ~ ( in @ SY58 @ ( relation_dom @ SV16 ) )
| ! [SY59: $i] :
( ~ ( in @ ( ordered_pair @ SY58 @ SY59 ) @ SV16 )
| ( SY59
= ( apply @ SV16 @ SY58 ) ) ) ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(286,plain,
! [SV16: $i] :
( ( ( ~ ! [SY60: $i] :
( ( in @ SY60 @ ( relation_dom @ SV16 ) )
| ! [SY61: $i] :
( ( SY61
!= ( apply @ SV16 @ SY60 ) )
| ( SY61 = empty_set ) ) ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(287,plain,
! [SV16: $i] :
( ( ( ~ ! [SY62: $i] :
( ( in @ SY62 @ ( relation_dom @ SV16 ) )
| ! [SY63: $i] :
( ( SY63 != empty_set )
| ( SY63
= ( apply @ SV16 @ SY62 ) ) ) ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(288,plain,
! [SV17: $i,SV29: $i] :
( ( ( ~ ( ! [SY70: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ SY70 ) @ SV17 )
| ~ ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) ) )
= $false )
| ( ( SV29
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(289,plain,
! [SV17: $i,SV29: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ ( sK13_SY46 @ SV29 @ SV17 ) ) @ SV17 )
| ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) ) )
= $false )
| ( ( SV29
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[282]) ).
thf(290,plain,
! [SV30: $i,SV17: $i] :
( ( ( ~ ! [SY71: $i] :
( ! [SY68: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY68 ) @ SV17 )
| ( in @ SY71 @ SV30 ) )
| ~ ! [SY73: $i] :
( ~ ( in @ SY73 @ SV30 )
| ( in @ ( ordered_pair @ SY73 @ ( sK11_D @ SY73 @ SV30 @ SV17 ) ) @ SV17 ) ) )
= $false )
| ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(291,plain,
! [SV16: $i] :
( ( ( ! [SY56: $i] :
( ~ ( in @ SY56 @ ( relation_dom @ SV16 ) )
| ! [SY57: $i] :
( ( SY57
!= ( apply @ SV16 @ SY56 ) )
| ( in @ ( ordered_pair @ SY56 @ SY57 ) @ SV16 ) ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(292,plain,
! [SV16: $i] :
( ( ( ! [SY58: $i] :
( ~ ( in @ SY58 @ ( relation_dom @ SV16 ) )
| ! [SY59: $i] :
( ~ ( in @ ( ordered_pair @ SY58 @ SY59 ) @ SV16 )
| ( SY59
= ( apply @ SV16 @ SY58 ) ) ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(293,plain,
! [SV16: $i] :
( ( ( ! [SY60: $i] :
( ( in @ SY60 @ ( relation_dom @ SV16 ) )
| ! [SY61: $i] :
( ( SY61
!= ( apply @ SV16 @ SY60 ) )
| ( SY61 = empty_set ) ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(294,plain,
! [SV16: $i] :
( ( ( ! [SY62: $i] :
( ( in @ SY62 @ ( relation_dom @ SV16 ) )
| ! [SY63: $i] :
( ( SY63 != empty_set )
| ( SY63
= ( apply @ SV16 @ SY62 ) ) ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(295,plain,
! [SV17: $i,SV29: $i] :
( ( ( ! [SY70: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ SY70 ) @ SV17 )
| ~ ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) )
= $true )
| ( ( SV29
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(296,plain,
! [SV17: $i,SV29: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ ( sK13_SY46 @ SV29 @ SV17 ) ) @ SV17 )
| ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) )
= $true )
| ( ( SV29
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(297,plain,
! [SV30: $i,SV17: $i] :
( ( ( ~ ! [SY71: $i] :
( ! [SY68: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY68 ) @ SV17 )
| ( in @ SY71 @ SV30 ) ) )
= $false )
| ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(298,plain,
! [SV17: $i,SV30: $i] :
( ( ( ~ ! [SY73: $i] :
( ~ ( in @ SY73 @ SV30 )
| ( in @ ( ordered_pair @ SY73 @ ( sK11_D @ SY73 @ SV30 @ SV17 ) ) @ SV17 ) ) )
= $false )
| ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(299,plain,
! [SV16: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ ( relation_dom @ SV16 ) )
| ! [SY74: $i] :
( ( SY74
!= ( apply @ SV16 @ SV31 ) )
| ( in @ ( ordered_pair @ SV31 @ SY74 ) @ SV16 ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(300,plain,
! [SV16: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ ( relation_dom @ SV16 ) )
| ! [SY75: $i] :
( ~ ( in @ ( ordered_pair @ SV32 @ SY75 ) @ SV16 )
| ( SY75
= ( apply @ SV16 @ SV32 ) ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(301,plain,
! [SV16: $i,SV33: $i] :
( ( ( ( in @ SV33 @ ( relation_dom @ SV16 ) )
| ! [SY76: $i] :
( ( SY76
!= ( apply @ SV16 @ SV33 ) )
| ( SY76 = empty_set ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(302,plain,
! [SV16: $i,SV34: $i] :
( ( ( ( in @ SV34 @ ( relation_dom @ SV16 ) )
| ! [SY77: $i] :
( ( SY77 != empty_set )
| ( SY77
= ( apply @ SV16 @ SV34 ) ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(303,plain,
! [SV17: $i,SV29: $i] :
( ( ( ! [SY70: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ SY70 ) @ SV17 ) )
= $true )
| ( ( ~ ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) )
= $true )
| ( ( SV29
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(304,plain,
! [SV17: $i,SV29: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ ( sK13_SY46 @ SV29 @ SV17 ) ) @ SV17 )
= $true )
| ( ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 )
= $true )
| ( ( SV29
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(305,plain,
! [SV30: $i,SV17: $i] :
( ( ( ! [SY71: $i] :
( ! [SY68: $i] :
~ ( in @ ( ordered_pair @ SY71 @ SY68 ) @ SV17 )
| ( in @ SY71 @ SV30 ) ) )
= $true )
| ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(306,plain,
! [SV17: $i,SV30: $i] :
( ( ( ! [SY73: $i] :
( ~ ( in @ SY73 @ SV30 )
| ( in @ ( ordered_pair @ SY73 @ ( sK11_D @ SY73 @ SV30 @ SV17 ) ) @ SV17 ) ) )
= $true )
| ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(307,plain,
! [SV16: $i,SV31: $i] :
( ( ( ~ ( in @ SV31 @ ( relation_dom @ SV16 ) ) )
= $true )
| ( ( ! [SY74: $i] :
( ( SY74
!= ( apply @ SV16 @ SV31 ) )
| ( in @ ( ordered_pair @ SV31 @ SY74 ) @ SV16 ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(308,plain,
! [SV16: $i,SV32: $i] :
( ( ( ~ ( in @ SV32 @ ( relation_dom @ SV16 ) ) )
= $true )
| ( ( ! [SY75: $i] :
( ~ ( in @ ( ordered_pair @ SV32 @ SY75 ) @ SV16 )
| ( SY75
= ( apply @ SV16 @ SV32 ) ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(309,plain,
! [SV16: $i,SV33: $i] :
( ( ( in @ SV33 @ ( relation_dom @ SV16 ) )
= $true )
| ( ( ! [SY76: $i] :
( ( SY76
!= ( apply @ SV16 @ SV33 ) )
| ( SY76 = empty_set ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(310,plain,
! [SV16: $i,SV34: $i] :
( ( ( in @ SV34 @ ( relation_dom @ SV16 ) )
= $true )
| ( ( ! [SY77: $i] :
( ( SY77 != empty_set )
| ( SY77
= ( apply @ SV16 @ SV34 ) ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(311,plain,
! [SV35: $i,SV17: $i,SV29: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ SV35 ) @ SV17 ) )
= $true )
| ( ( ~ ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) )
= $true )
| ( ( SV29
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(312,plain,
! [SV30: $i,SV17: $i,SV36: $i] :
( ( ( ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SV36 @ SY78 ) @ SV17 )
| ( in @ SV36 @ SV30 ) )
= $true )
| ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(313,plain,
! [SV17: $i,SV30: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ SV30 )
| ( in @ ( ordered_pair @ SV37 @ ( sK11_D @ SV37 @ SV30 @ SV17 ) ) @ SV17 ) )
