TSTP Solution File: SEU383+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU383+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 : n032.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 12:11:20 EDT 2022
% Result : Theorem 5.77s 5.98s
% Output : CNFRefutation 5.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 85
% Syntax : Number of formulae : 567 ( 283 unt; 40 typ; 0 def)
% Number of atoms : 3697 ( 993 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 6529 (1288 ~;1080 |; 148 &;3923 @)
% ( 14 <=>; 76 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 40 usr; 11 con; 0-3 aty)
% Number of variables : 768 ( 0 ^ 742 !; 26 ?; 768 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
thf(tp_bottom_of_relstr,type,
bottom_of_relstr: $i > $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_carrier,type,
empty_carrier: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_filtered_subset,type,
filtered_subset: $i > $i > $o ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_join_on_relstr,type,
join_on_relstr: $i > $i > $i ).
thf(tp_lower_bounded_relstr,type,
lower_bounded_relstr: $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_element,type,
proper_element: $i > $i > $o ).
thf(tp_reflexive_relstr,type,
reflexive_relstr: $i > $o ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_related,type,
related: $i > $i > $i > $o ).
thf(tp_sK10_A,type,
sK10_A: $i ).
thf(tp_sK11_B,type,
sK11_B: $i > $i ).
thf(tp_sK12_A,type,
sK12_A: $i ).
thf(tp_sK13_B,type,
sK13_B: $i > $i ).
thf(tp_sK14_B,type,
sK14_B: $i > $i ).
thf(tp_sK15_A,type,
sK15_A: $i ).
thf(tp_sK16_A,type,
sK16_A: $i ).
thf(tp_sK17_C,type,
sK17_C: $i > $i > $i ).
thf(tp_sK18_SY68,type,
sK18_SY68: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY67,type,
sK2_SY67: $i ).
thf(tp_sK3_C,type,
sK3_C: $i > $i > $i ).
thf(tp_sK4_B,type,
sK4_B: $i > $i ).
thf(tp_sK5_B,type,
sK5_B: $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_B,type,
sK7_B: $i > $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_B,type,
sK9_B: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_transitive_relstr,type,
transitive_relstr: $i > $o ).
thf(tp_upper_relstr_subset,type,
upper_relstr_subset: $i > $i > $o ).
thf(tp_v1_yellow_3,type,
v1_yellow_3: $i > $o ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(7,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( related @ A @ ( bottom_of_relstr @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_yellow_0) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(12,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(13,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(14,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(15,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(16,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(17,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(18,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(19,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(20,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(21,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(22,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc10_waybel_0) ).
thf(23,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(24,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(25,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(26,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(27,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(28,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(30,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(31,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(32,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(33,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_yellow_0) ).
thf(34,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_0) ).
thf(36,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(37,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( upper_relstr_subset @ B @ A )
<=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ B )
& ( related @ A @ C @ D ) )
=> ( in @ D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d20_waybel_0) ).
thf(38,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( bottom_of_relstr @ A )
= ( join_on_relstr @ A @ empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_yellow_0) ).
thf(39,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ~ ( v1_yellow_3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_yellow_3) ).
thf(40,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ~ ( v1_yellow_3 @ A )
=> ~ ( empty_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_yellow_3) ).
thf(41,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(42,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( empty_carrier @ A )
=> ( v1_yellow_3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_yellow_3) ).
thf(43,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(45,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) )
<=> ~ ( in @ ( bottom_of_relstr @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_waybel_7) ).
thf(46,negated_conjecture,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) )
<=> ~ ( in @ ( bottom_of_relstr @ A ) @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[45]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A )
& ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
=> ( ( proper_element @ B @ ( powerset @ ( the_carrier @ A ) ) )
<=> ~ ( in @ ( bottom_of_relstr @ A ) @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[46]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( proper_element @ B @ ( powerset @ A ) )
<=> ( B != A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(52,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(53,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( related @ A @ ( bottom_of_relstr @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(59,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(61,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(62,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(63,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(64,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(65,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(66,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(67,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(68,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( rel_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B )
& ( filtered_subset @ B @ A )
& ( upper_relstr_subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(70,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(71,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(72,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(73,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(74,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(75,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(76,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(77,plain,
$true = $true,
inference(unfold_def,[status(thm)],[30]) ).
thf(78,plain,
$true = $true,
inference(unfold_def,[status(thm)],[31]) ).
thf(79,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(80,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(81,plain,
$true = $true,
inference(unfold_def,[status(thm)],[34]) ).
thf(82,plain,
( ( ! [A: $i,B: $i] :
( ( rel_str @ A )
=> ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(83,plain,
$true = $true,
inference(unfold_def,[status(thm)],[36]) ).
thf(84,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( upper_relstr_subset @ B @ A )
<=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( in @ C @ B )
& ( related @ A @ C @ D ) )
=> ( in @ D @ B ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(85,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( bottom_of_relstr @ A )
= ( join_on_relstr @ A @ empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(86,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( ~ ( empty_carrier @ A )
& ( reflexive_relstr @ A ) )
=> ( ~ ( empty_carrier @ A )
& ~ ( v1_yellow_3 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(87,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ~ ( v1_yellow_3 @ A )
=> ~ ( empty_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(88,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(89,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( empty_carrier @ A )
=> ( v1_yellow_3 @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(90,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(92,plain,
( ( ( ~ ( empty_carrier @ sK1_A )
& ( reflexive_relstr @ sK1_A )
& ( transitive_relstr @ sK1_A )
& ( antisymmetric_relstr @ sK1_A )
& ( lower_bounded_relstr @ sK1_A )
& ( rel_str @ sK1_A ) )
=> ! [SY67: $i] :
( ( ~ ( empty @ SY67 )
& ( filtered_subset @ SY67 @ sK1_A )
& ( upper_relstr_subset @ SY67 @ sK1_A )
& ( element @ SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
=> ( ( proper_element @ SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
<=> ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ SY67 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[47]) ).
thf(93,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[92]) ).
thf(94,plain,
( ( reflexive_relstr @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[92]) ).
thf(95,plain,
( ( transitive_relstr @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[92]) ).
thf(96,plain,
( ( antisymmetric_relstr @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[92]) ).
thf(97,plain,
( ( lower_bounded_relstr @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[92]) ).
thf(98,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[92]) ).
thf(99,plain,
( ( ! [SY67: $i] :
( ( ~ ( empty @ SY67 )
& ( filtered_subset @ SY67 @ sK1_A )
& ( upper_relstr_subset @ SY67 @ sK1_A )
& ( element @ SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
=> ( ( proper_element @ SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
<=> ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ SY67 ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[92]) ).
thf(100,plain,
( ( ~ ! [SY67: $i] :
( ( ~ ( empty @ SY67 )
& ( filtered_subset @ SY67 @ sK1_A )
& ( upper_relstr_subset @ SY67 @ sK1_A )
& ( element @ SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
=> ( ( proper_element @ SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
<=> ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ SY67 ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[99]) ).
thf(101,plain,
( ( ~ ( empty @ sK2_SY67 )
& ( filtered_subset @ sK2_SY67 @ sK1_A )
& ( upper_relstr_subset @ sK2_SY67 @ sK1_A )
& ( element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) )
& ( ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(102,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(104,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( B = A )
| ( proper_element @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( proper_element @ B @ ( powerset @ A ) )
| ( B != A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(106,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(107,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(108,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( lower_bounded_relstr @ A )
| ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ( related @ A @ ( bottom_of_relstr @ A ) @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_C @ B @ A ) @ A )
| ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
& ( ( in @ ( sK3_C @ B @ A ) @ A )
| ( in @ ( sK3_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(113,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(114,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK4_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK4_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(115,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK5_B @ A ) )
& ( finite @ ( sK5_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(116,plain,
( ( ( one_sorted_str @ sK6_A )
& ~ ( empty_carrier @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(117,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK7_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK7_B @ A ) )
& ( finite @ ( sK7_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(118,plain,
( ( ~ ( empty @ sK8_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(119,plain,
( ( ! [A: $i] :
( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK9_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(120,plain,
( ( empty @ sK10_A )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(121,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK11_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK11_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(122,plain,
( ( ~ ( empty @ sK12_A )
& ( finite @ sK12_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(123,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( rel_str @ A )
| ( ( element @ ( sK13_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK13_B @ A ) )
& ( filtered_subset @ ( sK13_B @ A ) @ A )
& ( upper_relstr_subset @ ( sK13_B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(124,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(125,plain,
( ( ! [A: $i] : ( element @ ( sK14_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(126,plain,
( ( one_sorted_str @ sK15_A )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(127,plain,
( ( rel_str @ sK16_A )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(128,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(129,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(130,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ! [B: $i] : ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(131,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( ( element @ ( sK17_C @ B @ A ) @ ( the_carrier @ A ) )
& ( element @ ( sK18_SY68 @ B @ A ) @ ( the_carrier @ A ) )
& ( in @ ( sK17_C @ B @ A ) @ B )
& ( related @ A @ ( sK17_C @ B @ A ) @ ( sK18_SY68 @ B @ A ) )
& ~ ( in @ ( sK18_SY68 @ B @ A ) @ B ) )
| ( upper_relstr_subset @ B @ A ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( upper_relstr_subset @ B @ A )
| ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ! [D: $i] :
( ~ ( element @ D @ ( the_carrier @ A ) )
| ~ ( in @ C @ B )
| ~ ( related @ A @ C @ D )
| ( in @ D @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(132,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ( bottom_of_relstr @ A )
= ( join_on_relstr @ A @ empty_set ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(133,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( empty_carrier @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( v1_yellow_3 @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(134,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( v1_yellow_3 @ A )
| ~ ( empty_carrier @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(135,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(136,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( empty_carrier @ A )
| ( v1_yellow_3 @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(137,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(138,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(139,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(140,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(141,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( empty_carrier @ A )
| ( v1_yellow_3 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(142,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(143,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( v1_yellow_3 @ A )
| ~ ( empty_carrier @ A ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(144,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( empty_carrier @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( v1_yellow_3 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(145,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ( bottom_of_relstr @ A )
= ( join_on_relstr @ A @ empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(146,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ( ( element @ ( sK17_C @ B @ A ) @ ( the_carrier @ A ) )
& ( element @ ( sK18_SY68 @ B @ A ) @ ( the_carrier @ A ) )
& ( in @ ( sK17_C @ B @ A ) @ B )
& ( related @ A @ ( sK17_C @ B @ A ) @ ( sK18_SY68 @ B @ A ) )
& ~ ( in @ ( sK18_SY68 @ B @ A ) @ B ) )
| ( upper_relstr_subset @ B @ A ) )
& ! [B: $i] :
( ~ ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
| ~ ( upper_relstr_subset @ B @ A )
| ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ! [D: $i] :
( ~ ( element @ D @ ( the_carrier @ A ) )
| ~ ( in @ C @ B )
| ~ ( related @ A @ C @ D )
| ( in @ D @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(147,plain,
$true = $true,
inference(copy,[status(thm)],[83]) ).
