TSTP Solution File: SEU368+1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU368+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 : n023.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 12:11:09 EDT 2022
% Result : Theorem 0.58s 0.86s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 94
% Syntax : Number of formulae : 1198 ( 762 unt; 41 typ; 0 def)
% Number of atoms : 8132 (2142 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 14042 (3238 ~;2809 |; 204 &;7743 @)
% ( 4 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 11 con; 0-3 aty)
% Number of variables : 2109 ( 0 ^2083 !; 26 ?;2109 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_carrier,type,
empty_carrier: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_incl_POSet,type,
incl_POSet: $i > $i ).
thf(tp_inclusion_order,type,
inclusion_order: $i > $i ).
thf(tp_inclusion_relation,type,
inclusion_relation: $i > $i ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_reflexive,type,
reflexive: $i > $o ).
thf(tp_reflexive_relstr,type,
reflexive_relstr: $i > $o ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_rel_str_of,type,
rel_str_of: $i > $i > $i ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_sK10_B,type,
sK10_B: $i > $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_A,type,
sK14_A: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_A,type,
sK2_A: $i ).
thf(tp_sK3_C,type,
sK3_C: $i > $i > $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $i ).
thf(tp_sK7_C,type,
sK7_C: $i > $i > $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_A,type,
sK9_A: $i ).
thf(tp_strict_rel_str,type,
strict_rel_str: $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_the_InternalRel,type,
the_InternalRel: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
thf(tp_transitive_relstr,type,
transitive_relstr: $i > $o ).
thf(tp_v1_partfun1,type,
v1_partfun1: $i > $i > $i > $o ).
thf(1,axiom,
! [A: $i] :
( ( incl_POSet @ A )
= ( rel_str_of @ A @ ( inclusion_order @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow_1) ).
thf(2,axiom,
! [A: $i] :
( ( strict_rel_str @ ( incl_POSet @ A ) )
& ( reflexive_relstr @ ( incl_POSet @ A ) )
& ( transitive_relstr @ ( incl_POSet @ A ) )
& ( antisymmetric_relstr @ ( incl_POSet @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_yellow_1) ).
thf(3,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(4,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(5,axiom,
! [A: $i] :
( ( strict_rel_str @ ( incl_POSet @ A ) )
& ( rel_str @ ( incl_POSet @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
thf(6,axiom,
! [A: $i] :
( ( reflexive @ ( inclusion_order @ A ) )
& ( antisymmetric @ ( inclusion_order @ A ) )
& ( transitive @ ( inclusion_order @ A ) )
& ( v1_partfun1 @ ( inclusion_order @ A ) @ A @ A )
& ( relation_of2_as_subset @ ( inclusion_order @ A ) @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_1) ).
thf(7,axiom,
! [A: $i] :
( ( inclusion_order @ A )
= ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_yellow_1) ).
thf(8,axiom,
! [A: $i] :
( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ( ( relation @ ( the_InternalRel @ A ) )
& ( reflexive @ ( the_InternalRel @ A ) )
& ( antisymmetric @ ( the_InternalRel @ A ) )
& ( transitive @ ( the_InternalRel @ A ) )
& ( v1_partfun1 @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_orders_2) ).
thf(9,axiom,
? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_orders_2) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(11,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(12,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(13,axiom,
! [A: $i] : ( relation @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_orders_2) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(16,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(17,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(18,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(19,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
= ( rel_str_of @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(22,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( reflexive @ B )
& ( antisymmetric @ B )
& ( transitive @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( relation_of2 @ B @ A @ A ) )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( reflexive_relstr @ ( rel_str_of @ A @ B ) )
& ( transitive_relstr @ ( rel_str_of @ A @ B ) )
& ( antisymmetric_relstr @ ( rel_str_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_orders_2) ).
thf(25,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(26,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(27,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(29,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(30,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(31,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(32,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(33,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(35,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(36,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(37,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(39,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation_of2 @ B @ A @ A ) )
=> ( ~ ( empty_carrier @ ( rel_str_of @ A @ B ) )
& ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_orders_2) ).
thf(41,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ( ~ ( empty_carrier @ ( incl_POSet @ A ) )
& ( strict_rel_str @ ( incl_POSet @ A ) )
& ( reflexive_relstr @ ( incl_POSet @ A ) )
& ( transitive_relstr @ ( incl_POSet @ A ) )
& ( antisymmetric_relstr @ ( incl_POSet @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_yellow_1) ).
thf(42,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(43,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(44,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(45,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(46,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(47,axiom,
? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_orders_2) ).
thf(48,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(49,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(50,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(51,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(53,conjecture,
! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_yellow_1) ).
thf(54,negated_conjecture,
( ( ! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[53]) ).
thf(55,plain,
( ( ! [A: $i] :
( ( ( the_carrier @ ( incl_POSet @ A ) )
= A )
& ( ( the_InternalRel @ ( incl_POSet @ A ) )
= ( inclusion_order @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[54]) ).
thf(56,plain,
( ( ! [A: $i] :
( ( incl_POSet @ A )
= ( rel_str_of @ A @ ( inclusion_order @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(57,plain,
( ( ! [A: $i] :
( ( strict_rel_str @ ( incl_POSet @ A ) )
& ( reflexive_relstr @ ( incl_POSet @ A ) )
& ( transitive_relstr @ ( incl_POSet @ A ) )
& ( antisymmetric_relstr @ ( incl_POSet @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(58,plain,
$true = $true,
inference(unfold_def,[status(thm)],[3]) ).
thf(59,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( strict_rel_str @ ( incl_POSet @ A ) )
& ( rel_str @ ( incl_POSet @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( reflexive @ ( inclusion_order @ A ) )
& ( antisymmetric @ ( inclusion_order @ A ) )
& ( transitive @ ( inclusion_order @ A ) )
& ( v1_partfun1 @ ( inclusion_order @ A ) @ A @ A )
& ( relation_of2_as_subset @ ( inclusion_order @ A ) @ A @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(62,plain,
( ( ! [A: $i] :
( ( inclusion_order @ A )
= ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ( ( relation @ ( the_InternalRel @ A ) )
& ( reflexive @ ( the_InternalRel @ A ) )
& ( antisymmetric @ ( the_InternalRel @ A ) )
& ( transitive @ ( the_InternalRel @ A ) )
& ( v1_partfun1 @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(64,plain,
( ( ? [A: $i] :
( ( rel_str @ A )
& ( strict_rel_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(65,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(66,plain,
$true = $true,
inference(unfold_def,[status(thm)],[11]) ).
thf(67,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(68,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( rel_str @ ( rel_str_of @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(70,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(72,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(73,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(74,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( strict_rel_str @ A )
=> ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(75,plain,
( ( ! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
= ( rel_str_of @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(76,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(77,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(78,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ( ( reflexive @ B )
& ( antisymmetric @ B )
& ( transitive @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( relation_of2 @ B @ A @ A ) )
=> ( ( strict_rel_str @ ( rel_str_of @ A @ B ) )
& ( reflexive_relstr @ ( rel_str_of @ A @ B ) )
& ( transitive_relstr @ ( rel_str_of @ A @ B ) )
& ( antisymmetric_relstr @ ( rel_str_of @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(80,plain,
$true = $true,
inference(unfold_def,[status(thm)],[25]) ).
thf(81,plain,
$true = $true,
inference(unfold_def,[status(thm)],[26]) ).
thf(82,plain,
$true = $true,
inference(unfold_def,[status(thm)],[27]) ).