= $true )
| ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(314,plain,
! [SV16: $i,SV31: $i] :
( ( ( in @ SV31 @ ( relation_dom @ SV16 ) )
= $false )
| ( ( ! [SY74: $i] :
( ( SY74
!= ( apply @ SV16 @ SV31 ) )
| ( in @ ( ordered_pair @ SV31 @ SY74 ) @ SV16 ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(315,plain,
! [SV16: $i,SV32: $i] :
( ( ( in @ SV32 @ ( relation_dom @ SV16 ) )
= $false )
| ( ( ! [SY75: $i] :
( ~ ( in @ ( ordered_pair @ SV32 @ SY75 ) @ SV16 )
| ( SY75
= ( apply @ SV16 @ SV32 ) ) ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(316,plain,
! [SV33: $i,SV16: $i,SV38: $i] :
( ( ( ( SV38
!= ( apply @ SV16 @ SV33 ) )
| ( SV38 = empty_set ) )
= $true )
| ( ( in @ SV33 @ ( relation_dom @ SV16 ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(317,plain,
! [SV34: $i,SV16: $i,SV39: $i] :
( ( ( ( SV39 != empty_set )
| ( SV39
= ( apply @ SV16 @ SV34 ) ) )
= $true )
| ( ( in @ SV34 @ ( relation_dom @ SV16 ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(318,plain,
! [SV35: $i,SV17: $i,SV29: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ SV35 ) @ SV17 )
= $false )
| ( ( ~ ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 ) )
= $true )
| ( ( SV29
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(319,plain,
! [SV30: $i,SV17: $i,SV36: $i] :
( ( ( ! [SY78: $i] :
~ ( in @ ( ordered_pair @ SV36 @ SY78 ) @ SV17 ) )
= $true )
| ( ( in @ SV36 @ SV30 )
= $true )
| ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(320,plain,
! [SV17: $i,SV30: $i,SV37: $i] :
( ( ( ~ ( in @ SV37 @ SV30 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV37 @ ( sK11_D @ SV37 @ SV30 @ SV17 ) ) @ SV17 )
= $true )
| ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(321,plain,
! [SV31: $i,SV16: $i,SV40: $i] :
( ( ( ( SV40
!= ( apply @ SV16 @ SV31 ) )
| ( in @ ( ordered_pair @ SV31 @ SV40 ) @ SV16 ) )
= $true )
| ( ( in @ SV31 @ ( relation_dom @ SV16 ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(322,plain,
! [SV16: $i,SV41: $i,SV32: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV32 @ SV41 ) @ SV16 )
| ( SV41
= ( apply @ SV16 @ SV32 ) ) )
= $true )
| ( ( in @ SV32 @ ( relation_dom @ SV16 ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(323,plain,
! [SV33: $i,SV16: $i,SV38: $i] :
( ( ( ( SV38
!= ( apply @ SV16 @ SV33 ) ) )
= $true )
| ( ( SV38 = empty_set )
= $true )
| ( ( in @ SV33 @ ( relation_dom @ SV16 ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(324,plain,
! [SV34: $i,SV16: $i,SV39: $i] :
( ( ( ( SV39 != empty_set ) )
= $true )
| ( ( SV39
= ( apply @ SV16 @ SV34 ) )
= $true )
| ( ( in @ SV34 @ ( relation_dom @ SV16 ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(325,plain,
! [SV35: $i,SV17: $i,SV29: $i] :
( ( ( in @ ( sK12_C @ SV29 @ SV17 ) @ SV29 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK12_C @ SV29 @ SV17 ) @ SV35 ) @ SV17 )
= $false )
| ( ( SV29
= ( relation_dom @ SV17 ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(326,plain,
! [SV30: $i,SV17: $i,SV42: $i,SV36: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV36 @ SV42 ) @ SV17 ) )
= $true )
| ( ( in @ SV36 @ SV30 )
= $true )
| ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(327,plain,
! [SV17: $i,SV30: $i,SV37: $i] :
( ( ( in @ SV37 @ SV30 )
= $false )
| ( ( in @ ( ordered_pair @ SV37 @ ( sK11_D @ SV37 @ SV30 @ SV17 ) ) @ SV17 )
= $true )
| ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(328,plain,
! [SV31: $i,SV16: $i,SV40: $i] :
( ( ( ( SV40
!= ( apply @ SV16 @ SV31 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV31 @ SV40 ) @ SV16 )
= $true )
| ( ( in @ SV31 @ ( relation_dom @ SV16 ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(329,plain,
! [SV16: $i,SV41: $i,SV32: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV32 @ SV41 ) @ SV16 ) )
= $true )
| ( ( SV41
= ( apply @ SV16 @ SV32 ) )
= $true )
| ( ( in @ SV32 @ ( relation_dom @ SV16 ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(330,plain,
! [SV33: $i,SV16: $i,SV38: $i] :
( ( ( SV38
= ( apply @ SV16 @ SV33 ) )
= $false )
| ( ( SV38 = empty_set )
= $true )
| ( ( in @ SV33 @ ( relation_dom @ SV16 ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(331,plain,
! [SV34: $i,SV16: $i,SV39: $i] :
( ( ( SV39 = empty_set )
= $false )
| ( ( SV39
= ( apply @ SV16 @ SV34 ) )
= $true )
| ( ( in @ SV34 @ ( relation_dom @ SV16 ) )
= $true )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(332,plain,
! [SV30: $i,SV17: $i,SV42: $i,SV36: $i] :
( ( ( in @ ( ordered_pair @ SV36 @ SV42 ) @ SV17 )
= $false )
| ( ( in @ SV36 @ SV30 )
= $true )
| ( ( SV30
= ( relation_dom @ SV17 ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(333,plain,
! [SV31: $i,SV16: $i,SV40: $i] :
( ( ( SV40
= ( apply @ SV16 @ SV31 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV31 @ SV40 ) @ SV16 )
= $true )
| ( ( in @ SV31 @ ( relation_dom @ SV16 ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(334,plain,
! [SV16: $i,SV41: $i,SV32: $i] :
( ( ( in @ ( ordered_pair @ SV32 @ SV41 ) @ SV16 )
= $false )
| ( ( SV41
= ( apply @ SV16 @ SV32 ) )
= $true )
| ( ( in @ SV32 @ ( relation_dom @ SV16 ) )
= $false )
| ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(335,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[110,334,333,332,331,330,327,325,304,271,270,267,266,264,263,253,252,251,250,247,239,236,235,232,231,230,229,228,225,222,221,219,216,212,211,210,209,182,180,179,160,155,138,137,128,119,116,115,114,113,112,111]) ).
thf(336,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(337,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(338,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(339,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(340,plain,
( ( ! [A: $i] :
( ~ ( function @ A )
| ~ ( relation @ A )
| ( ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( C
= ( apply @ A @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C
!= ( apply @ A @ B ) )
| ( C = empty_set ) ) )
& ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
| ! [C: $i] :
( ( C != empty_set )
| ( C
= ( apply @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(341,plain,
( ( ! [A: $i] :
( ~ ( relation @ A )
| ( ! [B: $i] :
( ( ( ! [SY45: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ SY45 ) @ A )
| ~ ( in @ ( sK12_C @ B @ A ) @ B ) )
& ( ( in @ ( ordered_pair @ ( sK12_C @ B @ A ) @ ( sK13_SY46 @ B @ A ) ) @ A )
| ( in @ ( sK12_C @ B @ A ) @ B ) ) )
| ( B
= ( relation_dom @ A ) ) )
& ! [B: $i] :
( ( B
!= ( relation_dom @ A ) )
| ( ! [C: $i] :
( ! [D: $i] :
~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) )
& ! [C: $i] :
( ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sK11_D @ C @ B @ A ) ) @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(342,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(343,plain,
$true = $true,
inference(copy,[status(thm)],[64]) ).
thf(344,plain,
$true = $true,
inference(copy,[status(thm)],[63]) ).
thf(345,plain,
$true = $true,
inference(copy,[status(thm)],[62]) ).