thf(148,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ! [B: $i] : ( element @ ( join_on_relstr @ A @ B ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(149,plain,
$true = $true,
inference(copy,[status(thm)],[81]) ).
thf(150,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( element @ ( bottom_of_relstr @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(151,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(152,plain,
$true = $true,
inference(copy,[status(thm)],[78]) ).
thf(153,plain,
$true = $true,
inference(copy,[status(thm)],[77]) ).
thf(154,plain,
$true = $true,
inference(copy,[status(thm)],[76]) ).
thf(155,plain,
( ( rel_str @ sK16_A )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(156,plain,
( ( one_sorted_str @ sK15_A )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(157,plain,
( ( ! [A: $i] : ( element @ ( sK14_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(158,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(159,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(160,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(161,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( rel_str @ A )
| ( ( element @ ( sK13_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK13_B @ A ) )
& ( filtered_subset @ ( sK13_B @ A ) @ A )
& ( upper_relstr_subset @ ( sK13_B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(162,plain,
( ( ~ ( empty @ sK12_A )
& ( finite @ sK12_A ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(163,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK11_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK11_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(164,plain,
( ( empty @ sK10_A )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(165,plain,
( ( ! [A: $i] :
( ( element @ ( sK9_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK9_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(166,plain,
( ( ~ ( empty @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(167,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK7_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK7_B @ A ) )
& ( finite @ ( sK7_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(168,plain,
( ( ( one_sorted_str @ sK6_A )
& ~ ( empty_carrier @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(169,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK5_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK5_B @ A ) )
& ( finite @ ( sK5_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(170,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK4_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK4_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(171,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(172,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(173,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(174,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK3_C @ B @ A ) @ A )
| ~ ( in @ ( sK3_C @ B @ A ) @ B ) )
& ( ( in @ ( sK3_C @ B @ A ) @ A )
| ( in @ ( sK3_C @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(175,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(176,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( lower_bounded_relstr @ A )
| ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ( related @ A @ ( bottom_of_relstr @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(177,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(178,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(179,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( B = A )
| ( proper_element @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ~ ( proper_element @ B @ ( powerset @ A ) )
| ( B != A ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(180,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(181,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(182,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(183,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(184,plain,
( ( lower_bounded_relstr @ sK1_A )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(185,plain,
( ( antisymmetric_relstr @ sK1_A )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(186,plain,
( ( transitive_relstr @ sK1_A )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(187,plain,
( ( reflexive_relstr @ sK1_A )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(188,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(189,plain,
( ( ~ ( empty @ sK2_SY67 )
& ( filtered_subset @ sK2_SY67 @ sK1_A )
& ( upper_relstr_subset @ sK2_SY67 @ sK1_A )
& ( element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
& ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) )
& ( ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(190,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK11_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK11_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(191,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ( element @ ( sK4_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(192,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK9_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK9_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(193,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( ~ ( element @ ( sK17_C @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( element @ ( sK18_SY68 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SX1 @ SX0 ) @ SX1 )
| ~ ( related @ SX0 @ ( sK17_C @ SX1 @ SX0 ) @ ( sK18_SY68 @ SX1 @ SX0 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SX1 @ SX0 ) @ SX1 ) ) ) )
| ( upper_relstr_subset @ SX1 @ SX0 ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ( upper_relstr_subset @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ~ ( related @ SX0 @ SX2 @ SX3 )
| ( in @ SX3 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(194,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK7_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK7_B @ SX0 ) ) )
| ~ ( finite @ ( sK7_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(195,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( SX1 = SX0 )
| ( proper_element @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( proper_element @ SX1 @ ( powerset @ SX0 ) )
| ( SX1 != SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(196,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK3_C @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(197,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(198,plain,
( ( ~ ( ~ ~ ( empty @ sK12_A )
| ~ ( finite @ sK12_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(199,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK5_B @ SX0 ) ) )
| ~ ( finite @ ( sK5_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(200,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( reflexive_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( reflexive_relstr @ SX0 )
| ~ ( v1_yellow_3 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(201,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SX0 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SX0 ) @ SX0 ) )
| ~ ( upper_relstr_subset @ ( sK13_B @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(202,plain,
( ( ~ ( ~ ( one_sorted_str @ sK6_A )
| ~ ~ ( empty_carrier @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(203,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY67 )
| ~ ( filtered_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( upper_relstr_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
| ~ ~ ( ~ ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) )
| ~ ( ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(204,plain,
! [SV1: $i] :
( ( ! [SY69: $i] :
( ~ ( in @ SV1 @ SY69 )
| ~ ( in @ SY69 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(205,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( finite @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(206,plain,
! [SV3: $i] :
( ( ~ ( rel_str @ SV3 )
| ~ ( empty_carrier @ SV3 )
| ( v1_yellow_3 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(207,plain,
! [SV4: $i] :
( ( ~ ( finite @ SV4 )
| ! [SY70: $i] :
( ~ ( element @ SY70 @ ( powerset @ SV4 ) )
| ( finite @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(208,plain,
! [SV5: $i] :
( ( ~ ( rel_str @ SV5 )
| ( v1_yellow_3 @ SV5 )
| ~ ( empty_carrier @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(209,plain,
! [SV6: $i] :
( ( ~ ( rel_str @ SV6 )
| ( ( bottom_of_relstr @ SV6 )
= ( join_on_relstr @ SV6 @ empty_set ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(210,plain,
! [SV7: $i] :
( ( ~ ( rel_str @ SV7 )
| ! [SY71: $i] : ( element @ ( join_on_relstr @ SV7 @ SY71 ) @ ( the_carrier @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(211,plain,
! [SV8: $i] :
( ( ~ ( rel_str @ SV8 )
| ( element @ ( bottom_of_relstr @ SV8 ) @ ( the_carrier @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(212,plain,
! [SV9: $i] :
( ( ~ ( rel_str @ SV9 )
| ( one_sorted_str @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(213,plain,
! [SV10: $i] :
( ( element @ ( sK14_B @ SV10 ) @ SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(214,plain,
! [SV11: $i] :
( ( ( empty_carrier @ SV11 )
| ~ ( one_sorted_str @ SV11 )
| ~ ( empty @ ( the_carrier @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(215,plain,
! [SV12: $i] :
( ( ~ ( empty @ ( powerset @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(216,plain,
( ( empty @ sK8_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(217,plain,
! [SV13: $i] :
( ( subset @ SV13 @ SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(218,plain,
! [SV14: $i] :
( ( ! [SY72: $i] :
( ~ ( in @ SV14 @ SY72 )
| ( element @ SV14 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(219,plain,
! [SV15: $i] :
( ( ! [SY73: $i] :
( ~ ( element @ SV15 @ SY73 )
| ( empty @ SY73 )
| ( in @ SV15 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(220,plain,
! [SV16: $i] :
( ( ( empty_carrier @ SV16 )
| ~ ( antisymmetric_relstr @ SV16 )
| ~ ( lower_bounded_relstr @ SV16 )
| ~ ( rel_str @ SV16 )
| ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV16 ) )
| ( related @ SV16 @ ( bottom_of_relstr @ SV16 ) @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(221,plain,
! [SV17: $i] :
( ( ! [SY75: $i,SY76: $i] :
( ~ ( element @ SY75 @ ( powerset @ SY76 ) )
| ~ ( in @ SV17 @ SY75 )
| ( element @ SV17 @ SY76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(222,plain,
! [SV18: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ~ ( element @ SY77 @ ( powerset @ SY78 ) )
| ~ ( in @ SV18 @ SY77 )
| ~ ( empty @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(223,plain,
! [SV19: $i] :
( ( ~ ( empty @ SV19 )
| ( SV19 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(224,plain,
! [SV20: $i] :
( ( ! [SY79: $i] :
( ~ ( empty @ SY79 )
| ~ ( in @ SV20 @ SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(225,plain,