thf(83,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(84,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(88,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(89,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(90,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(91,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(92,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(94,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(95,plain,
( ( ! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ( relation_of2 @ B @ A @ A ) )
=> ( ~ ( empty_carrier @ ( rel_str_of @ A @ B ) )
& ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(96,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ( ~ ( empty_carrier @ ( incl_POSet @ A ) )
& ( strict_rel_str @ ( incl_POSet @ A ) )
& ( reflexive_relstr @ ( incl_POSet @ A ) )
& ( transitive_relstr @ ( incl_POSet @ A ) )
& ( antisymmetric_relstr @ ( incl_POSet @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(98,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(99,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(100,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(101,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(102,plain,
( ( ? [A: $i] :
( ( rel_str @ A )
& ~ ( empty_carrier @ A )
& ( strict_rel_str @ A )
& ( reflexive_relstr @ A )
& ( transitive_relstr @ A )
& ( antisymmetric_relstr @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(103,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)],[48]) ).
thf(104,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(105,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(106,plain,
$true = $true,
inference(unfold_def,[status(thm)],[51]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(108,plain,
( ( ( ( the_carrier @ ( incl_POSet @ sK1_A ) )
= sK1_A )
& ( ( the_InternalRel @ ( incl_POSet @ sK1_A ) )
= ( inclusion_order @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(109,plain,
( ( ( the_carrier @ ( incl_POSet @ sK1_A ) )
= sK1_A )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[108]) ).
thf(110,plain,
( ( ( the_InternalRel @ ( incl_POSet @ sK1_A ) )
= ( inclusion_order @ sK1_A ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[108]) ).
thf(111,plain,
( ( ( ( the_carrier @ ( incl_POSet @ sK1_A ) )
!= sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[109]) ).
thf(112,plain,
( ( ( ( the_InternalRel @ ( incl_POSet @ sK1_A ) )
!= ( inclusion_order @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[110]) ).
thf(113,plain,
( ( ! [A: $i] : ( reflexive_relstr @ ( incl_POSet @ A ) )
& ! [A: $i] : ( strict_rel_str @ ( incl_POSet @ A ) )
& ! [A: $i] : ( transitive_relstr @ ( incl_POSet @ A ) )
& ! [A: $i] : ( antisymmetric_relstr @ ( incl_POSet @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(114,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(115,plain,
( ( ! [A: $i] : ( rel_str @ ( incl_POSet @ A ) )
& ! [A: $i] : ( strict_rel_str @ ( incl_POSet @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(116,plain,
( ( ! [A: $i] : ( antisymmetric @ ( inclusion_order @ A ) )
& ! [A: $i] : ( reflexive @ ( inclusion_order @ A ) )
& ! [A: $i] : ( transitive @ ( inclusion_order @ A ) )
& ! [A: $i] : ( v1_partfun1 @ ( inclusion_order @ A ) @ A @ A )
& ! [A: $i] : ( relation_of2_as_subset @ ( inclusion_order @ A ) @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(117,plain,
( ( ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( reflexive @ ( the_InternalRel @ A ) ) )
& ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( relation @ ( the_InternalRel @ A ) ) )
& ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( antisymmetric @ ( the_InternalRel @ A ) ) )
& ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( transitive @ ( the_InternalRel @ A ) ) )
& ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( v1_partfun1 @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(118,plain,
( ( ( rel_str @ sK2_A )
& ( strict_rel_str @ sK2_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(119,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(120,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(121,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( rel_str @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(122,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(123,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK3_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(124,plain,
( ( one_sorted_str @ sK4_A )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(125,plain,
( ( rel_str @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(126,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( strict_rel_str @ A )
| ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(127,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( ! [C: $i] :
( ! [D: $i] :
( ( rel_str_of @ A @ B )
!= ( rel_str_of @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
!= ( rel_str_of @ C @ D ) )
| ( B = D ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(128,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)],[76]) ).
thf(129,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ~ ( antisymmetric @ B )
| ~ ( reflexive @ B )
| ~ ( transitive @ B )
| ~ ( v1_partfun1 @ B @ A @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( reflexive_relstr @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( antisymmetric @ B )
| ~ ( reflexive @ B )
| ~ ( transitive @ B )
| ~ ( v1_partfun1 @ B @ A @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( strict_rel_str @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( antisymmetric @ B )
| ~ ( reflexive @ B )
| ~ ( transitive @ B )
| ~ ( v1_partfun1 @ B @ A @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( transitive_relstr @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( antisymmetric @ B )
| ~ ( reflexive @ B )
| ~ ( transitive @ B )
| ~ ( v1_partfun1 @ B @ A @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( antisymmetric_relstr @ ( rel_str_of @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(131,plain,
( ( ! [A: $i] : ( element @ ( sK6_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(132,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK7_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(133,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(134,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(135,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(136,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(137,plain,
( ( ~ ( empty @ sK8_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(138,plain,
( ( empty @ sK9_A )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(139,plain,
( ( ! [A: $i] :
( ( element @ ( sK10_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK10_B @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(140,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(141,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK11_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK11_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(142,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ~ ( empty_carrier @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(143,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( empty_carrier @ ( incl_POSet @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ( strict_rel_str @ ( incl_POSet @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ( reflexive_relstr @ ( incl_POSet @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ( transitive_relstr @ ( incl_POSet @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ( antisymmetric_relstr @ ( incl_POSet @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(144,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(145,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(146,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(147,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(148,plain,
( ( ( rel_str @ sK12_A )
& ~ ( empty_carrier @ sK12_A )
& ( strict_rel_str @ sK12_A )
& ( reflexive_relstr @ sK12_A )
& ( transitive_relstr @ sK12_A )
& ( antisymmetric_relstr @ sK12_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(149,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK13_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK13_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[103]) ).
thf(150,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(151,plain,
( ( ( one_sorted_str @ sK14_A )
& ~ ( empty_carrier @ sK14_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(152,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(153,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(154,plain,
$true = $true,
inference(copy,[status(thm)],[106]) ).
thf(155,plain,
( ( ( one_sorted_str @ sK14_A )
& ~ ( empty_carrier @ sK14_A ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(156,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(157,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK13_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK13_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(158,plain,
( ( ( rel_str @ sK12_A )
& ~ ( empty_carrier @ sK12_A )
& ( strict_rel_str @ sK12_A )
& ( reflexive_relstr @ sK12_A )
& ( transitive_relstr @ sK12_A )
& ( antisymmetric_relstr @ sK12_A ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(159,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(160,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(161,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(162,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(163,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(164,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( empty_carrier @ ( incl_POSet @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ( strict_rel_str @ ( incl_POSet @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ( reflexive_relstr @ ( incl_POSet @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ( transitive_relstr @ ( incl_POSet @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ( antisymmetric_relstr @ ( incl_POSet @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(165,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ~ ( empty_carrier @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(166,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK11_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK11_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(167,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(168,plain,
( ( ! [A: $i] :
( ( element @ ( sK10_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK10_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(169,plain,
( ( empty @ sK9_A )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(170,plain,
( ( ~ ( empty @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(171,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(172,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(173,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(174,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(175,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK7_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(176,plain,
( ( ! [A: $i] : ( element @ ( sK6_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(177,plain,
$true = $true,
inference(copy,[status(thm)],[83]) ).
thf(178,plain,
$true = $true,
inference(copy,[status(thm)],[82]) ).
thf(179,plain,
$true = $true,
inference(copy,[status(thm)],[81]) ).
thf(180,plain,
$true = $true,
inference(copy,[status(thm)],[80]) ).
thf(181,plain,
( ( ! [A: $i,B: $i] :
( ~ ( antisymmetric @ B )
| ~ ( reflexive @ B )
| ~ ( transitive @ B )
| ~ ( v1_partfun1 @ B @ A @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( reflexive_relstr @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( antisymmetric @ B )
| ~ ( reflexive @ B )
| ~ ( transitive @ B )
| ~ ( v1_partfun1 @ B @ A @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( strict_rel_str @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( antisymmetric @ B )
| ~ ( reflexive @ B )
| ~ ( transitive @ B )
| ~ ( v1_partfun1 @ B @ A @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( transitive_relstr @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( antisymmetric @ B )
| ~ ( reflexive @ B )
| ~ ( transitive @ B )
| ~ ( v1_partfun1 @ B @ A @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( antisymmetric_relstr @ ( rel_str_of @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(182,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(183,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(184,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)],[128]) ).