thf(346,plain,
$true = $true,
inference(copy,[status(thm)],[61]) ).
thf(347,plain,
$true = $true,
inference(copy,[status(thm)],[60]) ).
thf(348,plain,
$true = $true,
inference(copy,[status(thm)],[59]) ).
thf(349,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(350,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(351,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(352,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(354,plain,
( ( ! [A: $i] :
~ ( empty @ ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(355,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(356,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(357,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(358,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) )
& ! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(359,plain,
( ( ( function @ sK9_A )
& ( relation @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(360,plain,
( ( ( empty @ sK8_A )
& ( relation @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(361,plain,
( ( empty @ sK7_A )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(362,plain,
( ( ~ ( empty @ sK6_A )
& ( relation @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(363,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(364,plain,
( ( ( relation @ sK4_A )
& ( relation_empty_yielding @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(365,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(366,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(367,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(368,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(369,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(370,plain,
( ( function @ sK3_SY44 )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(371,plain,
( ( relation @ sK3_SY44 )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(372,plain,
( ( ( sK2_SY42
= ( apply @ sK3_SY44 @ sK1_A ) )
& ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) )
& ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(373,plain,
( ( ~ ( ~ ( empty @ sK8_A )
| ~ ( relation @ sK8_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(374,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(375,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( ! [SX2: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
| ~ ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SX1 @ SX0 ) @ ( sK13_SY46 @ SX1 @ SX0 ) ) @ SX0 )
| ( in @ ( sK12_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX1
= ( relation_dom @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ( SX1
!= ( relation_dom @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
~ ( in @ ( ordered_pair @ SX2 @ SX3 ) @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ ( ordered_pair @ SX2 @ ( sK11_D @ SX2 @ SX1 @ SX0 ) ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(376,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(377,plain,
( ( ! [SX0: $i] :
( ~ ( function @ SX0 )
| ~ ( relation @ SX0 )
| ~ ( ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ SX0 )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2
!= ( apply @ SX0 @ SX1 ) )
| ( SX2 = empty_set ) ) )
| ~ ! [SX1: $i] :
( ( in @ SX1 @ ( relation_dom @ SX0 ) )
| ! [SX2: $i] :
( ( SX2 != empty_set )
| ( SX2
= ( apply @ SX0 @ SX1 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(378,plain,
( ( ~ ( ~ ~ ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) )
| ~ ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(379,plain,
( ( ~ ( ~ ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(380,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(381,plain,
( ( ~ ( ~ ( function @ sK9_A )
| ~ ( relation @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(382,plain,
( ( ~ ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(383,plain,
! [SV43: $i] :
( ( ! [SY79: $i] :
( ~ ( in @ SV43 @ SY79 )
| ~ ( in @ SY79 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(384,plain,
! [SV44: $i] :
( ( ~ ( empty @ SV44 )
| ( function @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(385,plain,
! [SV45: $i] :
( ( ~ ( empty @ SV45 )
| ( relation @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(386,plain,
! [SV46: $i] :
( ( ! [SY80: $i] :
( ( unordered_pair @ SV46 @ SY80 )
= ( unordered_pair @ SY80 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(387,plain,
! [SV47: $i] :
( ( ! [SY81: $i] :
( ( ordered_pair @ SV47 @ SY81 )
= ( unordered_pair @ ( unordered_pair @ SV47 @ SY81 ) @ ( singleton @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(388,plain,
! [SV48: $i] :
( ( element @ ( sK10_B @ SV48 ) @ SV48 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(389,plain,
! [SV49: $i] :
( ( ! [SY82: $i] :
~ ( empty @ ( ordered_pair @ SV49 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(390,plain,
! [SV50: $i] :
( ( ~ ( empty @ ( singleton @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(391,plain,
! [SV51: $i] :
( ( ! [SY83: $i] :
~ ( empty @ ( unordered_pair @ SV51 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(392,plain,
! [SV52: $i] :
( ( ( empty @ SV52 )
| ~ ( relation @ SV52 )
| ~ ( empty @ ( relation_dom @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(393,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(394,plain,
! [SV53: $i] :
( ( ! [SY84: $i] :
( ~ ( in @ SV53 @ SY84 )
| ( element @ SV53 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(395,plain,
! [SV54: $i] :
( ( ! [SY85: $i] :
( ~ ( element @ SV54 @ SY85 )
| ( empty @ SY85 )
| ( in @ SV54 @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(396,plain,
! [SV55: $i] :
( ( ~ ( empty @ SV55 )
| ( SV55 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(397,plain,
! [SV56: $i] :
( ( ! [SY86: $i] :
( ~ ( empty @ SY86 )
| ~ ( in @ SV56 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(398,plain,
! [SV57: $i] :
( ( ! [SY87: $i] :
( ( SV57 = SY87 )
| ~ ( empty @ SV57 )
| ~ ( empty @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(399,plain,
( ( ~ ( empty @ sK8_A )
| ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(400,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(401,plain,
! [SV58: $i] :
( ( ~ ( relation @ SV58 )
| ~ ( ~ ! [SY88: $i] :
( ~ ( ~ ( ! [SY89: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SY88 @ SV58 ) @ SY89 ) @ SV58 )
| ~ ( in @ ( sK12_C @ SY88 @ SV58 ) @ SY88 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY88 @ SV58 ) @ ( sK13_SY46 @ SY88 @ SV58 ) ) @ SV58 )
| ( in @ ( sK12_C @ SY88 @ SV58 ) @ SY88 ) ) )
| ( SY88
= ( relation_dom @ SV58 ) ) )
| ~ ! [SY90: $i] :
( ( SY90
!= ( relation_dom @ SV58 ) )
| ~ ( ~ ! [SY91: $i] :
( ! [SY92: $i] :
~ ( in @ ( ordered_pair @ SY91 @ SY92 ) @ SV58 )
| ( in @ SY91 @ SY90 ) )
| ~ ! [SY93: $i] :
( ~ ( in @ SY93 @ SY90 )
| ( in @ ( ordered_pair @ SY93 @ ( sK11_D @ SY93 @ SY90 @ SV58 ) ) @ SV58 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(402,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(403,plain,
! [SV59: $i] :
( ( ~ ( function @ SV59 )
| ~ ( relation @ SV59 )
| ~ ( ~ ~ ( ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( relation_dom @ SV59 ) )
| ! [SY95: $i] :
( ( SY95
!= ( apply @ SV59 @ SY94 ) )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV59 ) ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ ( relation_dom @ SV59 ) )
| ! [SY97: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV59 )
| ( SY97