! [SV21: $i] :
( ( ! [SY80: $i] :
( ( SV21 = SY80 )
| ~ ( empty @ SV21 )
| ~ ( empty @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(226,plain,
( ( empty_carrier @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(227,plain,
! [SV22: $i] :
( ( ( empty @ SV22 )
| ~ ( ~ ( element @ ( sK11_B @ SV22 ) @ ( powerset @ SV22 ) )
| ~ ~ ( empty @ ( sK11_B @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(228,plain,
! [SV23: $i] :
( ( ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 )
| ~ ( ~ ( element @ ( sK4_B @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(229,plain,
! [SV24: $i] :
( ( ~ ( ~ ( element @ ( sK9_B @ SV24 ) @ ( powerset @ SV24 ) )
| ~ ( empty @ ( sK9_B @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(230,plain,
! [SV25: $i] :
( ( ~ ( rel_str @ SV25 )
| ~ ( ~ ! [SY81: $i] :
( ~ ( element @ SY81 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK17_C @ SY81 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ( element @ ( sK18_SY68 @ SY81 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SY81 @ SV25 ) @ SY81 )
| ~ ( related @ SV25 @ ( sK17_C @ SY81 @ SV25 ) @ ( sK18_SY68 @ SY81 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SY81 @ SV25 ) @ SY81 ) ) ) )
| ( upper_relstr_subset @ SY81 @ SV25 ) )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( upper_relstr_subset @ SY82 @ SV25 )
| ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV25 ) )
| ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SY83 @ SY82 )
| ~ ( related @ SV25 @ SY83 @ SY84 )
| ( in @ SY84 @ SY82 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(231,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
| ~ ( ~ ~ ( ~ ( element @ ( sK7_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK7_B @ SV26 ) ) )
| ~ ( finite @ ( sK7_B @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(232,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( SX1 = SX0 )
| ( proper_element @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( proper_element @ SX1 @ ( powerset @ SX0 ) )
| ( SX1 != SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(233,plain,
! [SV27: $i] :
( ( ! [SY85: $i] :
( ~ ( ~ ( ~ ( in @ ( sK3_C @ SY85 @ SV27 ) @ SV27 )
| ~ ( in @ ( sK3_C @ SY85 @ SV27 ) @ SY85 ) )
| ~ ( ( in @ ( sK3_C @ SY85 @ SV27 ) @ SV27 )
| ( in @ ( sK3_C @ SY85 @ SV27 ) @ SY85 ) ) )
| ( SV27 = SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(234,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(235,plain,
( ( ~ ~ ( empty @ sK12_A )
| ~ ( finite @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(236,plain,
! [SV28: $i] :
( ( ( empty @ SV28 )
| ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ ( sK5_B @ SV28 ) ) )
| ~ ( finite @ ( sK5_B @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(237,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( reflexive_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( reflexive_relstr @ SX0 )
| ~ ( v1_yellow_3 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(238,plain,
! [SV29: $i] :
( ( ( empty_carrier @ SV29 )
| ~ ( reflexive_relstr @ SV29 )
| ~ ( transitive_relstr @ SV29 )
| ~ ( rel_str @ SV29 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
| ~ ( upper_relstr_subset @ ( sK13_B @ SV29 ) @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(239,plain,
( ( ~ ( one_sorted_str @ sK6_A )
| ~ ~ ( empty_carrier @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(240,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY67 )
| ~ ( filtered_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( upper_relstr_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
| ~ ~ ( ~ ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) )
| ~ ( ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(241,plain,
! [SV30: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV30 )
| ~ ( in @ SV30 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(242,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( finite @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(243,plain,
! [SV3: $i] :
( ( ( ~ ( rel_str @ SV3 ) )
= $true )
| ( ( ~ ( empty_carrier @ SV3 )
| ( v1_yellow_3 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(244,plain,
! [SV4: $i] :
( ( ( ~ ( finite @ SV4 ) )
= $true )
| ( ( ! [SY70: $i] :
( ~ ( element @ SY70 @ ( powerset @ SV4 ) )
| ( finite @ SY70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(245,plain,
! [SV5: $i] :
( ( ( ~ ( rel_str @ SV5 ) )
= $true )
| ( ( ( v1_yellow_3 @ SV5 )
| ~ ( empty_carrier @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(246,plain,
! [SV6: $i] :
( ( ( ~ ( rel_str @ SV6 ) )
= $true )
| ( ( ( bottom_of_relstr @ SV6 )
= ( join_on_relstr @ SV6 @ empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(247,plain,
! [SV7: $i] :
( ( ( ~ ( rel_str @ SV7 ) )
= $true )
| ( ( ! [SY71: $i] : ( element @ ( join_on_relstr @ SV7 @ SY71 ) @ ( the_carrier @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(248,plain,
! [SV8: $i] :
( ( ( ~ ( rel_str @ SV8 ) )
= $true )
| ( ( element @ ( bottom_of_relstr @ SV8 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(249,plain,
! [SV9: $i] :
( ( ( ~ ( rel_str @ SV9 ) )
= $true )
| ( ( one_sorted_str @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(250,plain,
! [SV11: $i] :
( ( ( ( empty_carrier @ SV11 )
| ~ ( one_sorted_str @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(251,plain,
! [SV12: $i] :
( ( empty @ ( powerset @ SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(252,plain,
! [SV31: $i,SV14: $i] :
( ( ~ ( in @ SV14 @ SV31 )
| ( element @ SV14 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(253,plain,
! [SV32: $i,SV15: $i] :
( ( ~ ( element @ SV15 @ SV32 )
| ( empty @ SV32 )
| ( in @ SV15 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(254,plain,
! [SV16: $i] :
( ( ( ( empty_carrier @ SV16 )
| ~ ( antisymmetric_relstr @ SV16 )
| ~ ( lower_bounded_relstr @ SV16 )
| ~ ( rel_str @ SV16 ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV16 ) )
| ( related @ SV16 @ ( bottom_of_relstr @ SV16 ) @ SY74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(255,plain,
! [SV17: $i,SV33: $i] :
( ( ! [SY86: $i] :
( ~ ( element @ SV33 @ ( powerset @ SY86 ) )
| ~ ( in @ SV17 @ SV33 )
| ( element @ SV17 @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(256,plain,
! [SV18: $i,SV34: $i] :
( ( ! [SY87: $i] :
( ~ ( element @ SV34 @ ( powerset @ SY87 ) )
| ~ ( in @ SV18 @ SV34 )
| ~ ( empty @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(257,plain,
! [SV19: $i] :
( ( ( ~ ( empty @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(258,plain,
! [SV20: $i,SV35: $i] :
( ( ~ ( empty @ SV35 )
| ~ ( in @ SV20 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(259,plain,
! [SV36: $i,SV21: $i] :
( ( ( SV21 = SV36 )
| ~ ( empty @ SV21 )
| ~ ( empty @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(260,plain,
! [SV22: $i] :
( ( ( empty @ SV22 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_B @ SV22 ) @ ( powerset @ SV22 ) )
| ~ ~ ( empty @ ( sK11_B @ SV22 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(261,plain,
! [SV23: $i] :
( ( ( ( empty_carrier @ SV23 )
| ~ ( one_sorted_str @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK4_B @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(262,plain,
! [SV24: $i] :
( ( ~ ( element @ ( sK9_B @ SV24 ) @ ( powerset @ SV24 ) )
| ~ ( empty @ ( sK9_B @ SV24 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(263,plain,
! [SV25: $i] :
( ( ( ~ ( rel_str @ SV25 ) )
= $true )
| ( ( ~ ( ~ ! [SY81: $i] :
( ~ ( element @ SY81 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK17_C @ SY81 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ( element @ ( sK18_SY68 @ SY81 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SY81 @ SV25 ) @ SY81 )
| ~ ( related @ SV25 @ ( sK17_C @ SY81 @ SV25 ) @ ( sK18_SY68 @ SY81 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SY81 @ SV25 ) @ SY81 ) ) ) )
| ( upper_relstr_subset @ SY81 @ SV25 ) )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( upper_relstr_subset @ SY82 @ SV25 )
| ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV25 ) )
| ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SY83 @ SY82 )
| ~ ( related @ SV25 @ SY83 @ SY84 )
| ( in @ SY84 @ SY82 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(264,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK7_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK7_B @ SV26 ) ) )
| ~ ( finite @ ( sK7_B @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(265,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( SX1 = SX0 )
| ( proper_element @ SX1 @ ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(266,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( proper_element @ SX1 @ ( powerset @ SX0 ) )
| ( SX1 != SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(267,plain,
! [SV27: $i,SV37: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
| ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 ) )
| ~ ( ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
| ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 ) ) )
| ( SV27 = SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(268,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(269,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(270,plain,
( ( ~ ~ ( empty @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(271,plain,
( ( ~ ( finite @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(272,plain,
! [SV28: $i] :
( ( ( empty @ SV28 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK5_B @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ ( sK5_B @ SV28 ) ) )
| ~ ( finite @ ( sK5_B @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(273,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( reflexive_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(274,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( reflexive_relstr @ SX0 )
| ~ ( v1_yellow_3 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(275,plain,
! [SV29: $i] :
( ( ( ( empty_carrier @ SV29 )
| ~ ( reflexive_relstr @ SV29 )
| ~ ( transitive_relstr @ SV29 )
| ~ ( rel_str @ SV29 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
| ~ ( upper_relstr_subset @ ( sK13_B @ SV29 ) @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(276,plain,
( ( ~ ( one_sorted_str @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(277,plain,
( ( ~ ~ ( empty_carrier @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(278,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY67 )
| ~ ( filtered_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( upper_relstr_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(279,plain,
( ( ~ ~ ( ~ ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) )
| ~ ( ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(280,plain,
! [SV30: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV30 ) )