thf(185,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( ! [C: $i] :
( ! [D: $i] :
( ( rel_str_of @ A @ B )
!= ( rel_str_of @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
!= ( rel_str_of @ C @ D ) )
| ( B = D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(186,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( strict_rel_str @ A )
| ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(187,plain,
( ( rel_str @ sK5_A )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(188,plain,
( ( one_sorted_str @ sK4_A )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK3_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(190,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(191,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( rel_str @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(192,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(193,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(194,plain,
$true = $true,
inference(copy,[status(thm)],[66]) ).
thf(195,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(196,plain,
( ( ( rel_str @ sK2_A )
& ( strict_rel_str @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(197,plain,
( ( ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( reflexive @ ( the_InternalRel @ A ) ) )
& ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( relation @ ( the_InternalRel @ A ) ) )
& ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( antisymmetric @ ( the_InternalRel @ A ) ) )
& ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( transitive @ ( the_InternalRel @ A ) ) )
& ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( v1_partfun1 @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(198,plain,
( ( ! [A: $i] :
( ( inclusion_order @ A )
= ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(199,plain,
( ( ! [A: $i] : ( antisymmetric @ ( inclusion_order @ A ) )
& ! [A: $i] : ( reflexive @ ( inclusion_order @ A ) )
& ! [A: $i] : ( transitive @ ( inclusion_order @ A ) )
& ! [A: $i] : ( v1_partfun1 @ ( inclusion_order @ A ) @ A @ A )
& ! [A: $i] : ( relation_of2_as_subset @ ( inclusion_order @ A ) @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(200,plain,
( ( ! [A: $i] : ( rel_str @ ( incl_POSet @ A ) )
& ! [A: $i] : ( strict_rel_str @ ( incl_POSet @ A ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(201,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(202,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(203,plain,
( ( ! [A: $i] : ( reflexive_relstr @ ( incl_POSet @ A ) )
& ! [A: $i] : ( strict_rel_str @ ( incl_POSet @ A ) )
& ! [A: $i] : ( transitive_relstr @ ( incl_POSet @ A ) )
& ! [A: $i] : ( antisymmetric_relstr @ ( incl_POSet @ A ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(204,plain,
( ( ! [A: $i] :
( ( incl_POSet @ A )
= ( rel_str_of @ A @ ( inclusion_order @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(205,plain,
( ( ( ( the_carrier @ ( incl_POSet @ sK1_A ) )
!= sK1_A ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(206,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(207,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) )
| ~ ( transitive_relstr @ sK12_A ) )
| ~ ( antisymmetric_relstr @ sK12_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(208,plain,
( ( ~ ( ~ ( one_sorted_str @ sK14_A )
| ~ ~ ( empty_carrier @ sK14_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(209,plain,
( ( ~ ( ~ ( rel_str @ sK2_A )
| ~ ( strict_rel_str @ sK2_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(210,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( empty_carrier @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(211,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( v1_partfun1 @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(212,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(213,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(214,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(215,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( rel_str_of @ SX0 @ SX1 )
!= ( rel_str_of @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( rel_str_of @ SX0 @ SX1 )
!= ( rel_str_of @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(216,plain,
( ( ~ ( ~ ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(217,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK11_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK11_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(218,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)],[184]) ).
thf(219,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ( element @ ( sK13_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(220,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
| ~ ! [SX0: $i] : ( relation_of2_as_subset @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(221,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( antisymmetric_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(222,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK10_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK10_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(223,plain,
! [SV1: $i] :
( ( ! [SY77: $i] :
( ~ ( in @ SV1 @ SY77 )
| ~ ( in @ SY77 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(224,plain,
! [SV2: $i] :
( ( ( empty_carrier @ SV2 )
| ~ ( one_sorted_str @ SV2 )
| ~ ( empty @ ( the_carrier @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(225,plain,
! [SV3: $i] :
( ( ! [SY78: $i] :
( ~ ( in @ SV3 @ SY78 )
| ( element @ SV3 @ SY78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(226,plain,
! [SV4: $i] :
( ( ! [SY79: $i,SY80: $i] :
( ~ ( element @ SY79 @ ( powerset @ SY80 ) )
| ~ ( in @ SV4 @ SY79 )
| ( element @ SV4 @ SY80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(227,plain,
! [SV5: $i] :
( ( ! [SY81: $i,SY82: $i] :
( ~ ( element @ SY81 @ ( powerset @ SY82 ) )
| ~ ( in @ SV5 @ SY81 )
| ~ ( empty @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(228,plain,
! [SV6: $i] :
( ( subset @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(229,plain,
! [SV7: $i] :
( ( ! [SY83: $i] :
( ( empty @ SV7 )
| ( empty @ SY83 )
| ~ ( empty @ ( cartesian_product2 @ SV7 @ SY83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(230,plain,
( ( empty @ sK8_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(231,plain,
! [SV8: $i] :
( ( ! [SY84: $i] :
( ~ ( element @ SV8 @ SY84 )
| ( empty @ SY84 )
| ( in @ SV8 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(232,plain,
! [SV9: $i] :
( ( ~ ( empty @ SV9 )
| ( SV9 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(233,plain,
! [SV10: $i] :
( ( ! [SY85: $i] :
( ~ ( empty @ SY85 )
| ~ ( in @ SV10 @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(234,plain,
! [SV11: $i] :
( ( ! [SY86: $i] :
( ( SV11 = SY86 )
| ~ ( empty @ SV11 )
| ~ ( empty @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(235,plain,
! [SV12: $i] :
( ( ! [SY87: $i] : ( relation_of2 @ ( sK7_C @ SY87 @ SV12 ) @ SV12 @ SY87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(236,plain,
! [SV13: $i] :
( ( element @ ( sK6_B @ SV13 ) @ SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(237,plain,
! [SV14: $i] :
( ( ! [SY88: $i,SY89: $i] :
( ~ ( element @ SY89 @ ( powerset @ ( cartesian_product2 @ SV14 @ SY88 ) ) )
| ( relation @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(238,plain,
! [SV15: $i] :
( ( ~ ( empty @ ( powerset @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(239,plain,
! [SV16: $i] :
( ( ~ ( rel_str @ SV16 )
| ~ ( strict_rel_str @ SV16 )
| ( SV16
= ( rel_str_of @ ( the_carrier @ SV16 ) @ ( the_InternalRel @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(240,plain,
! [SV17: $i] :
( ( ! [SY90: $i] : ( relation_of2_as_subset @ ( sK3_C @ SY90 @ SV17 ) @ SV17 @ SY90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(241,plain,
! [SV18: $i] :
( ( relation @ ( inclusion_relation @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(242,plain,
! [SV19: $i] :
( ( ~ ( rel_str @ SV19 )
| ( one_sorted_str @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(243,plain,
! [SV20: $i] :
( ( ! [SY91: $i,SY92: $i] :
( ~ ( relation_of2_as_subset @ SY92 @ SV20 @ SY91 )
| ( element @ SY92 @ ( powerset @ ( cartesian_product2 @ SV20 @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(244,plain,
! [SV21: $i] :
( ( ( inclusion_order @ SV21 )
= ( inclusion_relation @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(245,plain,
! [SV22: $i] :
( ( ~ ( rel_str @ SV22 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SV22 ) @ ( the_carrier @ SV22 ) @ ( the_carrier @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(246,plain,
! [SV23: $i] :
( ( ( incl_POSet @ SV23 )
= ( rel_str_of @ SV23 @ ( inclusion_order @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(247,plain,
( ( ( the_carrier @ ( incl_POSet @ sK1_A ) )
= sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(248,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(249,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) )
| ~ ( transitive_relstr @ sK12_A ) )
| ~ ( antisymmetric_relstr @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(250,plain,
( ( ~ ( one_sorted_str @ sK14_A )
| ~ ~ ( empty_carrier @ sK14_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(251,plain,
( ( ~ ( rel_str @ sK2_A )
| ~ ( strict_rel_str @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(252,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( empty_carrier @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(253,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( v1_partfun1 @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(254,plain,
! [SV24: $i] :
( ( ~ ( ~ ! [SY93: $i,SY94: $i] :
( ~ ( relation_of2 @ SY94 @ SV24 @ SY93 )
| ( relation_of2_as_subset @ SY94 @ SV24 @ SY93 ) )
| ~ ! [SY95: $i,SY96: $i] :
( ~ ( relation_of2_as_subset @ SY96 @ SV24 @ SY95 )
| ( relation_of2 @ SY96 @ SV24 @ SY95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(255,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(256,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(257,plain,
! [SV25: $i] :
( ( ! [SY97: $i] :
( ~ ( relation_of2 @ SY97 @ SV25 @ SV25 )
| ~ ( ~ ! [SY98: $i] :
( ! [SY99: $i] :
( ( rel_str_of @ SV25 @ SY97 )
!= ( rel_str_of @ SY98 @ SY99 ) )
| ( SV25 = SY98 ) )
| ~ ! [SY100: $i,SY101: $i] :
( ( ( rel_str_of @ SV25 @ SY97 )
!= ( rel_str_of @ SY100 @ SY101 ) )
| ( SY97 = SY101 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(258,plain,
( ( ~ ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(259,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
| ~ ( ~ ( element @ ( sK11_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK11_B @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(260,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)],[218]) ).