= ( apply @ SV59 @ SY96 ) ) ) ) )
| ~ ~ ( ~ ! [SY98: $i] :
( ( in @ SY98 @ ( relation_dom @ SV59 ) )
| ! [SY99: $i] :
( ( SY99
!= ( apply @ SV59 @ SY98 ) )
| ( SY99 = empty_set ) ) )
| ~ ! [SY100: $i] :
( ( in @ SY100 @ ( relation_dom @ SV59 ) )
| ! [SY101: $i] :
( ( SY101 != empty_set )
| ( SY101
= ( apply @ SV59 @ SY100 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(404,plain,
( ( ~ ~ ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) )
| ~ ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(405,plain,
( ( ~ ~ ( empty @ sK6_A )
| ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(406,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(407,plain,
( ( ~ ( function @ sK9_A )
| ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(408,plain,
( ( ~ ( relation @ sK4_A )
| ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(409,plain,
! [SV60: $i,SV43: $i] :
( ( ~ ( in @ SV43 @ SV60 )
| ~ ( in @ SV60 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(410,plain,
! [SV44: $i] :
( ( ( ~ ( empty @ SV44 ) )
= $true )
| ( ( function @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(411,plain,
! [SV45: $i] :
( ( ( ~ ( empty @ SV45 ) )
= $true )
| ( ( relation @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(412,plain,
! [SV61: $i,SV46: $i] :
( ( ( unordered_pair @ SV46 @ SV61 )
= ( unordered_pair @ SV61 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(413,plain,
! [SV62: $i,SV47: $i] :
( ( ( ordered_pair @ SV47 @ SV62 )
= ( unordered_pair @ ( unordered_pair @ SV47 @ SV62 ) @ ( singleton @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(414,plain,
! [SV63: $i,SV49: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV49 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(415,plain,
! [SV50: $i] :
( ( empty @ ( singleton @ SV50 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(416,plain,
! [SV64: $i,SV51: $i] :
( ( ~ ( empty @ ( unordered_pair @ SV51 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(417,plain,
! [SV52: $i] :
( ( ( ( empty @ SV52 )
| ~ ( relation @ SV52 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(418,plain,
! [SV65: $i,SV53: $i] :
( ( ~ ( in @ SV53 @ SV65 )
| ( element @ SV53 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(419,plain,
! [SV66: $i,SV54: $i] :
( ( ~ ( element @ SV54 @ SV66 )
| ( empty @ SV66 )
| ( in @ SV54 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(420,plain,
! [SV55: $i] :
( ( ( ~ ( empty @ SV55 ) )
= $true )
| ( ( SV55 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(421,plain,
! [SV56: $i,SV67: $i] :
( ( ~ ( empty @ SV67 )
| ~ ( in @ SV56 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(422,plain,
! [SV68: $i,SV57: $i] :
( ( ( SV57 = SV68 )
| ~ ( empty @ SV57 )
| ~ ( empty @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(423,plain,
( ( ~ ( empty @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(424,plain,
( ( ~ ( relation @ sK8_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(425,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(426,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(427,plain,
! [SV58: $i] :
( ( ( ~ ( relation @ SV58 ) )
= $true )
| ( ( ~ ( ~ ! [SY88: $i] :
( ~ ( ~ ( ! [SY89: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SY88 @ SV58 ) @ SY89 ) @ SV58 )
| ~ ( in @ ( sK12_C @ SY88 @ SV58 ) @ SY88 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY88 @ SV58 ) @ ( sK13_SY46 @ SY88 @ SV58 ) ) @ SV58 )
| ( in @ ( sK12_C @ SY88 @ SV58 ) @ SY88 ) ) )
| ( SY88
= ( relation_dom @ SV58 ) ) )
| ~ ! [SY90: $i] :
( ( SY90
!= ( relation_dom @ SV58 ) )
| ~ ( ~ ! [SY91: $i] :
( ! [SY92: $i] :
~ ( in @ ( ordered_pair @ SY91 @ SY92 ) @ SV58 )
| ( in @ SY91 @ SY90 ) )
| ~ ! [SY93: $i] :
( ~ ( in @ SY93 @ SY90 )
| ( in @ ( ordered_pair @ SY93 @ ( sK11_D @ SY93 @ SY90 @ SV58 ) ) @ SV58 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(428,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(429,plain,
( ( ~ ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(430,plain,
! [SV59: $i] :
( ( ( ~ ( function @ SV59 )
| ~ ( relation @ SV59 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( relation_dom @ SV59 ) )
| ! [SY95: $i] :
( ( SY95
!= ( apply @ SV59 @ SY94 ) )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV59 ) ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ ( relation_dom @ SV59 ) )
| ! [SY97: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV59 )
| ( SY97
= ( apply @ SV59 @ SY96 ) ) ) ) )
| ~ ~ ( ~ ! [SY98: $i] :
( ( in @ SY98 @ ( relation_dom @ SV59 ) )
| ! [SY99: $i] :
( ( SY99
!= ( apply @ SV59 @ SY98 ) )
| ( SY99 = empty_set ) ) )
| ~ ! [SY100: $i] :
( ( in @ SY100 @ ( relation_dom @ SV59 ) )
| ! [SY101: $i] :
( ( SY101 != empty_set )
| ( SY101
= ( apply @ SV59 @ SY100 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(431,plain,
( ( ~ ~ ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(432,plain,
( ( ~ ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(433,plain,
( ( ~ ~ ( empty @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(434,plain,
( ( ~ ( relation @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(435,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(436,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(437,plain,
( ( ~ ( function @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(438,plain,
( ( ~ ( relation @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(439,plain,
( ( ~ ( relation @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(440,plain,
( ( ~ ( relation_empty_yielding @ sK4_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(441,plain,
! [SV60: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ SV60 ) )
= $true )
| ( ( ~ ( in @ SV60 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(442,plain,
! [SV44: $i] :
( ( ( empty @ SV44 )
= $false )
| ( ( function @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(443,plain,
! [SV45: $i] :
( ( ( empty @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(444,plain,
! [SV63: $i,SV49: $i] :
( ( empty @ ( ordered_pair @ SV49 @ SV63 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(445,plain,
! [SV64: $i,SV51: $i] :
( ( empty @ ( unordered_pair @ SV51 @ SV64 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(446,plain,
! [SV52: $i] :
( ( ( empty @ SV52 )
= $true )
| ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(447,plain,
! [SV65: $i,SV53: $i] :
( ( ( ~ ( in @ SV53 @ SV65 ) )
= $true )
| ( ( element @ SV53 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(448,plain,
! [SV66: $i,SV54: $i] :
( ( ( ~ ( element @ SV54 @ SV66 ) )
= $true )
| ( ( ( empty @ SV66 )
| ( in @ SV54 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(449,plain,
! [SV55: $i] :
( ( ( empty @ SV55 )
= $false )
| ( ( SV55 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(450,plain,
! [SV56: $i,SV67: $i] :
( ( ( ~ ( empty @ SV67 ) )
= $true )
| ( ( ~ ( in @ SV56 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(451,plain,
! [SV68: $i,SV57: $i] :
( ( ( ( SV57 = SV68 )
| ~ ( empty @ SV57 ) )
= $true )
| ( ( ~ ( empty @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(452,plain,
( ( empty @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(453,plain,
( ( relation @ sK8_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(454,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[425]) ).
thf(455,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[426]) ).