= $true )
| ( ( ~ ( in @ SV30 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(281,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( finite @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(282,plain,
! [SV3: $i] :
( ( ( rel_str @ SV3 )
= $false )
| ( ( ~ ( empty_carrier @ SV3 )
| ( v1_yellow_3 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(283,plain,
! [SV4: $i] :
( ( ( finite @ SV4 )
= $false )
| ( ( ! [SY70: $i] :
( ~ ( element @ SY70 @ ( powerset @ SV4 ) )
| ( finite @ SY70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(284,plain,
! [SV5: $i] :
( ( ( rel_str @ SV5 )
= $false )
| ( ( ( v1_yellow_3 @ SV5 )
| ~ ( empty_carrier @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(285,plain,
! [SV6: $i] :
( ( ( rel_str @ SV6 )
= $false )
| ( ( ( bottom_of_relstr @ SV6 )
= ( join_on_relstr @ SV6 @ empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(286,plain,
! [SV7: $i] :
( ( ( rel_str @ SV7 )
= $false )
| ( ( ! [SY71: $i] : ( element @ ( join_on_relstr @ SV7 @ SY71 ) @ ( the_carrier @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(287,plain,
! [SV8: $i] :
( ( ( rel_str @ SV8 )
= $false )
| ( ( element @ ( bottom_of_relstr @ SV8 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(288,plain,
! [SV9: $i] :
( ( ( rel_str @ SV9 )
= $false )
| ( ( one_sorted_str @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(289,plain,
! [SV11: $i] :
( ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( one_sorted_str @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(290,plain,
! [SV31: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV31 ) )
= $true )
| ( ( element @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(291,plain,
! [SV32: $i,SV15: $i] :
( ( ( ~ ( element @ SV15 @ SV32 ) )
= $true )
| ( ( ( empty @ SV32 )
| ( in @ SV15 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(292,plain,
! [SV16: $i] :
( ( ( ( empty_carrier @ SV16 )
| ~ ( antisymmetric_relstr @ SV16 )
| ~ ( lower_bounded_relstr @ SV16 ) )
= $true )
| ( ( ~ ( rel_str @ SV16 ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV16 ) )
| ( related @ SV16 @ ( bottom_of_relstr @ SV16 ) @ SY74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(293,plain,
! [SV17: $i,SV38: $i,SV33: $i] :
( ( ~ ( element @ SV33 @ ( powerset @ SV38 ) )
| ~ ( in @ SV17 @ SV33 )
| ( element @ SV17 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(294,plain,
! [SV18: $i,SV39: $i,SV34: $i] :
( ( ~ ( element @ SV34 @ ( powerset @ SV39 ) )
| ~ ( in @ SV18 @ SV34 )
| ~ ( empty @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(295,plain,
! [SV19: $i] :
( ( ( empty @ SV19 )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(296,plain,
! [SV20: $i,SV35: $i] :
( ( ( ~ ( empty @ SV35 ) )
= $true )
| ( ( ~ ( in @ SV20 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(297,plain,
! [SV36: $i,SV21: $i] :
( ( ( ( SV21 = SV36 )
| ~ ( empty @ SV21 ) )
= $true )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(298,plain,
! [SV22: $i] :
( ( ( ~ ( element @ ( sK11_B @ SV22 ) @ ( powerset @ SV22 ) )
| ~ ~ ( empty @ ( sK11_B @ SV22 ) ) )
= $false )
| ( ( empty @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(299,plain,
! [SV23: $i] :
( ( ( empty_carrier @ SV23 )
= $true )
| ( ( ~ ( one_sorted_str @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK4_B @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(300,plain,
! [SV24: $i] :
( ( ~ ( element @ ( sK9_B @ SV24 ) @ ( powerset @ SV24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(301,plain,
! [SV24: $i] :
( ( ~ ( empty @ ( sK9_B @ SV24 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(302,plain,
! [SV25: $i] :
( ( ( rel_str @ SV25 )
= $false )
| ( ( ~ ( ~ ! [SY81: $i] :
( ~ ( element @ SY81 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK17_C @ SY81 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ( element @ ( sK18_SY68 @ SY81 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SY81 @ SV25 ) @ SY81 )
| ~ ( related @ SV25 @ ( sK17_C @ SY81 @ SV25 ) @ ( sK18_SY68 @ SY81 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SY81 @ SV25 ) @ SY81 ) ) ) )
| ( upper_relstr_subset @ SY81 @ SV25 ) )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( upper_relstr_subset @ SY82 @ SV25 )
| ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV25 ) )
| ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SY83 @ SY82 )
| ~ ( related @ SV25 @ SY83 @ SY84 )
| ( in @ SY84 @ SY82 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(303,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK7_B @ SV26 ) ) )
| ~ ( finite @ ( sK7_B @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(304,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( SX1 = SX0 )
| ( proper_element @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(305,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( proper_element @ SX1 @ ( powerset @ SX0 ) )
| ( SX1 != SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(306,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
| ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 ) )
| ~ ( ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
| ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 ) ) ) )
= $true )
| ( ( SV27 = SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(307,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(308,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(309,plain,
( ( ~ ( empty @ sK12_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(310,plain,
( ( finite @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(311,plain,
! [SV28: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK5_B @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ ( sK5_B @ SV28 ) ) )
| ~ ( finite @ ( sK5_B @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(312,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( reflexive_relstr @ SX0 )
| ~ ( empty_carrier @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(313,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( empty_carrier @ SX0 )
| ~ ( reflexive_relstr @ SX0 )
| ~ ( v1_yellow_3 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(314,plain,
! [SV29: $i] :
( ( ( ( empty_carrier @ SV29 )
| ~ ( reflexive_relstr @ SV29 )
| ~ ( transitive_relstr @ SV29 ) )
= $true )
| ( ( ~ ( rel_str @ SV29 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
| ~ ( upper_relstr_subset @ ( sK13_B @ SV29 ) @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(315,plain,
( ( one_sorted_str @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(316,plain,
( ( ~ ( empty_carrier @ sK6_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(317,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY67 )
| ~ ( filtered_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( upper_relstr_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(318,plain,
( ( ~ ( ~ ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) )
| ~ ( ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(319,plain,
! [SV30: $i,SV1: $i] :
( ( ( in @ SV1 @ SV30 )
= $false )
| ( ( ~ ( in @ SV30 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(320,plain,
! [SV3: $i] :
( ( ( ~ ( empty_carrier @ SV3 ) )
= $true )
| ( ( v1_yellow_3 @ SV3 )
= $true )
| ( ( rel_str @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(321,plain,
! [SV4: $i,SV40: $i] :
( ( ( ~ ( element @ SV40 @ ( powerset @ SV4 ) )
| ( finite @ SV40 ) )
= $true )
| ( ( finite @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(322,plain,
! [SV5: $i] :
( ( ( v1_yellow_3 @ SV5 )
= $true )
| ( ( ~ ( empty_carrier @ SV5 ) )
= $true )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(323,plain,
! [SV41: $i,SV7: $i] :
( ( ( element @ ( join_on_relstr @ SV7 @ SV41 ) @ ( the_carrier @ SV7 ) )
= $true )
| ( ( rel_str @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(324,plain,
! [SV11: $i] :
( ( ( one_sorted_str @ SV11 )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(325,plain,
! [SV31: $i,SV14: $i] :
( ( ( in @ SV14 @ SV31 )
= $false )
| ( ( element @ SV14 @ SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(326,plain,
! [SV32: $i,SV15: $i] :
( ( ( element @ SV15 @ SV32 )
= $false )
| ( ( ( empty @ SV32 )
| ( in @ SV15 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(327,plain,
! [SV16: $i] :
( ( ( ( empty_carrier @ SV16 )
| ~ ( antisymmetric_relstr @ SV16 ) )
= $true )
| ( ( ~ ( lower_bounded_relstr @ SV16 ) )
= $true )
| ( ( ~ ( rel_str @ SV16 ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV16 ) )
| ( related @ SV16 @ ( bottom_of_relstr @ SV16 ) @ SY74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(328,plain,
! [SV17: $i,SV38: $i,SV33: $i] :
( ( ( ~ ( element @ SV33 @ ( powerset @ SV38 ) )
| ~ ( in @ SV17 @ SV33 ) )
= $true )
| ( ( element @ SV17 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(329,plain,
! [SV18: $i,SV39: $i,SV34: $i] :
( ( ( ~ ( element @ SV34 @ ( powerset @ SV39 ) )
| ~ ( in @ SV18 @ SV34 ) )
= $true )
| ( ( ~ ( empty @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(330,plain,
! [SV20: $i,SV35: $i] :
( ( ( empty @ SV35 )
= $false )
| ( ( ~ ( in @ SV20 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(331,plain,
! [SV36: $i,SV21: $i] :
( ( ( SV21 = SV36 )
= $true )
| ( ( ~ ( empty @ SV21 ) )
= $true )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(332,plain,
! [SV22: $i] :
( ( ( ~ ( element @ ( sK11_B @ SV22 ) @ ( powerset @ SV22 ) ) )
= $false )
| ( ( empty @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(333,plain,
! [SV22: $i] :
( ( ( ~ ~ ( empty @ ( sK11_B @ SV22 ) ) )
= $false )
| ( ( empty @ SV22 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(334,plain,
! [SV23: $i] :
( ( ( one_sorted_str @ SV23 )
= $false )
| ( ( empty_carrier @ SV23 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK4_B @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(335,plain,
! [SV24: $i] :
( ( element @ ( sK9_B @ SV24 ) @ ( powerset @ SV24 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(336,plain,
! [SV24: $i] :
( ( empty @ ( sK9_B @ SV24 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(337,plain,
! [SV25: $i] :
( ( ( ~ ! [SY81: $i] :
( ~ ( element @ SY81 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK17_C @ SY81 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ( element @ ( sK18_SY68 @ SY81 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SY81 @ SV25 ) @ SY81 )
| ~ ( related @ SV25 @ ( sK17_C @ SY81 @ SV25 ) @ ( sK18_SY68 @ SY81 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SY81 @ SV25 ) @ SY81 ) ) ) )
| ( upper_relstr_subset @ SY81 @ SV25 ) )
| ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( upper_relstr_subset @ SY82 @ SV25 )
| ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV25 ) )
| ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SY83 @ SY82 )
| ~ ( related @ SV25 @ SY83 @ SY84 )