thf(261,plain,
! [SV27: $i] :
( ( ( empty_carrier @ SV27 )
| ~ ( one_sorted_str @ SV27 )
| ~ ( ~ ( element @ ( sK13_B @ SV27 ) @ ( powerset @ ( the_carrier @ SV27 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(262,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
| ~ ! [SX0: $i] : ( relation_of2_as_subset @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(263,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( antisymmetric_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(264,plain,
! [SV28: $i] :
( ( ~ ( ~ ( element @ ( sK10_B @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ( empty @ ( sK10_B @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(265,plain,
! [SV29: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV29 )
| ~ ( in @ SV29 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(266,plain,
! [SV2: $i] :
( ( ( ( empty_carrier @ SV2 )
| ~ ( one_sorted_str @ SV2 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(267,plain,
! [SV30: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV30 )
| ( element @ SV3 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(268,plain,
! [SV4: $i,SV31: $i] :
( ( ! [SY102: $i] :
( ~ ( element @ SV31 @ ( powerset @ SY102 ) )
| ~ ( in @ SV4 @ SV31 )
| ( element @ SV4 @ SY102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(269,plain,
! [SV5: $i,SV32: $i] :
( ( ! [SY103: $i] :
( ~ ( element @ SV32 @ ( powerset @ SY103 ) )
| ~ ( in @ SV5 @ SV32 )
| ~ ( empty @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(270,plain,
! [SV33: $i,SV7: $i] :
( ( ( empty @ SV7 )
| ( empty @ SV33 )
| ~ ( empty @ ( cartesian_product2 @ SV7 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(271,plain,
! [SV34: $i,SV8: $i] :
( ( ~ ( element @ SV8 @ SV34 )
| ( empty @ SV34 )
| ( in @ SV8 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(272,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $true )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(273,plain,
! [SV10: $i,SV35: $i] :
( ( ~ ( empty @ SV35 )
| ~ ( in @ SV10 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(274,plain,
! [SV36: $i,SV11: $i] :
( ( ( SV11 = SV36 )
| ~ ( empty @ SV11 )
| ~ ( empty @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(275,plain,
! [SV12: $i,SV37: $i] :
( ( relation_of2 @ ( sK7_C @ SV37 @ SV12 ) @ SV12 @ SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(276,plain,
! [SV38: $i,SV14: $i] :
( ( ! [SY104: $i] :
( ~ ( element @ SY104 @ ( powerset @ ( cartesian_product2 @ SV14 @ SV38 ) ) )
| ( relation @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(277,plain,
! [SV15: $i] :
( ( empty @ ( powerset @ SV15 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(278,plain,
! [SV16: $i] :
( ( ( ~ ( rel_str @ SV16 ) )
= $true )
| ( ( ~ ( strict_rel_str @ SV16 )
| ( SV16
= ( rel_str_of @ ( the_carrier @ SV16 ) @ ( the_InternalRel @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(279,plain,
! [SV17: $i,SV39: $i] :
( ( relation_of2_as_subset @ ( sK3_C @ SV39 @ SV17 ) @ SV17 @ SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(280,plain,
! [SV19: $i] :
( ( ( ~ ( rel_str @ SV19 ) )
= $true )
| ( ( one_sorted_str @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(281,plain,
! [SV40: $i,SV20: $i] :
( ( ! [SY105: $i] :
( ~ ( relation_of2_as_subset @ SY105 @ SV20 @ SV40 )
| ( element @ SY105 @ ( powerset @ ( cartesian_product2 @ SV20 @ SV40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(282,plain,
! [SV22: $i] :
( ( ( ~ ( rel_str @ SV22 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV22 ) @ ( the_carrier @ SV22 ) @ ( the_carrier @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(283,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(284,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(285,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) )
| ~ ( transitive_relstr @ sK12_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(286,plain,
( ( ~ ( antisymmetric_relstr @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(287,plain,
( ( ~ ( one_sorted_str @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(288,plain,
( ( ~ ~ ( empty_carrier @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(289,plain,
( ( ~ ( rel_str @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(290,plain,
( ( ~ ( strict_rel_str @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[251]) ).
thf(291,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( empty_carrier @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(292,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(293,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(294,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( v1_partfun1 @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(295,plain,
! [SV24: $i] :
( ( ~ ! [SY93: $i,SY94: $i] :
( ~ ( relation_of2 @ SY94 @ SV24 @ SY93 )
| ( relation_of2_as_subset @ SY94 @ SV24 @ SY93 ) )
| ~ ! [SY95: $i,SY96: $i] :
( ~ ( relation_of2_as_subset @ SY96 @ SV24 @ SY95 )
| ( relation_of2 @ SY96 @ SV24 @ SY95 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(296,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(297,plain,
( ( ~ ! [SX0: $i] : ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[255]) ).
thf(298,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(299,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[256]) ).