thf(456,plain,
! [SV58: $i] :
( ( ( relation @ SV58 )
= $false )
| ( ( ~ ( ~ ! [SY88: $i] :
( ~ ( ~ ( ! [SY89: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SY88 @ SV58 ) @ SY89 ) @ SV58 )
| ~ ( in @ ( sK12_C @ SY88 @ SV58 ) @ SY88 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY88 @ SV58 ) @ ( sK13_SY46 @ SY88 @ SV58 ) ) @ SV58 )
| ( in @ ( sK12_C @ SY88 @ SV58 ) @ SY88 ) ) )
| ( SY88
= ( relation_dom @ SV58 ) ) )
| ~ ! [SY90: $i] :
( ( SY90
!= ( relation_dom @ SV58 ) )
| ~ ( ~ ! [SY91: $i] :
( ! [SY92: $i] :
~ ( in @ ( ordered_pair @ SY91 @ SY92 ) @ SV58 )
| ( in @ SY91 @ SY90 ) )
| ~ ! [SY93: $i] :
( ~ ( in @ SY93 @ SY90 )
| ( in @ ( ordered_pair @ SY93 @ ( sK11_D @ SY93 @ SY90 @ SV58 ) ) @ SV58 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(457,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(458,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(459,plain,
! [SV59: $i] :
( ( ( ~ ( function @ SV59 ) )
= $true )
| ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( relation_dom @ SV59 ) )
| ! [SY95: $i] :
( ( SY95
!= ( apply @ SV59 @ SY94 ) )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV59 ) ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ ( relation_dom @ SV59 ) )
| ! [SY97: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV59 )
| ( SY97
= ( apply @ SV59 @ SY96 ) ) ) ) )
| ~ ~ ( ~ ! [SY98: $i] :
( ( in @ SY98 @ ( relation_dom @ SV59 ) )
| ! [SY99: $i] :
( ( SY99
!= ( apply @ SV59 @ SY98 ) )
| ( SY99 = empty_set ) ) )
| ~ ! [SY100: $i] :
( ( in @ SY100 @ ( relation_dom @ SV59 ) )
| ! [SY101: $i] :
( ( SY101 != empty_set )
| ( SY101
= ( apply @ SV59 @ SY100 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(460,plain,
( ( ~ ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(461,plain,
( ( ~ ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(462,plain,
( ( ~ ( empty @ sK6_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(463,plain,
( ( relation @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(464,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(465,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(466,plain,
( ( function @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(467,plain,
( ( relation @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(468,plain,
( ( relation @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(469,plain,
( ( relation_empty_yielding @ sK4_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(470,plain,
! [SV60: $i,SV43: $i] :
( ( ( in @ SV43 @ SV60 )
= $false )
| ( ( ~ ( in @ SV60 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(471,plain,
! [SV52: $i] :
( ( ( relation @ SV52 )
= $false )
| ( ( empty @ SV52 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(472,plain,
! [SV65: $i,SV53: $i] :
( ( ( in @ SV53 @ SV65 )
= $false )
| ( ( element @ SV53 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(473,plain,
! [SV66: $i,SV54: $i] :
( ( ( element @ SV54 @ SV66 )
= $false )
| ( ( ( empty @ SV66 )
| ( in @ SV54 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(474,plain,
! [SV56: $i,SV67: $i] :
( ( ( empty @ SV67 )
= $false )
| ( ( ~ ( in @ SV56 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(475,plain,
! [SV68: $i,SV57: $i] :
( ( ( SV57 = SV68 )
= $true )
| ( ( ~ ( empty @ SV57 ) )
= $true )
| ( ( ~ ( empty @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(476,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(477,plain,
! [SV58: $i] :
( ( ( ~ ! [SY88: $i] :
( ~ ( ~ ( ! [SY89: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SY88 @ SV58 ) @ SY89 ) @ SV58 )
| ~ ( in @ ( sK12_C @ SY88 @ SV58 ) @ SY88 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY88 @ SV58 ) @ ( sK13_SY46 @ SY88 @ SV58 ) ) @ SV58 )
| ( in @ ( sK12_C @ SY88 @ SV58 ) @ SY88 ) ) )
| ( SY88
= ( relation_dom @ SV58 ) ) )
| ~ ! [SY90: $i] :
( ( SY90
!= ( relation_dom @ SV58 ) )
| ~ ( ~ ! [SY91: $i] :
( ! [SY92: $i] :
~ ( in @ ( ordered_pair @ SY91 @ SY92 ) @ SV58 )
| ( in @ SY91 @ SY90 ) )
| ~ ! [SY93: $i] :
( ~ ( in @ SY93 @ SY90 )
| ( in @ ( ordered_pair @ SY93 @ ( sK11_D @ SY93 @ SY90 @ SV58 ) ) @ SV58 ) ) ) ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(478,plain,
! [SV69: $i] :
( ( ~ ( empty @ SV69 )
| ( empty @ ( relation_dom @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(479,plain,
! [SV70: $i] :
( ( ~ ( empty @ SV70 )
| ( relation @ ( relation_dom @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(480,plain,
! [SV59: $i] :
( ( ( function @ SV59 )
= $false )
| ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( relation_dom @ SV59 ) )
| ! [SY95: $i] :
( ( SY95
!= ( apply @ SV59 @ SY94 ) )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV59 ) ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ ( relation_dom @ SV59 ) )
| ! [SY97: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV59 )
| ( SY97
= ( apply @ SV59 @ SY96 ) ) ) ) )
| ~ ~ ( ~ ! [SY98: $i] :
( ( in @ SY98 @ ( relation_dom @ SV59 ) )
| ! [SY99: $i] :
( ( SY99
!= ( apply @ SV59 @ SY98 ) )
| ( SY99 = empty_set ) ) )
| ~ ! [SY100: $i] :
( ( in @ SY100 @ ( relation_dom @ SV59 ) )
| ! [SY101: $i] :
( ( SY101 != empty_set )
| ( SY101
= ( apply @ SV59 @ SY100 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(481,plain,
( ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) )
| ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(482,plain,
( ( in @ ( ordered_pair @ sK1_A @ sK2_SY42 ) @ sK3_SY44 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(483,plain,
( ( empty @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(484,plain,
! [SV43: $i,SV60: $i] :
( ( ( in @ SV60 @ SV43 )
= $false )
| ( ( in @ SV43 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(485,plain,
! [SV52: $i] :
( ( ( empty @ ( relation_dom @ SV52 ) )
= $false )
| ( ( empty @ SV52 )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(486,plain,
! [SV54: $i,SV66: $i] :
( ( ( empty @ SV66 )
= $true )
| ( ( in @ SV54 @ SV66 )
= $true )
| ( ( element @ SV54 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(487,plain,
! [SV67: $i,SV56: $i] :
( ( ( in @ SV56 @ SV67 )
= $false )
| ( ( empty @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(488,plain,
! [SV68: $i,SV57: $i] :
( ( ( empty @ SV57 )
= $false )
| ( ( SV57 = SV68 )
= $true )
| ( ( ~ ( empty @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(489,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(490,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(491,plain,
! [SV58: $i] :
( ( ( ~ ! [SY88: $i] :
( ~ ( ~ ( ! [SY89: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SY88 @ SV58 ) @ SY89 ) @ SV58 )
| ~ ( in @ ( sK12_C @ SY88 @ SV58 ) @ SY88 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY88 @ SV58 ) @ ( sK13_SY46 @ SY88 @ SV58 ) ) @ SV58 )
| ( in @ ( sK12_C @ SY88 @ SV58 ) @ SY88 ) ) )
| ( SY88
= ( relation_dom @ SV58 ) ) ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(492,plain,
! [SV58: $i] :
( ( ( ~ ! [SY90: $i] :
( ( SY90
!= ( relation_dom @ SV58 ) )
| ~ ( ~ ! [SY91: $i] :
( ! [SY92: $i] :
~ ( in @ ( ordered_pair @ SY91 @ SY92 ) @ SV58 )
| ( in @ SY91 @ SY90 ) )
| ~ ! [SY93: $i] :
( ~ ( in @ SY93 @ SY90 )
| ( in @ ( ordered_pair @ SY93 @ ( sK11_D @ SY93 @ SY90 @ SV58 ) ) @ SV58 ) ) ) ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[477]) ).