| ( in @ SY84 @ SY82 ) ) ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(338,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK7_B @ SV26 ) ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(339,plain,
! [SV26: $i] :
( ( ( ~ ( finite @ ( sK7_B @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(340,plain,
! [SV42: $i] :
( ( ! [SY88: $i] :
( ~ ( element @ SY88 @ ( powerset @ SV42 ) )
| ( SY88 = SV42 )
| ( proper_element @ SY88 @ ( powerset @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(341,plain,
! [SV43: $i] :
( ( ! [SY89: $i] :
( ~ ( element @ SY89 @ ( powerset @ SV43 ) )
| ~ ( proper_element @ SY89 @ ( powerset @ SV43 ) )
| ( SY89 != SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(342,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
| ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 ) )
| ~ ( ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
| ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 ) ) )
= $false )
| ( ( SV27 = SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(343,plain,
! [SV44: $i] :
( ( ! [SY90: $i] :
( ~ ( element @ SV44 @ ( powerset @ SY90 ) )
| ( subset @ SV44 @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(344,plain,
! [SV45: $i] :
( ( ! [SY91: $i] :
( ~ ( subset @ SV45 @ SY91 )
| ( element @ SV45 @ ( powerset @ SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(345,plain,
( ( empty @ sK12_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(346,plain,
! [SV28: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK5_B @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ ( sK5_B @ SV28 ) ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(347,plain,
! [SV28: $i] :
( ( ( ~ ( finite @ ( sK5_B @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(348,plain,
! [SV46: $i] :
( ( ~ ( rel_str @ SV46 )
| ( empty_carrier @ SV46 )
| ~ ( reflexive_relstr @ SV46 )
| ~ ( empty_carrier @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(349,plain,
! [SV47: $i] :
( ( ~ ( rel_str @ SV47 )
| ( empty_carrier @ SV47 )
| ~ ( reflexive_relstr @ SV47 )
| ~ ( v1_yellow_3 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(350,plain,
! [SV29: $i] :
( ( ( ( empty_carrier @ SV29 )
| ~ ( reflexive_relstr @ SV29 ) )
= $true )
| ( ( ~ ( transitive_relstr @ SV29 ) )
= $true )
| ( ( ~ ( rel_str @ SV29 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
| ~ ( upper_relstr_subset @ ( sK13_B @ SV29 ) @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(351,plain,
( ( empty_carrier @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(352,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY67 )
| ~ ( filtered_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( upper_relstr_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(353,plain,
( ( ~ ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) )
| ~ ( ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(354,plain,
! [SV1: $i,SV30: $i] :
( ( ( in @ SV30 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(355,plain,
! [SV3: $i] :
( ( ( empty_carrier @ SV3 )
= $false )
| ( ( v1_yellow_3 @ SV3 )
= $true )
| ( ( rel_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(356,plain,
! [SV4: $i,SV40: $i] :
( ( ( ~ ( element @ SV40 @ ( powerset @ SV4 ) ) )
= $true )
| ( ( finite @ SV40 )
= $true )
| ( ( finite @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(357,plain,
! [SV5: $i] :
( ( ( empty_carrier @ SV5 )
= $false )
| ( ( v1_yellow_3 @ SV5 )
= $true )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(358,plain,
! [SV11: $i] :
( ( ( empty @ ( the_carrier @ SV11 ) )
= $false )
| ( ( empty_carrier @ SV11 )
= $true )
| ( ( one_sorted_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(359,plain,
! [SV15: $i,SV32: $i] :
( ( ( empty @ SV32 )
= $true )
| ( ( in @ SV15 @ SV32 )
= $true )
| ( ( element @ SV15 @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(360,plain,
! [SV16: $i] :
( ( ( empty_carrier @ SV16 )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV16 ) )
= $true )
| ( ( ~ ( lower_bounded_relstr @ SV16 ) )
= $true )
| ( ( ~ ( rel_str @ SV16 ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV16 ) )
| ( related @ SV16 @ ( bottom_of_relstr @ SV16 ) @ SY74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(361,plain,
! [SV17: $i,SV38: $i,SV33: $i] :
( ( ( ~ ( element @ SV33 @ ( powerset @ SV38 ) ) )
= $true )
| ( ( ~ ( in @ SV17 @ SV33 ) )
= $true )
| ( ( element @ SV17 @ SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(362,plain,
! [SV18: $i,SV39: $i,SV34: $i] :
( ( ( ~ ( element @ SV34 @ ( powerset @ SV39 ) ) )
= $true )
| ( ( ~ ( in @ SV18 @ SV34 ) )
= $true )
| ( ( ~ ( empty @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(363,plain,
! [SV35: $i,SV20: $i] :
( ( ( in @ SV20 @ SV35 )
= $false )
| ( ( empty @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(364,plain,
! [SV36: $i,SV21: $i] :
( ( ( empty @ SV21 )
= $false )
| ( ( SV21 = SV36 )
= $true )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(365,plain,
! [SV22: $i] :
( ( ( element @ ( sK11_B @ SV22 ) @ ( powerset @ SV22 ) )
= $true )
| ( ( empty @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(366,plain,
! [SV22: $i] :
( ( ( ~ ( empty @ ( sK11_B @ SV22 ) ) )
= $true )
| ( ( empty @ SV22 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(367,plain,
! [SV23: $i] :
( ( ( ~ ( element @ ( sK4_B @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) )
| ~ ~ ( empty @ ( sK4_B @ SV23 ) ) )
= $false )
| ( ( empty_carrier @ SV23 )
= $true )
| ( ( one_sorted_str @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(368,plain,
! [SV25: $i] :
( ( ( ~ ! [SY81: $i] :
( ~ ( element @ SY81 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK17_C @ SY81 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ( element @ ( sK18_SY68 @ SY81 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SY81 @ SV25 ) @ SY81 )
| ~ ( related @ SV25 @ ( sK17_C @ SY81 @ SV25 ) @ ( sK18_SY68 @ SY81 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SY81 @ SV25 ) @ SY81 ) ) ) )
| ( upper_relstr_subset @ SY81 @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(369,plain,
! [SV25: $i] :
( ( ( ~ ! [SY82: $i] :
( ~ ( element @ SY82 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( upper_relstr_subset @ SY82 @ SV25 )
| ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV25 ) )
| ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SY83 @ SY82 )
| ~ ( related @ SV25 @ SY83 @ SY84 )
| ( in @ SY84 @ SY82 ) ) ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(370,plain,
! [SV26: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK7_B @ SV26 ) ) ) )
= $true )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(371,plain,
! [SV26: $i] :
( ( ( finite @ ( sK7_B @ SV26 ) )
= $true )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(372,plain,
! [SV42: $i,SV48: $i] :
( ( ~ ( element @ SV48 @ ( powerset @ SV42 ) )
| ( SV48 = SV42 )
| ( proper_element @ SV48 @ ( powerset @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(373,plain,
! [SV43: $i,SV49: $i] :
( ( ~ ( element @ SV49 @ ( powerset @ SV43 ) )
| ~ ( proper_element @ SV49 @ ( powerset @ SV43 ) )
| ( SV49 != SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(374,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
| ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 ) ) )
= $false )
| ( ( SV27 = SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(375,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
| ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 ) ) )
= $false )
| ( ( SV27 = SV37 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[342]) ).
thf(376,plain,
! [SV50: $i,SV44: $i] :
( ( ~ ( element @ SV44 @ ( powerset @ SV50 ) )
| ( subset @ SV44 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(377,plain,
! [SV51: $i,SV45: $i] :
( ( ~ ( subset @ SV45 @ SV51 )
| ( element @ SV45 @ ( powerset @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(378,plain,
! [SV28: $i] :
( ( ( ~ ( ~ ( element @ ( sK5_B @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ ( sK5_B @ SV28 ) ) ) )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(379,plain,
! [SV28: $i] :
( ( ( finite @ ( sK5_B @ SV28 ) )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(380,plain,
! [SV46: $i] :
( ( ( ~ ( rel_str @ SV46 ) )
= $true )
| ( ( ( empty_carrier @ SV46 )
| ~ ( reflexive_relstr @ SV46 )
| ~ ( empty_carrier @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(381,plain,
! [SV47: $i] :
( ( ( ~ ( rel_str @ SV47 ) )
= $true )
| ( ( ( empty_carrier @ SV47 )
| ~ ( reflexive_relstr @ SV47 )
| ~ ( v1_yellow_3 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(382,plain,
! [SV29: $i] :
( ( ( empty_carrier @ SV29 )
= $true )
| ( ( ~ ( reflexive_relstr @ SV29 ) )
= $true )
| ( ( ~ ( transitive_relstr @ SV29 ) )
= $true )
| ( ( ~ ( rel_str @ SV29 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
| ~ ( upper_relstr_subset @ ( sK13_B @ SV29 ) @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(383,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY67 )
| ~ ( filtered_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( upper_relstr_subset @ sK2_SY67 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(384,plain,
( ( ~ ( element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(385,plain,
( ( ~ ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(386,plain,
( ( ~ ( ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(387,plain,
! [SV4: $i,SV40: $i] :
( ( ( element @ SV40 @ ( powerset @ SV4 ) )
= $false )
| ( ( finite @ SV40 )
= $true )
| ( ( finite @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(388,plain,
! [SV16: $i] :
( ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( empty_carrier @ SV16 )
= $true )
| ( ( ~ ( lower_bounded_relstr @ SV16 ) )
= $true )
| ( ( ~ ( rel_str @ SV16 ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV16 ) )
| ( related @ SV16 @ ( bottom_of_relstr @ SV16 ) @ SY74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(389,plain,
! [SV17: $i,SV38: $i,SV33: $i] :
( ( ( element @ SV33 @ ( powerset @ SV38 ) )
= $false )
| ( ( ~ ( in @ SV17 @ SV33 ) )
= $true )
| ( ( element @ SV17 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(390,plain,
! [SV18: $i,SV39: $i,SV34: $i] :
( ( ( element @ SV34 @ ( powerset @ SV39 ) )
= $false )
| ( ( ~ ( in @ SV18 @ SV34 ) )
= $true )
| ( ( ~ ( empty @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(391,plain,
! [SV21: $i,SV36: $i] :
( ( ( empty @ SV36 )
= $false )
| ( ( SV21 = SV36 )
= $true )
| ( ( empty @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(392,plain,
! [SV22: $i] :
( ( ( empty @ ( sK11_B @ SV22 ) )
= $false )
| ( ( empty @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(393,plain,
! [SV23: $i] :
( ( ( ~ ( element @ ( sK4_B @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) ) )
= $false )
| ( ( empty_carrier @ SV23 )
= $true )
| ( ( one_sorted_str @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[367]) ).