thf(300,plain,
! [SV25: $i,SV41: $i] :
( ( ~ ( relation_of2 @ SV41 @ SV25 @ SV25 )
| ~ ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SY106 @ SY107 ) )
| ( SV25 = SY106 ) )
| ~ ! [SY108: $i,SY109: $i] :
( ( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SY108 @ SY109 ) )
| ( SV41 = SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(301,plain,
( ( ~ ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(302,plain,
( ( ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(303,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK11_B @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(304,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(305,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(306,plain,
! [SV27: $i] :
( ( ( ( empty_carrier @ SV27 )
| ~ ( one_sorted_str @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK13_B @ SV27 ) @ ( powerset @ ( the_carrier @ SV27 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(307,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(308,plain,
( ( ~ ! [SX0: $i] : ( relation_of2_as_subset @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(309,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(310,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( antisymmetric_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(311,plain,
! [SV28: $i] :
( ( ~ ( element @ ( sK10_B @ SV28 ) @ ( powerset @ SV28 ) )
| ~ ( empty @ ( sK10_B @ SV28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(312,plain,
! [SV29: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV29 ) )
= $true )
| ( ( ~ ( in @ SV29 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(313,plain,
! [SV2: $i] :
( ( ( empty_carrier @ SV2 )
= $true )
| ( ( ~ ( one_sorted_str @ SV2 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(314,plain,
! [SV30: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV30 ) )
= $true )
| ( ( element @ SV3 @ SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(315,plain,
! [SV4: $i,SV42: $i,SV31: $i] :
( ( ~ ( element @ SV31 @ ( powerset @ SV42 ) )
| ~ ( in @ SV4 @ SV31 )
| ( element @ SV4 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(316,plain,
! [SV5: $i,SV43: $i,SV32: $i] :
( ( ~ ( element @ SV32 @ ( powerset @ SV43 ) )
| ~ ( in @ SV5 @ SV32 )
| ~ ( empty @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(317,plain,
! [SV33: $i,SV7: $i] :
( ( ( ( empty @ SV7 )
| ( empty @ SV33 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV7 @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(318,plain,
! [SV34: $i,SV8: $i] :
( ( ( ~ ( element @ SV8 @ SV34 ) )
= $true )
| ( ( ( empty @ SV34 )
| ( in @ SV8 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(319,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $false )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(320,plain,
! [SV10: $i,SV35: $i] :
( ( ( ~ ( empty @ SV35 ) )
= $true )
| ( ( ~ ( in @ SV10 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(321,plain,
! [SV36: $i,SV11: $i] :
( ( ( ( SV11 = SV36 )
| ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(322,plain,
! [SV38: $i,SV14: $i,SV44: $i] :
( ( ~ ( element @ SV44 @ ( powerset @ ( cartesian_product2 @ SV14 @ SV38 ) ) )
| ( relation @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(323,plain,
! [SV16: $i] :
( ( ( rel_str @ SV16 )
= $false )
| ( ( ~ ( strict_rel_str @ SV16 )
| ( SV16
= ( rel_str_of @ ( the_carrier @ SV16 ) @ ( the_InternalRel @ SV16 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(324,plain,
! [SV19: $i] :
( ( ( rel_str @ SV19 )
= $false )
| ( ( one_sorted_str @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(325,plain,
! [SV40: $i,SV20: $i,SV45: $i] :
( ( ~ ( relation_of2_as_subset @ SV45 @ SV20 @ SV40 )
| ( element @ SV45 @ ( powerset @ ( cartesian_product2 @ SV20 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(326,plain,
! [SV22: $i] :
( ( ( rel_str @ SV22 )
= $false )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV22 ) @ ( the_carrier @ SV22 ) @ ( the_carrier @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(327,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(328,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(329,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) )
| ~ ( transitive_relstr @ sK12_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(330,plain,
( ( antisymmetric_relstr @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(331,plain,
( ( one_sorted_str @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(332,plain,
( ( ~ ( empty_carrier @ sK14_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(333,plain,
( ( rel_str @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(334,plain,
( ( strict_rel_str @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(335,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( empty_carrier @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(336,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(337,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(338,plain,
( ( ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( v1_partfun1 @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(339,plain,
! [SV24: $i] :
( ( ~ ! [SY93: $i,SY94: $i] :
( ~ ( relation_of2 @ SY94 @ SV24 @ SY93 )
| ( relation_of2_as_subset @ SY94 @ SV24 @ SY93 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(340,plain,
! [SV24: $i] :
( ( ~ ! [SY95: $i,SY96: $i] :
( ~ ( relation_of2_as_subset @ SY96 @ SV24 @ SY95 )
| ( relation_of2 @ SY96 @ SV24 @ SY95 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(341,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(342,plain,
( ( ! [SX0: $i] : ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(343,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(344,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(345,plain,
! [SV25: $i,SV41: $i] :
( ( ( ~ ( relation_of2 @ SV41 @ SV25 @ SV25 ) )
= $true )
| ( ( ~ ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SY106 @ SY107 ) )
| ( SV25 = SY106 ) )
| ~ ! [SY108: $i,SY109: $i] :
( ( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SY108 @ SY109 ) )
| ( SV41 = SY109 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(346,plain,
( ( ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(347,plain,
( ( ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(348,plain,
! [SV26: $i] :
( ( ( ~ ( element @ ( sK11_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK11_B @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(349,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(350,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(351,plain,
! [SV27: $i] :
( ( ( empty_carrier @ SV27 )
= $true )
| ( ( ~ ( one_sorted_str @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK13_B @ SV27 ) @ ( powerset @ ( the_carrier @ SV27 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(352,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(353,plain,
( ( ! [SX0: $i] : ( relation_of2_as_subset @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(354,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(355,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( antisymmetric_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(356,plain,
! [SV28: $i] :
( ( ~ ( element @ ( sK10_B @ SV28 ) @ ( powerset @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(357,plain,
! [SV28: $i] :
( ( ~ ( empty @ ( sK10_B @ SV28 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(358,plain,
! [SV29: $i,SV1: $i] :
( ( ( in @ SV1 @ SV29 )
= $false )
| ( ( ~ ( in @ SV29 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(359,plain,
! [SV2: $i] :
( ( ( one_sorted_str @ SV2 )
= $false )
| ( ( empty_carrier @ SV2 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(360,plain,
! [SV30: $i,SV3: $i] :
( ( ( in @ SV3 @ SV30 )
= $false )
| ( ( element @ SV3 @ SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(361,plain,
! [SV4: $i,SV42: $i,SV31: $i] :
( ( ( ~ ( element @ SV31 @ ( powerset @ SV42 ) )
| ~ ( in @ SV4 @ SV31 ) )
= $true )
| ( ( element @ SV4 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(362,plain,
! [SV5: $i,SV43: $i,SV32: $i] :
( ( ( ~ ( element @ SV32 @ ( powerset @ SV43 ) )
| ~ ( in @ SV5 @ SV32 ) )
= $true )
| ( ( ~ ( empty @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(363,plain,
! [SV33: $i,SV7: $i] :
( ( ( empty @ SV7 )
= $true )
| ( ( empty @ SV33 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV7 @ SV33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(364,plain,
! [SV34: $i,SV8: $i] :
( ( ( element @ SV8 @ SV34 )
= $false )
| ( ( ( empty @ SV34 )
| ( in @ SV8 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(365,plain,
! [SV10: $i,SV35: $i] :
( ( ( empty @ SV35 )
= $false )
| ( ( ~ ( in @ SV10 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(366,plain,
! [SV36: $i,SV11: $i] :
( ( ( SV11 = SV36 )
= $true )
| ( ( ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(367,plain,
! [SV38: $i,SV14: $i,SV44: $i] :