thf(493,plain,
! [SV69: $i] :
( ( ( ~ ( empty @ SV69 ) )
= $true )
| ( ( empty @ ( relation_dom @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(494,plain,
! [SV70: $i] :
( ( ( ~ ( empty @ SV70 ) )
= $true )
| ( ( relation @ ( relation_dom @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(495,plain,
! [SV59: $i] :
( ( ( relation @ SV59 )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( relation_dom @ SV59 ) )
| ! [SY95: $i] :
( ( SY95
!= ( apply @ SV59 @ SY94 ) )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV59 ) ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ ( relation_dom @ SV59 ) )
| ! [SY97: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV59 )
| ( SY97
= ( apply @ SV59 @ SY96 ) ) ) ) )
| ~ ~ ( ~ ! [SY98: $i] :
( ( in @ SY98 @ ( relation_dom @ SV59 ) )
| ! [SY99: $i] :
( ( SY99
!= ( apply @ SV59 @ SY98 ) )
| ( SY99 = empty_set ) ) )
| ~ ! [SY100: $i] :
( ( in @ SY100 @ ( relation_dom @ SV59 ) )
| ! [SY101: $i] :
( ( SY101 != empty_set )
| ( SY101
= ( apply @ SV59 @ SY100 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(496,plain,
( ( ( sK2_SY42
!= ( apply @ sK3_SY44 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(497,plain,
( ( ~ ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(498,plain,
! [SV57: $i,SV68: $i] :
( ( ( empty @ SV68 )
= $false )
| ( ( SV57 = SV68 )
= $true )
| ( ( empty @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(499,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(500,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(501,plain,
! [SV58: $i] :
( ( ( ! [SY88: $i] :
( ~ ( ~ ( ! [SY89: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SY88 @ SV58 ) @ SY89 ) @ SV58 )
| ~ ( in @ ( sK12_C @ SY88 @ SV58 ) @ SY88 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SY88 @ SV58 ) @ ( sK13_SY46 @ SY88 @ SV58 ) ) @ SV58 )
| ( in @ ( sK12_C @ SY88 @ SV58 ) @ SY88 ) ) )
| ( SY88
= ( relation_dom @ SV58 ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(502,plain,
! [SV58: $i] :
( ( ( ! [SY90: $i] :
( ( SY90
!= ( relation_dom @ SV58 ) )
| ~ ( ~ ! [SY91: $i] :
( ! [SY92: $i] :
~ ( in @ ( ordered_pair @ SY91 @ SY92 ) @ SV58 )
| ( in @ SY91 @ SY90 ) )
| ~ ! [SY93: $i] :
( ~ ( in @ SY93 @ SY90 )
| ( in @ ( ordered_pair @ SY93 @ ( sK11_D @ SY93 @ SY90 @ SV58 ) ) @ SV58 ) ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(503,plain,
! [SV69: $i] :
( ( ( empty @ SV69 )
= $false )
| ( ( empty @ ( relation_dom @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(504,plain,
! [SV70: $i] :
( ( ( empty @ SV70 )
= $false )
| ( ( relation @ ( relation_dom @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(505,plain,
! [SV59: $i] :
( ( ( ~ ~ ( ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( relation_dom @ SV59 ) )
| ! [SY95: $i] :
( ( SY95
!= ( apply @ SV59 @ SY94 ) )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV59 ) ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ ( relation_dom @ SV59 ) )
| ! [SY97: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV59 )
| ( SY97
= ( apply @ SV59 @ SY96 ) ) ) ) )
| ~ ~ ( ~ ! [SY98: $i] :
( ( in @ SY98 @ ( relation_dom @ SV59 ) )
| ! [SY99: $i] :
( ( SY99
!= ( apply @ SV59 @ SY98 ) )
| ( SY99 = empty_set ) ) )
| ~ ! [SY100: $i] :
( ( in @ SY100 @ ( relation_dom @ SV59 ) )
| ! [SY101: $i] :
( ( SY101 != empty_set )
| ( SY101
= ( apply @ SV59 @ SY100 ) ) ) ) ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(506,plain,
( ( sK2_SY42
= ( apply @ sK3_SY44 @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(507,plain,
( ( in @ sK1_A @ ( relation_dom @ sK3_SY44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(508,plain,
! [SV58: $i,SV71: $i] :
( ( ( ~ ( ~ ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ SY102 ) @ SV58 )
| ~ ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ ( sK13_SY46 @ SV71 @ SV58 ) ) @ SV58 )
| ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) ) )
| ( SV71
= ( relation_dom @ SV58 ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(509,plain,
! [SV58: $i,SV72: $i] :
( ( ( ( SV72
!= ( relation_dom @ SV58 ) )
| ~ ( ~ ! [SY103: $i] :
( ! [SY92: $i] :
~ ( in @ ( ordered_pair @ SY103 @ SY92 ) @ SV58 )
| ( in @ SY103 @ SV72 ) )
| ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ SV72 )
| ( in @ ( ordered_pair @ SY105 @ ( sK11_D @ SY105 @ SV72 @ SV58 ) ) @ SV58 ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(510,plain,
! [SV59: $i] :
( ( ( ~ ~ ( ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( relation_dom @ SV59 ) )
| ! [SY95: $i] :
( ( SY95
!= ( apply @ SV59 @ SY94 ) )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV59 ) ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ ( relation_dom @ SV59 ) )
| ! [SY97: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV59 )
| ( SY97
= ( apply @ SV59 @ SY96 ) ) ) ) ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(511,plain,
! [SV59: $i] :
( ( ( ~ ~ ( ~ ! [SY98: $i] :
( ( in @ SY98 @ ( relation_dom @ SV59 ) )
| ! [SY99: $i] :
( ( SY99
!= ( apply @ SV59 @ SY98 ) )
| ( SY99 = empty_set ) ) )
| ~ ! [SY100: $i] :
( ( in @ SY100 @ ( relation_dom @ SV59 ) )
| ! [SY101: $i] :
( ( SY101 != empty_set )
| ( SY101
= ( apply @ SV59 @ SY100 ) ) ) ) ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[505]) ).
thf(512,plain,
! [SV58: $i,SV71: $i] :
( ( ( ~ ( ~ ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ SY102 ) @ SV58 )
| ~ ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ ( sK13_SY46 @ SV71 @ SV58 ) ) @ SV58 )
| ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) ) ) )
= $true )
| ( ( SV71
= ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(513,plain,
! [SV58: $i,SV72: $i] :
( ( ( ( SV72
!= ( relation_dom @ SV58 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY103: $i] :
( ! [SY92: $i] :
~ ( in @ ( ordered_pair @ SY103 @ SY92 ) @ SV58 )
| ( in @ SY103 @ SV72 ) )
| ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ SV72 )
| ( in @ ( ordered_pair @ SY105 @ ( sK11_D @ SY105 @ SV72 @ SV58 ) ) @ SV58 ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(514,plain,
! [SV59: $i] :
( ( ( ~ ( ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( relation_dom @ SV59 ) )
| ! [SY95: $i] :
( ( SY95
!= ( apply @ SV59 @ SY94 ) )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV59 ) ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ ( relation_dom @ SV59 ) )
| ! [SY97: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV59 )
| ( SY97
= ( apply @ SV59 @ SY96 ) ) ) ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(515,plain,
! [SV59: $i] :
( ( ( ~ ( ~ ! [SY98: $i] :
( ( in @ SY98 @ ( relation_dom @ SV59 ) )
| ! [SY99: $i] :
( ( SY99
!= ( apply @ SV59 @ SY98 ) )
| ( SY99 = empty_set ) ) )
| ~ ! [SY100: $i] :
( ( in @ SY100 @ ( relation_dom @ SV59 ) )
| ! [SY101: $i] :
( ( SY101 != empty_set )
| ( SY101
= ( apply @ SV59 @ SY100 ) ) ) ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(516,plain,
! [SV58: $i,SV71: $i] :
( ( ( ~ ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ SY102 ) @ SV58 )
| ~ ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) )
| ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ ( sK13_SY46 @ SV71 @ SV58 ) ) @ SV58 )
| ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) ) )
= $false )
| ( ( SV71
= ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(517,plain,
! [SV58: $i,SV72: $i] :
( ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( ~ ( ~ ! [SY103: $i] :
( ! [SY92: $i] :
~ ( in @ ( ordered_pair @ SY103 @ SY92 ) @ SV58 )
| ( in @ SY103 @ SV72 ) )
| ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ SV72 )
| ( in @ ( ordered_pair @ SY105 @ ( sK11_D @ SY105 @ SV72 @ SV58 ) ) @ SV58 ) ) ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(518,plain,
! [SV59: $i] :
( ( ( ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( relation_dom @ SV59 ) )
| ! [SY95: $i] :
( ( SY95
!= ( apply @ SV59 @ SY94 ) )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV59 ) ) )
| ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ ( relation_dom @ SV59 ) )
| ! [SY97: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV59 )
| ( SY97
= ( apply @ SV59 @ SY96 ) ) ) ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(519,plain,
! [SV59: $i] :
( ( ( ~ ! [SY98: $i] :
( ( in @ SY98 @ ( relation_dom @ SV59 ) )
| ! [SY99: $i] :
( ( SY99
!= ( apply @ SV59 @ SY98 ) )
| ( SY99 = empty_set ) ) )
| ~ ! [SY100: $i] :
( ( in @ SY100 @ ( relation_dom @ SV59 ) )
| ! [SY101: $i] :
( ( SY101 != empty_set )
| ( SY101
= ( apply @ SV59 @ SY100 ) ) ) ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(520,plain,
! [SV58: $i,SV71: $i] :
( ( ( ~ ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ SY102 ) @ SV58 )
| ~ ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) ) )
= $false )
| ( ( SV71
= ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(521,plain,
! [SV58: $i,SV71: $i] :
( ( ( ~ ( ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ ( sK13_SY46 @ SV71 @ SV58 ) ) @ SV58 )
| ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) ) )
= $false )
| ( ( SV71
= ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[516]) ).