thf(394,plain,
! [SV23: $i] :
( ( ( ~ ~ ( empty @ ( sK4_B @ SV23 ) ) )
= $false )
| ( ( empty_carrier @ SV23 )
= $true )
| ( ( one_sorted_str @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[367]) ).
thf(395,plain,
! [SV25: $i] :
( ( ( ! [SY81: $i] :
( ~ ( element @ SY81 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK17_C @ SY81 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ( element @ ( sK18_SY68 @ SY81 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SY81 @ SV25 ) @ SY81 )
| ~ ( related @ SV25 @ ( sK17_C @ SY81 @ SV25 ) @ ( sK18_SY68 @ SY81 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SY81 @ SV25 ) @ SY81 ) ) ) )
| ( upper_relstr_subset @ SY81 @ SV25 ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(396,plain,
! [SV25: $i] :
( ( ( ! [SY82: $i] :
( ~ ( element @ SY82 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( upper_relstr_subset @ SY82 @ SV25 )
| ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV25 ) )
| ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SY83 @ SY82 )
| ~ ( related @ SV25 @ SY83 @ SY84 )
| ( in @ SY84 @ SY82 ) ) ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(397,plain,
! [SV26: $i] :
( ( ( ~ ( element @ ( sK7_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK7_B @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(398,plain,
! [SV42: $i,SV48: $i] :
( ( ( ~ ( element @ SV48 @ ( powerset @ SV42 ) ) )
= $true )
| ( ( ( SV48 = SV42 )
| ( proper_element @ SV48 @ ( powerset @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(399,plain,
! [SV43: $i,SV49: $i] :
( ( ( ~ ( element @ SV49 @ ( powerset @ SV43 ) ) )
= $true )
| ( ( ~ ( proper_element @ SV49 @ ( powerset @ SV43 ) )
| ( SV49 != SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(400,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
| ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 ) )
= $true )
| ( ( SV27 = SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(401,plain,
! [SV27: $i,SV37: $i] :
( ( ( ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
| ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 ) )
= $true )
| ( ( SV27 = SV37 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(402,plain,
! [SV50: $i,SV44: $i] :
( ( ( ~ ( element @ SV44 @ ( powerset @ SV50 ) ) )
= $true )
| ( ( subset @ SV44 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(403,plain,
! [SV51: $i,SV45: $i] :
( ( ( ~ ( subset @ SV45 @ SV51 ) )
= $true )
| ( ( element @ SV45 @ ( powerset @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(404,plain,
! [SV28: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ~ ( empty @ ( sK5_B @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(405,plain,
! [SV46: $i] :
( ( ( rel_str @ SV46 )
= $false )
| ( ( ( empty_carrier @ SV46 )
| ~ ( reflexive_relstr @ SV46 )
| ~ ( empty_carrier @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(406,plain,
! [SV47: $i] :
( ( ( rel_str @ SV47 )
= $false )
| ( ( ( empty_carrier @ SV47 )
| ~ ( reflexive_relstr @ SV47 )
| ~ ( v1_yellow_3 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(407,plain,
! [SV29: $i] :
( ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( ~ ( transitive_relstr @ SV29 ) )
= $true )
| ( ( ~ ( rel_str @ SV29 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
| ~ ( upper_relstr_subset @ ( sK13_B @ SV29 ) @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(408,plain,
( ( ~ ( ~ ~ ( ~ ~ ( empty @ sK2_SY67 )
| ~ ( filtered_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( upper_relstr_subset @ sK2_SY67 @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(409,plain,
( ( element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(410,plain,
( ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(411,plain,
( ( ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
| ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(412,plain,
! [SV16: $i] :
( ( ( lower_bounded_relstr @ SV16 )
= $false )
| ( ( empty_carrier @ SV16 )
= $true )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( ~ ( rel_str @ SV16 ) )
= $true )
| ( ( ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV16 ) )
| ( related @ SV16 @ ( bottom_of_relstr @ SV16 ) @ SY74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(413,plain,
! [SV38: $i,SV33: $i,SV17: $i] :
( ( ( in @ SV17 @ SV33 )
= $false )
| ( ( element @ SV33 @ ( powerset @ SV38 ) )
= $false )
| ( ( element @ SV17 @ SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(414,plain,
! [SV39: $i,SV34: $i,SV18: $i] :
( ( ( in @ SV18 @ SV34 )
= $false )
| ( ( element @ SV34 @ ( powerset @ SV39 ) )
= $false )
| ( ( ~ ( empty @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(415,plain,
! [SV23: $i] :
( ( ( element @ ( sK4_B @ SV23 ) @ ( powerset @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( empty_carrier @ SV23 )
= $true )
| ( ( one_sorted_str @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[393]) ).
thf(416,plain,
! [SV23: $i] :
( ( ( ~ ( empty @ ( sK4_B @ SV23 ) ) )
= $true )
| ( ( empty_carrier @ SV23 )
= $true )
| ( ( one_sorted_str @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(417,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( ~ ( element @ ( sK17_C @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ( element @ ( sK18_SY68 @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) ) ) )
| ( upper_relstr_subset @ SV52 @ SV25 ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(418,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
| ~ ( upper_relstr_subset @ SV53 @ SV25 )
| ! [SY92: $i] :
( ~ ( element @ SY92 @ ( the_carrier @ SV25 ) )
| ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SY92 @ SV53 )
| ~ ( related @ SV25 @ SY92 @ SY93 )
| ( in @ SY93 @ SV53 ) ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(419,plain,
! [SV26: $i] :
( ( ( ~ ( element @ ( sK7_B @ SV26 ) @ ( powerset @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(420,plain,
! [SV26: $i] :
( ( ( ~ ~ ( empty @ ( sK7_B @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(421,plain,
! [SV42: $i,SV48: $i] :
( ( ( element @ SV48 @ ( powerset @ SV42 ) )
= $false )
| ( ( ( SV48 = SV42 )
| ( proper_element @ SV48 @ ( powerset @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(422,plain,
! [SV43: $i,SV49: $i] :
( ( ( element @ SV49 @ ( powerset @ SV43 ) )
= $false )
| ( ( ~ ( proper_element @ SV49 @ ( powerset @ SV43 ) )
| ( SV49 != SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(423,plain,
! [SV27: $i,SV37: $i] :
( ( ( ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 ) )
= $true )
| ( ( ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 ) )
= $true )
| ( ( SV27 = SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(424,plain,
! [SV27: $i,SV37: $i] :
( ( ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
= $true )
| ( ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 )
= $true )
| ( ( SV27 = SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(425,plain,
! [SV50: $i,SV44: $i] :
( ( ( element @ SV44 @ ( powerset @ SV50 ) )
= $false )
| ( ( subset @ SV44 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(426,plain,
! [SV51: $i,SV45: $i] :
( ( ( subset @ SV45 @ SV51 )
= $false )
| ( ( element @ SV45 @ ( powerset @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(427,plain,
! [SV28: $i] :
( ( ( ~ ( element @ ( sK5_B @ SV28 ) @ ( powerset @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(428,plain,
! [SV28: $i] :
( ( ( ~ ~ ( empty @ ( sK5_B @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(429,plain,
! [SV46: $i] :
( ( ( ( empty_carrier @ SV46 )
| ~ ( reflexive_relstr @ SV46 ) )
= $true )
| ( ( ~ ( empty_carrier @ SV46 ) )
= $true )
| ( ( rel_str @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(430,plain,
! [SV47: $i] :
( ( ( ( empty_carrier @ SV47 )
| ~ ( reflexive_relstr @ SV47 ) )
= $true )
| ( ( ~ ( v1_yellow_3 @ SV47 ) )
= $true )
| ( ( rel_str @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(431,plain,
! [SV29: $i] :
( ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( ~ ( rel_str @ SV29 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
| ~ ( upper_relstr_subset @ ( sK13_B @ SV29 ) @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(432,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK2_SY67 )
| ~ ( filtered_subset @ sK2_SY67 @ sK1_A ) )
| ~ ( upper_relstr_subset @ sK2_SY67 @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(433,plain,
( ( ( ~ ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) ) )
= $true )
| ( ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(434,plain,
( ( ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( ~ ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(435,plain,
! [SV16: $i] :
( ( ( rel_str @ SV16 )
= $false )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( empty_carrier @ SV16 )
= $true )
| ( ( lower_bounded_relstr @ SV16 )
= $false )
| ( ( ! [SY74: $i] :
( ~ ( element @ SY74 @ ( the_carrier @ SV16 ) )
| ( related @ SV16 @ ( bottom_of_relstr @ SV16 ) @ SY74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(436,plain,
! [SV18: $i,SV34: $i,SV39: $i] :
( ( ( empty @ SV39 )
= $false )
| ( ( element @ SV34 @ ( powerset @ SV39 ) )
= $false )
| ( ( in @ SV18 @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(437,plain,
! [SV23: $i] :
( ( ( empty @ ( sK4_B @ SV23 ) )
= $false )
| ( ( empty_carrier @ SV23 )
= $true )