( ( ( ~ ( element @ SV44 @ ( powerset @ ( cartesian_product2 @ SV14 @ SV38 ) ) ) )
= $true )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(368,plain,
! [SV16: $i] :
( ( ( ~ ( strict_rel_str @ SV16 ) )
= $true )
| ( ( SV16
= ( rel_str_of @ ( the_carrier @ SV16 ) @ ( the_InternalRel @ SV16 ) ) )
= $true )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(369,plain,
! [SV40: $i,SV20: $i,SV45: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV45 @ SV20 @ SV40 ) )
= $true )
| ( ( element @ SV45 @ ( powerset @ ( cartesian_product2 @ SV20 @ SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(370,plain,
! [SV46: $i] :
( ( ! [SY110: $i] :
( ~ ( relation_of2 @ SY110 @ SV46 @ SV46 )
| ( rel_str @ ( rel_str_of @ SV46 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(371,plain,
! [SV47: $i] :
( ( ! [SY111: $i] :
( ~ ( relation_of2 @ SY111 @ SV47 @ SV47 )
| ( strict_rel_str @ ( rel_str_of @ SV47 @ SY111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(372,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) )
| ~ ( transitive_relstr @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(373,plain,
( ( empty_carrier @ sK14_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(374,plain,
! [SV48: $i] :
( ( ! [SY112: $i] :
( ( empty @ SV48 )
| ~ ( relation_of2 @ SY112 @ SV48 @ SV48 )
| ~ ( empty_carrier @ ( rel_str_of @ SV48 @ SY112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(375,plain,
! [SV49: $i] :
( ( ! [SY113: $i] :
( ( empty @ SV49 )
| ~ ( relation_of2 @ SY113 @ SV49 @ SV49 )
| ( strict_rel_str @ ( rel_str_of @ SV49 @ SY113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(376,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(377,plain,
! [SV50: $i] :
( ( ~ ( reflexive_relstr @ SV50 )
| ~ ( transitive_relstr @ SV50 )
| ~ ( antisymmetric_relstr @ SV50 )
| ~ ( rel_str @ SV50 )
| ( v1_partfun1 @ ( the_InternalRel @ SV50 ) @ ( the_carrier @ SV50 ) @ ( the_carrier @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(378,plain,
! [SV24: $i] :
( ( ! [SY93: $i,SY94: $i] :
( ~ ( relation_of2 @ SY94 @ SV24 @ SY93 )
| ( relation_of2_as_subset @ SY94 @ SV24 @ SY93 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(379,plain,
! [SV24: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ~ ( relation_of2_as_subset @ SY96 @ SV24 @ SY95 )
| ( relation_of2 @ SY96 @ SV24 @ SY95 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(380,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(381,plain,
! [SV51: $i] :
( ( antisymmetric_relstr @ ( incl_POSet @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(382,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(383,plain,
! [SV52: $i] :
( ( ( empty @ SV52 )
| ( antisymmetric_relstr @ ( incl_POSet @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(384,plain,
! [SV25: $i,SV41: $i] :
( ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false )
| ( ( ~ ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SY106 @ SY107 ) )
| ( SV25 = SY106 ) )
| ~ ! [SY108: $i,SY109: $i] :
( ( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SY108 @ SY109 ) )
| ( SV41 = SY109 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(385,plain,
! [SV53: $i] :
( ( rel_str @ ( incl_POSet @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(386,plain,
! [SV54: $i] :
( ( strict_rel_str @ ( incl_POSet @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(387,plain,
! [SV26: $i] :
( ( ( ~ ( element @ ( sK11_B @ SV26 ) @ ( powerset @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(388,plain,
! [SV26: $i] :
( ( ( ~ ~ ( empty @ ( sK11_B @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(389,plain,
! [SV55: $i] :
( ( ! [SY114: $i] :
( ~ ( element @ SV55 @ ( powerset @ SY114 ) )
| ( subset @ SV55 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(390,plain,
! [SV56: $i] :
( ( ! [SY115: $i] :
( ~ ( subset @ SV56 @ SY115 )
| ( element @ SV56 @ ( powerset @ SY115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(391,plain,
! [SV27: $i] :
( ( ( one_sorted_str @ SV27 )
= $false )
| ( ( empty_carrier @ SV27 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK13_B @ SV27 ) @ ( powerset @ ( the_carrier @ SV27 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(392,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(393,plain,
! [SV57: $i] :
( ( relation_of2_as_subset @ ( inclusion_order @ SV57 ) @ SV57 @ SV57 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(394,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(395,plain,
! [SV58: $i] :
( ( ! [SY116: $i] :
( ~ ( antisymmetric @ SY116 )
| ~ ( reflexive @ SY116 )
| ~ ( transitive @ SY116 )
| ~ ( v1_partfun1 @ SY116 @ SV58 @ SV58 )
| ~ ( relation_of2 @ SY116 @ SV58 @ SV58 )
| ( antisymmetric_relstr @ ( rel_str_of @ SV58 @ SY116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(396,plain,
! [SV28: $i] :
( ( element @ ( sK10_B @ SV28 ) @ ( powerset @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(397,plain,
! [SV28: $i] :
( ( empty @ ( sK10_B @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(398,plain,
! [SV1: $i,SV29: $i] :
( ( ( in @ SV29 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(399,plain,
! [SV2: $i] :
( ( ( empty @ ( the_carrier @ SV2 ) )
= $false )
| ( ( empty_carrier @ SV2 )
= $true )
| ( ( one_sorted_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(400,plain,
! [SV4: $i,SV42: $i,SV31: $i] :
( ( ( ~ ( element @ SV31 @ ( powerset @ SV42 ) ) )
= $true )
| ( ( ~ ( in @ SV4 @ SV31 ) )
= $true )
| ( ( element @ SV4 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(401,plain,
! [SV5: $i,SV43: $i,SV32: $i] :
( ( ( ~ ( element @ SV32 @ ( powerset @ SV43 ) ) )
= $true )
| ( ( ~ ( in @ SV5 @ SV32 ) )
= $true )
| ( ( ~ ( empty @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(402,plain,
! [SV33: $i,SV7: $i] :
( ( ( empty @ ( cartesian_product2 @ SV7 @ SV33 ) )
= $false )
| ( ( empty @ SV33 )
= $true )
| ( ( empty @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(403,plain,
! [SV8: $i,SV34: $i] :
( ( ( empty @ SV34 )
= $true )
| ( ( in @ SV8 @ SV34 )
= $true )
| ( ( element @ SV8 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(404,plain,
! [SV35: $i,SV10: $i] :
( ( ( in @ SV10 @ SV35 )
= $false )
| ( ( empty @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(405,plain,
! [SV36: $i,SV11: $i] :
( ( ( empty @ SV11 )
= $false )
| ( ( SV11 = SV36 )
= $true )
| ( ( ~ ( empty @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(406,plain,
! [SV38: $i,SV14: $i,SV44: $i] :
( ( ( element @ SV44 @ ( powerset @ ( cartesian_product2 @ SV14 @ SV38 ) ) )
= $false )
| ( ( relation @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(407,plain,
! [SV16: $i] :
( ( ( strict_rel_str @ SV16 )
= $false )
| ( ( SV16
= ( rel_str_of @ ( the_carrier @ SV16 ) @ ( the_InternalRel @ SV16 ) ) )
= $true )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(408,plain,
! [SV40: $i,SV20: $i,SV45: $i] :
( ( ( relation_of2_as_subset @ SV45 @ SV20 @ SV40 )
= $false )
| ( ( element @ SV45 @ ( powerset @ ( cartesian_product2 @ SV20 @ SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(409,plain,
! [SV46: $i,SV59: $i] :
( ( ~ ( relation_of2 @ SV59 @ SV46 @ SV46 )
| ( rel_str @ ( rel_str_of @ SV46 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(410,plain,
! [SV47: $i,SV60: $i] :
( ( ~ ( relation_of2 @ SV60 @ SV47 @ SV47 )
| ( strict_rel_str @ ( rel_str_of @ SV47 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(411,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(412,plain,
( ( ~ ( transitive_relstr @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(413,plain,
! [SV61: $i,SV48: $i] :
( ( ( empty @ SV48 )
| ~ ( relation_of2 @ SV61 @ SV48 @ SV48 )
| ~ ( empty_carrier @ ( rel_str_of @ SV48 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(414,plain,
! [SV62: $i,SV49: $i] :
( ( ( empty @ SV49 )
| ~ ( relation_of2 @ SV62 @ SV49 @ SV49 )
| ( strict_rel_str @ ( rel_str_of @ SV49 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(415,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(416,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[376]) ).
thf(417,plain,
! [SV50: $i] :
( ( ( ~ ( reflexive_relstr @ SV50 )
| ~ ( transitive_relstr @ SV50 )
| ~ ( antisymmetric_relstr @ SV50 )
| ~ ( rel_str @ SV50 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV50 ) @ ( the_carrier @ SV50 ) @ ( the_carrier @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(418,plain,
! [SV63: $i,SV24: $i] :
( ( ! [SY117: $i] :
( ~ ( relation_of2 @ SY117 @ SV24 @ SV63 )
| ( relation_of2_as_subset @ SY117 @ SV24 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(419,plain,
! [SV64: $i,SV24: $i] :
( ( ! [SY118: $i] :
( ~ ( relation_of2_as_subset @ SY118 @ SV24 @ SV64 )
| ( relation_of2 @ SY118 @ SV24 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(420,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(421,plain,
( ( ~ ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[380]) ).