thf(522,plain,
! [SV72: $i,SV58: $i] :
( ( ( ~ ! [SY103: $i] :
( ! [SY92: $i] :
~ ( in @ ( ordered_pair @ SY103 @ SY92 ) @ SV58 )
| ( in @ SY103 @ SV72 ) )
| ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ SV72 )
| ( in @ ( ordered_pair @ SY105 @ ( sK11_D @ SY105 @ SV72 @ SV58 ) ) @ SV58 ) ) )
= $false )
| ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(523,plain,
! [SV59: $i] :
( ( ( ~ ! [SY94: $i] :
( ~ ( in @ SY94 @ ( relation_dom @ SV59 ) )
| ! [SY95: $i] :
( ( SY95
!= ( apply @ SV59 @ SY94 ) )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV59 ) ) ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(524,plain,
! [SV59: $i] :
( ( ( ~ ! [SY96: $i] :
( ~ ( in @ SY96 @ ( relation_dom @ SV59 ) )
| ! [SY97: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV59 )
| ( SY97
= ( apply @ SV59 @ SY96 ) ) ) ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(525,plain,
! [SV59: $i] :
( ( ( ~ ! [SY98: $i] :
( ( in @ SY98 @ ( relation_dom @ SV59 ) )
| ! [SY99: $i] :
( ( SY99
!= ( apply @ SV59 @ SY98 ) )
| ( SY99 = empty_set ) ) ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(526,plain,
! [SV59: $i] :
( ( ( ~ ! [SY100: $i] :
( ( in @ SY100 @ ( relation_dom @ SV59 ) )
| ! [SY101: $i] :
( ( SY101 != empty_set )
| ( SY101
= ( apply @ SV59 @ SY100 ) ) ) ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(527,plain,
! [SV58: $i,SV71: $i] :
( ( ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ SY102 ) @ SV58 )
| ~ ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) )
= $true )
| ( ( SV71
= ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(528,plain,
! [SV58: $i,SV71: $i] :
( ( ( ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ ( sK13_SY46 @ SV71 @ SV58 ) ) @ SV58 )
| ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) )
= $true )
| ( ( SV71
= ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(529,plain,
! [SV72: $i,SV58: $i] :
( ( ( ~ ! [SY103: $i] :
( ! [SY92: $i] :
~ ( in @ ( ordered_pair @ SY103 @ SY92 ) @ SV58 )
| ( in @ SY103 @ SV72 ) ) )
= $false )
| ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(530,plain,
! [SV58: $i,SV72: $i] :
( ( ( ~ ! [SY105: $i] :
( ~ ( in @ SY105 @ SV72 )
| ( in @ ( ordered_pair @ SY105 @ ( sK11_D @ SY105 @ SV72 @ SV58 ) ) @ SV58 ) ) )
= $false )
| ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(531,plain,
! [SV59: $i] :
( ( ( ! [SY94: $i] :
( ~ ( in @ SY94 @ ( relation_dom @ SV59 ) )
| ! [SY95: $i] :
( ( SY95
!= ( apply @ SV59 @ SY94 ) )
| ( in @ ( ordered_pair @ SY94 @ SY95 ) @ SV59 ) ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(532,plain,
! [SV59: $i] :
( ( ( ! [SY96: $i] :
( ~ ( in @ SY96 @ ( relation_dom @ SV59 ) )
| ! [SY97: $i] :
( ~ ( in @ ( ordered_pair @ SY96 @ SY97 ) @ SV59 )
| ( SY97
= ( apply @ SV59 @ SY96 ) ) ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(533,plain,
! [SV59: $i] :
( ( ( ! [SY98: $i] :
( ( in @ SY98 @ ( relation_dom @ SV59 ) )
| ! [SY99: $i] :
( ( SY99
!= ( apply @ SV59 @ SY98 ) )
| ( SY99 = empty_set ) ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(534,plain,
! [SV59: $i] :
( ( ( ! [SY100: $i] :
( ( in @ SY100 @ ( relation_dom @ SV59 ) )
| ! [SY101: $i] :
( ( SY101 != empty_set )
| ( SY101
= ( apply @ SV59 @ SY100 ) ) ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(535,plain,
! [SV58: $i,SV71: $i] :
( ( ( ! [SY102: $i] :
~ ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ SY102 ) @ SV58 ) )
= $true )
| ( ( ~ ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) )
= $true )
| ( ( SV71
= ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(536,plain,
! [SV58: $i,SV71: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ ( sK13_SY46 @ SV71 @ SV58 ) ) @ SV58 )
= $true )
| ( ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 )
= $true )
| ( ( SV71
= ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(537,plain,
! [SV72: $i,SV58: $i] :
( ( ( ! [SY103: $i] :
( ! [SY92: $i] :
~ ( in @ ( ordered_pair @ SY103 @ SY92 ) @ SV58 )
| ( in @ SY103 @ SV72 ) ) )
= $true )
| ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(538,plain,
! [SV58: $i,SV72: $i] :
( ( ( ! [SY105: $i] :
( ~ ( in @ SY105 @ SV72 )
| ( in @ ( ordered_pair @ SY105 @ ( sK11_D @ SY105 @ SV72 @ SV58 ) ) @ SV58 ) ) )
= $true )
| ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(539,plain,
! [SV59: $i,SV73: $i] :
( ( ( ~ ( in @ SV73 @ ( relation_dom @ SV59 ) )
| ! [SY106: $i] :
( ( SY106
!= ( apply @ SV59 @ SV73 ) )
| ( in @ ( ordered_pair @ SV73 @ SY106 ) @ SV59 ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(540,plain,
! [SV59: $i,SV74: $i] :
( ( ( ~ ( in @ SV74 @ ( relation_dom @ SV59 ) )
| ! [SY107: $i] :
( ~ ( in @ ( ordered_pair @ SV74 @ SY107 ) @ SV59 )
| ( SY107
= ( apply @ SV59 @ SV74 ) ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(541,plain,
! [SV59: $i,SV75: $i] :
( ( ( ( in @ SV75 @ ( relation_dom @ SV59 ) )
| ! [SY108: $i] :
( ( SY108
!= ( apply @ SV59 @ SV75 ) )
| ( SY108 = empty_set ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(542,plain,
! [SV59: $i,SV76: $i] :
( ( ( ( in @ SV76 @ ( relation_dom @ SV59 ) )
| ! [SY109: $i] :
( ( SY109 != empty_set )
| ( SY109
= ( apply @ SV59 @ SV76 ) ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(543,plain,
! [SV77: $i,SV58: $i,SV71: $i] :
( ( ( ~ ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ SV77 ) @ SV58 ) )
= $true )
| ( ( ~ ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) )
= $true )
| ( ( SV71
= ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(544,plain,
! [SV72: $i,SV58: $i,SV78: $i] :
( ( ( ! [SY110: $i] :
~ ( in @ ( ordered_pair @ SV78 @ SY110 ) @ SV58 )
| ( in @ SV78 @ SV72 ) )
= $true )
| ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(545,plain,
! [SV58: $i,SV72: $i,SV79: $i] :
( ( ( ~ ( in @ SV79 @ SV72 )
| ( in @ ( ordered_pair @ SV79 @ ( sK11_D @ SV79 @ SV72 @ SV58 ) ) @ SV58 ) )
= $true )
| ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(546,plain,
! [SV59: $i,SV73: $i] :
( ( ( ~ ( in @ SV73 @ ( relation_dom @ SV59 ) ) )
= $true )
| ( ( ! [SY106: $i] :
( ( SY106
!= ( apply @ SV59 @ SV73 ) )
| ( in @ ( ordered_pair @ SV73 @ SY106 ) @ SV59 ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(547,plain,
! [SV59: $i,SV74: $i] :
( ( ( ~ ( in @ SV74 @ ( relation_dom @ SV59 ) ) )
= $true )
| ( ( ! [SY107: $i] :
( ~ ( in @ ( ordered_pair @ SV74 @ SY107 ) @ SV59 )
| ( SY107
= ( apply @ SV59 @ SV74 ) ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(548,plain,
! [SV59: $i,SV75: $i] :
( ( ( in @ SV75 @ ( relation_dom @ SV59 ) )
= $true )
| ( ( ! [SY108: $i] :
( ( SY108
!= ( apply @ SV59 @ SV75 ) )
| ( SY108 = empty_set ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(549,plain,
! [SV59: $i,SV76: $i] :
( ( ( in @ SV76 @ ( relation_dom @ SV59 ) )
= $true )
| ( ( ! [SY109: $i] :
( ( SY109 != empty_set )
| ( SY109
= ( apply @ SV59 @ SV76 ) ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(550,plain,