| ( ( one_sorted_str @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(438,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK17_C @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ( element @ ( sK18_SY68 @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) ) ) )
| ( upper_relstr_subset @ SV52 @ SV25 ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(439,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) ) )
= $true )
| ( ( ~ ( upper_relstr_subset @ SV53 @ SV25 )
| ! [SY92: $i] :
( ~ ( element @ SY92 @ ( the_carrier @ SV25 ) )
| ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SY92 @ SV53 )
| ~ ( related @ SV25 @ SY92 @ SY93 )
| ( in @ SY93 @ SV53 ) ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(440,plain,
! [SV26: $i] :
( ( ( element @ ( sK7_B @ SV26 ) @ ( powerset @ SV26 ) )
= $true )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(441,plain,
! [SV26: $i] :
( ( ( ~ ( empty @ ( sK7_B @ SV26 ) ) )
= $true )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(442,plain,
! [SV42: $i,SV48: $i] :
( ( ( SV48 = SV42 )
= $true )
| ( ( proper_element @ SV48 @ ( powerset @ SV42 ) )
= $true )
| ( ( element @ SV48 @ ( powerset @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(443,plain,
! [SV43: $i,SV49: $i] :
( ( ( ~ ( proper_element @ SV49 @ ( powerset @ SV43 ) ) )
= $true )
| ( ( ( SV49 != SV43 ) )
= $true )
| ( ( element @ SV49 @ ( powerset @ SV43 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(444,plain,
! [SV27: $i,SV37: $i] :
( ( ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
= $false )
| ( ( ~ ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 ) )
= $true )
| ( ( SV27 = SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(445,plain,
! [SV28: $i] :
( ( ( element @ ( sK5_B @ SV28 ) @ ( powerset @ SV28 ) )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(446,plain,
! [SV28: $i] :
( ( ( ~ ( empty @ ( sK5_B @ SV28 ) ) )
= $true )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(447,plain,
! [SV46: $i] :
( ( ( empty_carrier @ SV46 )
= $true )
| ( ( ~ ( reflexive_relstr @ SV46 ) )
= $true )
| ( ( ~ ( empty_carrier @ SV46 ) )
= $true )
| ( ( rel_str @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(448,plain,
! [SV47: $i] :
( ( ( empty_carrier @ SV47 )
= $true )
| ( ( ~ ( reflexive_relstr @ SV47 ) )
= $true )
| ( ( ~ ( v1_yellow_3 @ SV47 ) )
= $true )
| ( ( rel_str @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(449,plain,
! [SV29: $i] :
( ( ( rel_str @ SV29 )
= $false )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
| ~ ( upper_relstr_subset @ ( sK13_B @ SV29 ) @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(450,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK2_SY67 )
| ~ ( filtered_subset @ sK2_SY67 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(451,plain,
( ( ~ ( upper_relstr_subset @ sK2_SY67 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(452,plain,
( ( ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(453,plain,
( ( ( in @ ( bottom_of_relstr @ sK1_A ) @ sK2_SY67 )
= $false )
| ( ( proper_element @ sK2_SY67 @ ( powerset @ ( the_carrier @ sK1_A ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(454,plain,
! [SV16: $i,SV54: $i] :
( ( ( ~ ( element @ SV54 @ ( the_carrier @ SV16 ) )
| ( related @ SV16 @ ( bottom_of_relstr @ SV16 ) @ SV54 ) )
= $true )
| ( ( lower_bounded_relstr @ SV16 )
= $false )
| ( ( empty_carrier @ SV16 )
= $true )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(455,plain,
! [SV25: $i,SV52: $i] :
( ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK17_C @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ( element @ ( sK18_SY68 @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) ) ) )
| ( upper_relstr_subset @ SV52 @ SV25 ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(456,plain,
! [SV25: $i,SV53: $i] :
( ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( ~ ( upper_relstr_subset @ SV53 @ SV25 )
| ! [SY92: $i] :
( ~ ( element @ SY92 @ ( the_carrier @ SV25 ) )
| ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SY92 @ SV53 )
| ~ ( related @ SV25 @ SY92 @ SY93 )
| ( in @ SY93 @ SV53 ) ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(457,plain,
! [SV26: $i] :
( ( ( empty @ ( sK7_B @ SV26 ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(458,plain,
! [SV43: $i,SV49: $i] :
( ( ( proper_element @ SV49 @ ( powerset @ SV43 ) )
= $false )
| ( ( ( SV49 != SV43 ) )
= $true )
| ( ( element @ SV49 @ ( powerset @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(459,plain,
! [SV27: $i,SV37: $i] :
( ( ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV37 )
= $false )
| ( ( in @ ( sK3_C @ SV37 @ SV27 ) @ SV27 )
= $false )
| ( ( SV27 = SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(460,plain,
! [SV28: $i] :
( ( ( empty @ ( sK5_B @ SV28 ) )
= $false )
| ( ( empty @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(461,plain,
! [SV46: $i] :
( ( ( reflexive_relstr @ SV46 )
= $false )
| ( ( empty_carrier @ SV46 )
= $true )
| ( ( ~ ( empty_carrier @ SV46 ) )
= $true )
| ( ( rel_str @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(462,plain,
! [SV47: $i] :
( ( ( reflexive_relstr @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( ~ ( v1_yellow_3 @ SV47 ) )
= $true )
| ( ( rel_str @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(463,plain,
! [SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
| ~ ( upper_relstr_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
= $false )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(464,plain,
( ( ~ ( ~ ~ ( empty @ sK2_SY67 )
| ~ ( filtered_subset @ sK2_SY67 @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(465,plain,
( ( upper_relstr_subset @ sK2_SY67 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(466,plain,
! [SV16: $i,SV54: $i] :
( ( ( ~ ( element @ SV54 @ ( the_carrier @ SV16 ) ) )
= $true )
| ( ( related @ SV16 @ ( bottom_of_relstr @ SV16 ) @ SV54 )
= $true )
| ( ( lower_bounded_relstr @ SV16 )
= $false )
| ( ( empty_carrier @ SV16 )
= $true )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(467,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( ~ ( element @ ( sK17_C @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ( element @ ( sK18_SY68 @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) ) ) ) )
= $true )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(468,plain,
! [SV25: $i,SV53: $i] :
( ( ( ~ ( upper_relstr_subset @ SV53 @ SV25 ) )
= $true )
| ( ( ! [SY92: $i] :
( ~ ( element @ SY92 @ ( the_carrier @ SV25 ) )
| ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SY92 @ SV53 )
| ~ ( related @ SV25 @ SY92 @ SY93 )
| ( in @ SY93 @ SV53 ) ) ) )
= $true )
| ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(469,plain,
! [SV43: $i,SV49: $i] :
( ( ( SV49 = SV43 )
= $false )
| ( ( proper_element @ SV49 @ ( powerset @ SV43 ) )
= $false )
| ( ( element @ SV49 @ ( powerset @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(470,plain,
! [SV46: $i] :
( ( ( empty_carrier @ SV46 )
= $false )
| ( ( empty_carrier @ SV46 )
= $true )
| ( ( reflexive_relstr @ SV46 )
= $false )
| ( ( rel_str @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(471,plain,
! [SV47: $i] :
( ( ( v1_yellow_3 @ SV47 )
= $false )
| ( ( empty_carrier @ SV47 )
= $true )
| ( ( reflexive_relstr @ SV47 )
= $false )
| ( ( rel_str @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(472,plain,
! [SV29: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) ) )
= $false )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(473,plain,
! [SV29: $i] :
( ( ( ~ ( upper_relstr_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
= $false )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(474,plain,
( ( ~ ~ ( empty @ sK2_SY67 )
| ~ ( filtered_subset @ sK2_SY67 @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(475,plain,
! [SV16: $i,SV54: $i] :
( ( ( element @ SV54 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( related @ SV16 @ ( bottom_of_relstr @ SV16 ) @ SV54 )
= $true )
| ( ( lower_bounded_relstr @ SV16 )
= $false )
| ( ( empty_carrier @ SV16 )
= $true )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(476,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( element @ ( sK17_C @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ( element @ ( sK18_SY68 @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) ) ) )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(477,plain,
! [SV25: $i,SV53: $i] :
( ( ( upper_relstr_subset @ SV53 @ SV25 )
= $false )
| ( ( ! [SY92: $i] :
( ~ ( element @ SY92 @ ( the_carrier @ SV25 ) )
| ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SY92 @ SV53 )
| ~ ( related @ SV25 @ SY92 @ SY93 )
| ( in @ SY93 @ SV53 ) ) ) )
= $true )
| ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(478,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) ) )
= $true )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(479,plain,
! [SV29: $i] :
( ( ( upper_relstr_subset @ ( sK13_B @ SV29 ) @ SV29 )
= $true )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(480,plain,
( ( ~ ~ ( empty @ sK2_SY67 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(481,plain,
( ( ~ ( filtered_subset @ sK2_SY67 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(482,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( element @ ( sK17_C @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(483,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK18_SY68 @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) ) ) )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[476]) ).