thf(422,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(423,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(424,plain,
! [SV52: $i] :
( ( ( empty @ SV52 )
= $true )
| ( ( antisymmetric_relstr @ ( incl_POSet @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(425,plain,
! [SV41: $i,SV25: $i] :
( ( ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SY106 @ SY107 ) )
| ( SV25 = SY106 ) )
| ~ ! [SY108: $i,SY109: $i] :
( ( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SY108 @ SY109 ) )
| ( SV41 = SY109 ) ) )
= $false )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(426,plain,
! [SV26: $i] :
( ( ( element @ ( sK11_B @ SV26 ) @ ( powerset @ SV26 ) )
= $true )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(427,plain,
! [SV26: $i] :
( ( ( ~ ( empty @ ( sK11_B @ SV26 ) ) )
= $true )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(428,plain,
! [SV65: $i,SV55: $i] :
( ( ~ ( element @ SV55 @ ( powerset @ SV65 ) )
| ( subset @ SV55 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(429,plain,
! [SV66: $i,SV56: $i] :
( ( ~ ( subset @ SV56 @ SV66 )
| ( element @ SV56 @ ( powerset @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(430,plain,
! [SV27: $i] :
( ( ( ~ ( element @ ( sK13_B @ SV27 ) @ ( powerset @ ( the_carrier @ SV27 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV27 ) ) )
= $false )
| ( ( empty_carrier @ SV27 )
= $true )
| ( ( one_sorted_str @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(431,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[392]) ).
thf(432,plain,
( ( ~ ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[392]) ).
thf(433,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[394]) ).
thf(434,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[394]) ).
thf(435,plain,
! [SV58: $i,SV67: $i] :
( ( ~ ( antisymmetric @ SV67 )
| ~ ( reflexive @ SV67 )
| ~ ( transitive @ SV67 )
| ~ ( v1_partfun1 @ SV67 @ SV58 @ SV58 )
| ~ ( relation_of2 @ SV67 @ SV58 @ SV58 )
| ( antisymmetric_relstr @ ( rel_str_of @ SV58 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(436,plain,
! [SV4: $i,SV42: $i,SV31: $i] :
( ( ( element @ SV31 @ ( powerset @ SV42 ) )
= $false )
| ( ( ~ ( in @ SV4 @ SV31 ) )
= $true )
| ( ( element @ SV4 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(437,plain,
! [SV5: $i,SV43: $i,SV32: $i] :
( ( ( element @ SV32 @ ( powerset @ SV43 ) )
= $false )
| ( ( ~ ( in @ SV5 @ SV32 ) )
= $true )
| ( ( ~ ( empty @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(438,plain,
! [SV11: $i,SV36: $i] :
( ( ( empty @ SV36 )
= $false )
| ( ( SV11 = SV36 )
= $true )
| ( ( empty @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(439,plain,
! [SV46: $i,SV59: $i] :
( ( ( ~ ( relation_of2 @ SV59 @ SV46 @ SV46 ) )
= $true )
| ( ( rel_str @ ( rel_str_of @ SV46 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(440,plain,
! [SV47: $i,SV60: $i] :
( ( ( ~ ( relation_of2 @ SV60 @ SV47 @ SV47 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV47 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(441,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(442,plain,
( ( transitive_relstr @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(443,plain,
! [SV61: $i,SV48: $i] :
( ( ( ( empty @ SV48 )
| ~ ( relation_of2 @ SV61 @ SV48 @ SV48 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( rel_str_of @ SV48 @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(444,plain,
! [SV62: $i,SV49: $i] :
( ( ( ( empty @ SV49 )
| ~ ( relation_of2 @ SV62 @ SV49 @ SV49 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV49 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(445,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(446,plain,
( ( ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(447,plain,
! [SV50: $i] :
( ( ( ~ ( reflexive_relstr @ SV50 )
| ~ ( transitive_relstr @ SV50 )
| ~ ( antisymmetric_relstr @ SV50 ) )
= $true )
| ( ( ~ ( rel_str @ SV50 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV50 ) @ ( the_carrier @ SV50 ) @ ( the_carrier @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(448,plain,
! [SV63: $i,SV24: $i,SV68: $i] :
( ( ~ ( relation_of2 @ SV68 @ SV24 @ SV63 )
| ( relation_of2_as_subset @ SV68 @ SV24 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(449,plain,
! [SV64: $i,SV24: $i,SV69: $i] :
( ( ~ ( relation_of2_as_subset @ SV69 @ SV24 @ SV64 )
| ( relation_of2 @ SV69 @ SV24 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(450,plain,
( ( ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[420]) ).
thf(451,plain,
( ( ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(452,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[422]) ).
thf(453,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[423]) ).
thf(454,plain,
! [SV41: $i,SV25: $i] :
( ( ( ~ ! [SY106: $i] :
( ! [SY107: $i] :
( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SY106 @ SY107 ) )
| ( SV25 = SY106 ) ) )
= $false )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(455,plain,
! [SV41: $i,SV25: $i] :
( ( ( ~ ! [SY108: $i,SY109: $i] :
( ( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SY108 @ SY109 ) )
| ( SV41 = SY109 ) ) )
= $false )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(456,plain,
! [SV26: $i] :
( ( ( empty @ ( sK11_B @ SV26 ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(457,plain,
! [SV65: $i,SV55: $i] :
( ( ( ~ ( element @ SV55 @ ( powerset @ SV65 ) ) )
= $true )
| ( ( subset @ SV55 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(458,plain,
! [SV66: $i,SV56: $i] :
( ( ( ~ ( subset @ SV56 @ SV66 ) )
= $true )
| ( ( element @ SV56 @ ( powerset @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(459,plain,
! [SV27: $i] :
( ( ( ~ ( element @ ( sK13_B @ SV27 ) @ ( powerset @ ( the_carrier @ SV27 ) ) ) )
= $false )
| ( ( empty_carrier @ SV27 )
= $true )
| ( ( one_sorted_str @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(460,plain,
! [SV27: $i] :
( ( ( ~ ~ ( empty @ ( sK13_B @ SV27 ) ) )
= $false )
| ( ( empty_carrier @ SV27 )
= $true )
| ( ( one_sorted_str @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(461,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(462,plain,
( ( ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(463,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(464,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(465,plain,
! [SV58: $i,SV67: $i] :
( ( ( ~ ( antisymmetric @ SV67 )
| ~ ( reflexive @ SV67 )
| ~ ( transitive @ SV67 )
| ~ ( v1_partfun1 @ SV67 @ SV58 @ SV58 )
| ~ ( relation_of2 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV58 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(466,plain,
! [SV42: $i,SV31: $i,SV4: $i] :
( ( ( in @ SV4 @ SV31 )
= $false )
| ( ( element @ SV31 @ ( powerset @ SV42 ) )
= $false )
| ( ( element @ SV4 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(467,plain,
! [SV43: $i,SV32: $i,SV5: $i] :
( ( ( in @ SV5 @ SV32 )
= $false )
| ( ( element @ SV32 @ ( powerset @ SV43 ) )
= $false )
| ( ( ~ ( empty @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(468,plain,
! [SV46: $i,SV59: $i] :
( ( ( relation_of2 @ SV59 @ SV46 @ SV46 )
= $false )
| ( ( rel_str @ ( rel_str_of @ SV46 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(469,plain,
! [SV47: $i,SV60: $i] :
( ( ( relation_of2 @ SV60 @ SV47 @ SV47 )
= $false )
| ( ( strict_rel_str @ ( rel_str_of @ SV47 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(470,plain,
( ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(471,plain,
! [SV61: $i,SV48: $i] :
( ( ( empty @ SV48 )
= $true )
| ( ( ~ ( relation_of2 @ SV61 @ SV48 @ SV48 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( rel_str_of @ SV48 @ SV61 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(472,plain,
! [SV62: $i,SV49: $i] :
( ( ( empty @ SV49 )
= $true )
| ( ( ~ ( relation_of2 @ SV62 @ SV49 @ SV49 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV49 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(473,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(474,plain,
! [SV70: $i] :
( ( ~ ( reflexive_relstr @ SV70 )
| ~ ( transitive_relstr @ SV70 )
| ~ ( antisymmetric_relstr @ SV70 )
| ~ ( rel_str @ SV70 )
| ( transitive @ ( the_InternalRel @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(475,plain,
! [SV50: $i] :
( ( ( ~ ( reflexive_relstr @ SV50 )
| ~ ( transitive_relstr @ SV50 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV50 ) )
= $true )
| ( ( ~ ( rel_str @ SV50 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV50 ) @ ( the_carrier @ SV50 ) @ ( the_carrier @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(476,plain,
! [SV63: $i,SV24: $i,SV68: $i] :
( ( ( ~ ( relation_of2 @ SV68 @ SV24 @ SV63 ) )
= $true )
| ( ( relation_of2_as_subset @ SV68 @ SV24 @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(477,plain,
! [SV64: $i,SV24: $i,SV69: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV69 @ SV24 @ SV64 ) )
= $true )
| ( ( relation_of2 @ SV69 @ SV24 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(478,plain,
( ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(479,plain,
! [SV71: $i] :
( ( transitive_relstr @ ( incl_POSet @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(480,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(481,plain,
! [SV72: $i] :
( ( ( empty @ SV72 )
| ( transitive_relstr @ ( incl_POSet @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(482,plain,
! [SV41: $i,SV25: $i] :
( ( ( ! [SY106: $i] :
( ! [SY107: $i] :
( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SY106 @ SY107 ) )
| ( SV25 = SY106 ) ) )
= $true )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(483,plain,
! [SV41: $i,SV25: $i] :
( ( ( ! [SY108: $i,SY109: $i] :
( ( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SY108 @ SY109 ) )
| ( SV41 = SY109 ) ) )
= $true )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[455]) ).