! [SV77: $i,SV58: $i,SV71: $i] :
( ( ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ SV77 ) @ SV58 )
= $false )
| ( ( ~ ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 ) )
= $true )
| ( ( SV71
= ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(551,plain,
! [SV72: $i,SV58: $i,SV78: $i] :
( ( ( ! [SY110: $i] :
~ ( in @ ( ordered_pair @ SV78 @ SY110 ) @ SV58 ) )
= $true )
| ( ( in @ SV78 @ SV72 )
= $true )
| ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(552,plain,
! [SV58: $i,SV72: $i,SV79: $i] :
( ( ( ~ ( in @ SV79 @ SV72 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV79 @ ( sK11_D @ SV79 @ SV72 @ SV58 ) ) @ SV58 )
= $true )
| ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(553,plain,
! [SV59: $i,SV73: $i] :
( ( ( in @ SV73 @ ( relation_dom @ SV59 ) )
= $false )
| ( ( ! [SY106: $i] :
( ( SY106
!= ( apply @ SV59 @ SV73 ) )
| ( in @ ( ordered_pair @ SV73 @ SY106 ) @ SV59 ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(554,plain,
! [SV59: $i,SV74: $i] :
( ( ( in @ SV74 @ ( relation_dom @ SV59 ) )
= $false )
| ( ( ! [SY107: $i] :
( ~ ( in @ ( ordered_pair @ SV74 @ SY107 ) @ SV59 )
| ( SY107
= ( apply @ SV59 @ SV74 ) ) ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(555,plain,
! [SV75: $i,SV59: $i,SV80: $i] :
( ( ( ( SV80
!= ( apply @ SV59 @ SV75 ) )
| ( SV80 = empty_set ) )
= $true )
| ( ( in @ SV75 @ ( relation_dom @ SV59 ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(556,plain,
! [SV76: $i,SV59: $i,SV81: $i] :
( ( ( ( SV81 != empty_set )
| ( SV81
= ( apply @ SV59 @ SV76 ) ) )
= $true )
| ( ( in @ SV76 @ ( relation_dom @ SV59 ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(557,plain,
! [SV77: $i,SV58: $i,SV71: $i] :
( ( ( in @ ( sK12_C @ SV71 @ SV58 ) @ SV71 )
= $false )
| ( ( in @ ( ordered_pair @ ( sK12_C @ SV71 @ SV58 ) @ SV77 ) @ SV58 )
= $false )
| ( ( SV71
= ( relation_dom @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(558,plain,
! [SV72: $i,SV58: $i,SV82: $i,SV78: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV78 @ SV82 ) @ SV58 ) )
= $true )
| ( ( in @ SV78 @ SV72 )
= $true )
| ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(559,plain,
! [SV58: $i,SV72: $i,SV79: $i] :
( ( ( in @ SV79 @ SV72 )
= $false )
| ( ( in @ ( ordered_pair @ SV79 @ ( sK11_D @ SV79 @ SV72 @ SV58 ) ) @ SV58 )
= $true )
| ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(560,plain,
! [SV73: $i,SV59: $i,SV83: $i] :
( ( ( ( SV83
!= ( apply @ SV59 @ SV73 ) )
| ( in @ ( ordered_pair @ SV73 @ SV83 ) @ SV59 ) )
= $true )
| ( ( in @ SV73 @ ( relation_dom @ SV59 ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(561,plain,
! [SV59: $i,SV84: $i,SV74: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV74 @ SV84 ) @ SV59 )
| ( SV84
= ( apply @ SV59 @ SV74 ) ) )
= $true )
| ( ( in @ SV74 @ ( relation_dom @ SV59 ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(562,plain,
! [SV75: $i,SV59: $i,SV80: $i] :
( ( ( ( SV80
!= ( apply @ SV59 @ SV75 ) ) )
= $true )
| ( ( SV80 = empty_set )
= $true )
| ( ( in @ SV75 @ ( relation_dom @ SV59 ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(563,plain,
! [SV76: $i,SV59: $i,SV81: $i] :
( ( ( ( SV81 != empty_set ) )
= $true )
| ( ( SV81
= ( apply @ SV59 @ SV76 ) )
= $true )
| ( ( in @ SV76 @ ( relation_dom @ SV59 ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(564,plain,
! [SV72: $i,SV58: $i,SV82: $i,SV78: $i] :
( ( ( in @ ( ordered_pair @ SV78 @ SV82 ) @ SV58 )
= $false )
| ( ( in @ SV78 @ SV72 )
= $true )
| ( ( SV72
= ( relation_dom @ SV58 ) )
= $false )
| ( ( relation @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(565,plain,
! [SV73: $i,SV59: $i,SV83: $i] :
( ( ( ( SV83
!= ( apply @ SV59 @ SV73 ) ) )
= $true )
| ( ( in @ ( ordered_pair @ SV73 @ SV83 ) @ SV59 )
= $true )
| ( ( in @ SV73 @ ( relation_dom @ SV59 ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(566,plain,
! [SV59: $i,SV84: $i,SV74: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV74 @ SV84 ) @ SV59 ) )
= $true )
| ( ( SV84
= ( apply @ SV59 @ SV74 ) )
= $true )
| ( ( in @ SV74 @ ( relation_dom @ SV59 ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(567,plain,
! [SV75: $i,SV59: $i,SV80: $i] :
( ( ( SV80
= ( apply @ SV59 @ SV75 ) )
= $false )
| ( ( SV80 = empty_set )
= $true )
| ( ( in @ SV75 @ ( relation_dom @ SV59 ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(568,plain,
! [SV76: $i,SV59: $i,SV81: $i] :
( ( ( SV81 = empty_set )
= $false )
| ( ( SV81
= ( apply @ SV59 @ SV76 ) )
= $true )
| ( ( in @ SV76 @ ( relation_dom @ SV59 ) )
= $true )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(569,plain,
! [SV73: $i,SV59: $i,SV83: $i] :
( ( ( SV83
= ( apply @ SV59 @ SV73 ) )
= $false )
| ( ( in @ ( ordered_pair @ SV73 @ SV83 ) @ SV59 )
= $true )
| ( ( in @ SV73 @ ( relation_dom @ SV59 ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(570,plain,
! [SV59: $i,SV84: $i,SV74: $i] :
( ( ( in @ ( ordered_pair @ SV74 @ SV84 ) @ SV59 )
= $false )
| ( ( SV84
= ( apply @ SV59 @ SV74 ) )
= $true )
| ( ( in @ SV74 @ ( relation_dom @ SV59 ) )
= $false )
| ( ( function @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(571,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[343,570,569,568,567,564,559,557,536,507,506,504,503,500,499,498,487,486,485,484,483,482,472,469,468,467,466,465,464,463,455,453,452,449,445,444,443,442,415,413,412,393,388,371,370,361,352,349,348,347,346,345,344]) ).
thf(572,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[571,335]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SEU212+1 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.16 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Sun Jun 19 18:52:14 EDT 2022
% 0.15/0.38 % CPUTime :
% 0.15/0.39
% 0.15/0.39 No.of.Axioms: 34
% 0.15/0.39
% 0.15/0.39 Length.of.Defs: 0
% 0.15/0.39
% 0.15/0.39 Contains.Choice.Funs: false
% 0.23/0.40 .
% 0.23/0.41 (rf:0,axioms:34,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:36,loop_count:0,foatp_calls:0,translation:fof_full).............................
% 0.61/0.85
% 0.61/0.85 ********************************
% 0.61/0.85 * All subproblems solved! *
% 0.61/0.85 ********************************
% 0.61/0.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:36,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:571,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.76/0.97
% 0.76/0.97 %**** Beginning of derivation protocol ****
% 0.76/0.97 % SZS output start CNFRefutation
% See solution above
% 0.76/0.97
% 0.76/0.97 %**** End of derivation protocol ****
% 0.76/0.97 %**** no. of clauses in derivation: 572 ****
% 0.76/0.97 %**** clause counter: 571 ****
% 0.76/0.97
% 0.76/0.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:36,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:571,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------