thf(484,plain,
! [SV53: $i,SV25: $i,SV55: $i] :
( ( ( ~ ( element @ SV55 @ ( the_carrier @ SV25 ) )
| ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SV55 @ SV53 )
| ~ ( related @ SV25 @ SV55 @ SY94 )
| ( in @ SY94 @ SV53 ) ) )
= $true )
| ( ( upper_relstr_subset @ SV53 @ SV25 )
= $false )
| ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(485,plain,
! [SV29: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
| ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
= $false )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(486,plain,
( ( ~ ( empty @ sK2_SY67 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(487,plain,
( ( filtered_subset @ sK2_SY67 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[481]) ).
thf(488,plain,
! [SV25: $i,SV52: $i] :
( ( ( element @ ( sK17_C @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
= $true )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(489,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( ~ ( element @ ( sK18_SY68 @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) ) ) )
= $true )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(490,plain,
! [SV53: $i,SV25: $i,SV55: $i] :
( ( ( ~ ( element @ SV55 @ ( the_carrier @ SV25 ) ) )
= $true )
| ( ( ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SV55 @ SV53 )
| ~ ( related @ SV25 @ SV55 @ SY94 )
| ( in @ SY94 @ SV53 ) ) )
= $true )
| ( ( upper_relstr_subset @ SV53 @ SV25 )
= $false )
| ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(491,plain,
! [SV29: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) ) )
= $false )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(492,plain,
! [SV29: $i] :
( ( ( ~ ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 ) )
= $false )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[485]) ).
thf(493,plain,
( ( empty @ sK2_SY67 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(494,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( element @ ( sK18_SY68 @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) ) )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(495,plain,
! [SV53: $i,SV25: $i,SV55: $i] :
( ( ( element @ SV55 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SV55 @ SV53 )
| ~ ( related @ SV25 @ SV55 @ SY94 )
| ( in @ SY94 @ SV53 ) ) )
= $true )
| ( ( upper_relstr_subset @ SV53 @ SV25 )
= $false )
| ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(496,plain,
! [SV29: $i] :
( ( ( ~ ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) ) )
= $true )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(497,plain,
! [SV29: $i] :
( ( ( filtered_subset @ ( sK13_B @ SV29 ) @ SV29 )
= $true )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(498,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( element @ ( sK18_SY68 @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(499,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) ) )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(500,plain,
! [SV53: $i,SV55: $i,SV25: $i,SV56: $i] :
( ( ( ~ ( element @ SV56 @ ( the_carrier @ SV25 ) )
| ~ ( in @ SV55 @ SV53 )
| ~ ( related @ SV25 @ SV55 @ SV56 )
| ( in @ SV56 @ SV53 ) )
= $true )
| ( ( element @ SV55 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( upper_relstr_subset @ SV53 @ SV25 )
= $false )
| ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(501,plain,
! [SV29: $i] :
( ( ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
= $false )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(502,plain,
! [SV25: $i,SV52: $i] :
( ( ( element @ ( sK18_SY68 @ SV52 @ SV25 ) @ ( the_carrier @ SV25 ) )
= $true )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(503,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) ) )
= $true )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(504,plain,
! [SV53: $i,SV55: $i,SV25: $i,SV56: $i] :
( ( ( ~ ( element @ SV56 @ ( the_carrier @ SV25 ) ) )
= $true )
| ( ( ~ ( in @ SV55 @ SV53 )
| ~ ( related @ SV25 @ SV55 @ SV56 )
| ( in @ SV56 @ SV53 ) )
= $true )
| ( ( element @ SV55 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( upper_relstr_subset @ SV53 @ SV25 )
= $false )
| ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(505,plain,
! [SV29: $i] :
( ( ( ~ ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) ) )
= $false )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(506,plain,
! [SV29: $i] :
( ( ( ~ ~ ( empty @ ( sK13_B @ SV29 ) ) )
= $false )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(507,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
| ~ ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(508,plain,
! [SV53: $i,SV55: $i,SV25: $i,SV56: $i] :
( ( ( element @ SV56 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( ~ ( in @ SV55 @ SV53 )
| ~ ( related @ SV25 @ SV55 @ SV56 )
| ( in @ SV56 @ SV53 ) )
= $true )
| ( ( element @ SV55 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( upper_relstr_subset @ SV53 @ SV25 )
= $false )
| ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(509,plain,
! [SV29: $i] :
( ( ( element @ ( sK13_B @ SV29 ) @ ( powerset @ ( the_carrier @ SV29 ) ) )
= $true )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(510,plain,
! [SV29: $i] :
( ( ( ~ ( empty @ ( sK13_B @ SV29 ) ) )
= $true )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(511,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) ) )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(512,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[507]) ).
thf(513,plain,
! [SV56: $i,SV25: $i,SV53: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV53 )
| ~ ( related @ SV25 @ SV55 @ SV56 ) )
= $true )
| ( ( in @ SV56 @ SV53 )
= $true )
| ( ( element @ SV56 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( element @ SV55 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( upper_relstr_subset @ SV53 @ SV25 )
= $false )
| ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(514,plain,
! [SV29: $i] :
( ( ( empty @ ( sK13_B @ SV29 ) )
= $false )
| ( ( transitive_relstr @ SV29 )
= $false )
| ( ( empty_carrier @ SV29 )
= $true )
| ( ( reflexive_relstr @ SV29 )
= $false )
| ( ( rel_str @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(515,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) ) )
= $true )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(516,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 ) )
= $true )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(517,plain,
! [SV56: $i,SV25: $i,SV53: $i,SV55: $i] :
( ( ( ~ ( in @ SV55 @ SV53 ) )
= $true )
| ( ( ~ ( related @ SV25 @ SV55 @ SV56 ) )
= $true )
| ( ( in @ SV56 @ SV53 )
= $true )
| ( ( element @ SV56 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( element @ SV55 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( upper_relstr_subset @ SV53 @ SV25 )
= $false )
| ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(518,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
| ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(519,plain,
! [SV25: $i,SV52: $i] :
( ( ( in @ ( sK18_SY68 @ SV52 @ SV25 ) @ SV52 )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(520,plain,
! [SV56: $i,SV25: $i,SV53: $i,SV55: $i] :
( ( ( in @ SV55 @ SV53 )
= $false )
| ( ( ~ ( related @ SV25 @ SV55 @ SV56 ) )
= $true )
| ( ( in @ SV56 @ SV53 )
= $true )
| ( ( element @ SV56 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( element @ SV55 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( upper_relstr_subset @ SV53 @ SV25 )
= $false )
| ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(521,plain,
! [SV25: $i,SV52: $i] :
( ( ( ~ ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 ) )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(522,plain,
! [SV52: $i,SV25: $i] :
( ( ( ~ ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) ) )
= $false )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(523,plain,
! [SV53: $i,SV56: $i,SV55: $i,SV25: $i] :
( ( ( related @ SV25 @ SV55 @ SV56 )
= $false )
| ( ( in @ SV55 @ SV53 )
= $false )
| ( ( in @ SV56 @ SV53 )
= $true )
| ( ( element @ SV56 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( element @ SV55 @ ( the_carrier @ SV25 ) )
= $false )
| ( ( upper_relstr_subset @ SV53 @ SV25 )
= $false )
| ( ( element @ SV53 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(524,plain,
! [SV25: $i,SV52: $i] :
( ( ( in @ ( sK17_C @ SV52 @ SV25 ) @ SV52 )
= $true )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(525,plain,
! [SV52: $i,SV25: $i] :
( ( ( related @ SV25 @ ( sK17_C @ SV52 @ SV25 ) @ ( sK18_SY68 @ SV52 @ SV25 ) )
= $true )
| ( ( upper_relstr_subset @ SV52 @ SV25 )
= $true )
| ( ( element @ SV52 @ ( powerset @ ( the_carrier @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(526,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[147,525,524,523,519,514,509,502,497,493,488,487,479,475,471,470,469,465,460,459,457,453,452,445,442,440,437,436,426,425,424,415,413,409,392,391,387,379,371,365,363,359,358,357,355,354,351,345,336,335,325,323,315,310,295,288,287,285,281,251,226,217,216,213,187,186,185,184,183,164,160,156,155,154,153,152,149]) ).
thf(527,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[526]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SEU383+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.11 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Mon Jun 20 07:10:33 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.15/0.33
% 0.15/0.33 No.of.Axioms: 44
% 0.15/0.33
% 0.15/0.33 Length.of.Defs: 0
% 0.15/0.33
% 0.15/0.33 Contains.Choice.Funs: false
% 0.15/0.33 ..
% 0.15/0.35 (rf:0,axioms:44,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:46,loop_count:0,foatp_calls:0,translation:fof_full)......................
% 5.77/5.98
% 5.77/5.98 ********************************
% 5.77/5.98 * All subproblems solved! *
% 5.77/5.98 ********************************
% 5.77/5.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:50,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:526,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.88/6.11
% 5.88/6.11 %**** Beginning of derivation protocol ****
% 5.88/6.11 % SZS output start CNFRefutation
% See solution above
% 5.88/6.11
% 5.88/6.11 %**** End of derivation protocol ****
% 5.88/6.11 %**** no. of clauses in derivation: 527 ****
% 5.88/6.11 %**** clause counter: 526 ****
% 5.88/6.11
% 5.88/6.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:50,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:526,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------