thf(484,plain,
! [SV65: $i,SV55: $i] :
( ( ( element @ SV55 @ ( powerset @ SV65 ) )
= $false )
| ( ( subset @ SV55 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(485,plain,
! [SV66: $i,SV56: $i] :
( ( ( subset @ SV56 @ SV66 )
= $false )
| ( ( element @ SV56 @ ( powerset @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(486,plain,
! [SV27: $i] :
( ( ( element @ ( sK13_B @ SV27 ) @ ( powerset @ ( the_carrier @ SV27 ) ) )
= $true )
| ( ( empty_carrier @ SV27 )
= $true )
| ( ( one_sorted_str @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(487,plain,
! [SV27: $i] :
( ( ( ~ ( empty @ ( sK13_B @ SV27 ) ) )
= $true )
| ( ( empty_carrier @ SV27 )
= $true )
| ( ( one_sorted_str @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(488,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(489,plain,
! [SV73: $i] :
( ( v1_partfun1 @ ( inclusion_order @ SV73 ) @ SV73 @ SV73 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(490,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(491,plain,
! [SV74: $i] :
( ( ! [SY119: $i] :
( ~ ( antisymmetric @ SY119 )
| ~ ( reflexive @ SY119 )
| ~ ( transitive @ SY119 )
| ~ ( v1_partfun1 @ SY119 @ SV74 @ SV74 )
| ~ ( relation_of2 @ SY119 @ SV74 @ SV74 )
| ( transitive_relstr @ ( rel_str_of @ SV74 @ SY119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(492,plain,
! [SV58: $i,SV67: $i] :
( ( ( ~ ( antisymmetric @ SV67 )
| ~ ( reflexive @ SV67 )
| ~ ( transitive @ SV67 )
| ~ ( v1_partfun1 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV58 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(493,plain,
! [SV5: $i,SV32: $i,SV43: $i] :
( ( ( empty @ SV43 )
= $false )
| ( ( element @ SV32 @ ( powerset @ SV43 ) )
= $false )
| ( ( in @ SV5 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(494,plain,
( ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(495,plain,
( ( ~ ( reflexive_relstr @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[470]) ).
thf(496,plain,
! [SV48: $i,SV61: $i] :
( ( ( relation_of2 @ SV61 @ SV48 @ SV48 )
= $false )
| ( ( empty @ SV48 )
= $true )
| ( ( ~ ( empty_carrier @ ( rel_str_of @ SV48 @ SV61 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(497,plain,
! [SV49: $i,SV62: $i] :
( ( ( relation_of2 @ SV62 @ SV49 @ SV49 )
= $false )
| ( ( empty @ SV49 )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV49 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(498,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[473]) ).
thf(499,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[473]) ).
thf(500,plain,
! [SV70: $i] :
( ( ( ~ ( reflexive_relstr @ SV70 )
| ~ ( transitive_relstr @ SV70 )
| ~ ( antisymmetric_relstr @ SV70 )
| ~ ( rel_str @ SV70 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(501,plain,
! [SV50: $i] :
( ( ( ~ ( reflexive_relstr @ SV50 ) )
= $true )
| ( ( ~ ( transitive_relstr @ SV50 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV50 ) )
= $true )
| ( ( ~ ( rel_str @ SV50 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV50 ) @ ( the_carrier @ SV50 ) @ ( the_carrier @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(502,plain,
! [SV63: $i,SV24: $i,SV68: $i] :
( ( ( relation_of2 @ SV68 @ SV24 @ SV63 )
= $false )
| ( ( relation_of2_as_subset @ SV68 @ SV24 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(503,plain,
! [SV64: $i,SV24: $i,SV69: $i] :
( ( ( relation_of2_as_subset @ SV69 @ SV24 @ SV64 )
= $false )
| ( ( relation_of2 @ SV69 @ SV24 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(504,plain,
( ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(505,plain,
( ( ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[478]) ).
thf(506,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(507,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[480]) ).
thf(508,plain,
! [SV72: $i] :
( ( ( empty @ SV72 )
= $true )
| ( ( transitive_relstr @ ( incl_POSet @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(509,plain,
! [SV75: $i,SV41: $i,SV25: $i] :
( ( ( ! [SY120: $i] :
( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SV75 @ SY120 ) )
| ( SV25 = SV75 ) )
= $true )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(510,plain,
! [SV76: $i,SV41: $i,SV25: $i] :
( ( ( ! [SY121: $i] :
( ( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SV76 @ SY121 ) )
| ( SV41 = SY121 ) ) )
= $true )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(511,plain,
! [SV27: $i] :
( ( ( empty @ ( sK13_B @ SV27 ) )
= $false )
| ( ( empty_carrier @ SV27 )
= $true )
| ( ( one_sorted_str @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(512,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(513,plain,
( ( ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(514,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(515,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(516,plain,
! [SV74: $i,SV77: $i] :
( ( ~ ( antisymmetric @ SV77 )
| ~ ( reflexive @ SV77 )
| ~ ( transitive @ SV77 )
| ~ ( v1_partfun1 @ SV77 @ SV74 @ SV74 )
| ~ ( relation_of2 @ SV77 @ SV74 @ SV74 )
| ( transitive_relstr @ ( rel_str_of @ SV74 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(517,plain,
! [SV58: $i,SV67: $i] :
( ( ( ~ ( antisymmetric @ SV67 )
| ~ ( reflexive @ SV67 )
| ~ ( transitive @ SV67 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV58 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(518,plain,
( ( ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(519,plain,
( ( reflexive_relstr @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(520,plain,
! [SV61: $i,SV48: $i] :
( ( ( empty_carrier @ ( rel_str_of @ SV48 @ SV61 ) )
= $false )
| ( ( empty @ SV48 )
= $true )
| ( ( relation_of2 @ SV61 @ SV48 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(521,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(522,plain,
( ( ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(523,plain,
! [SV70: $i] :
( ( ( ~ ( reflexive_relstr @ SV70 )
| ~ ( transitive_relstr @ SV70 )
| ~ ( antisymmetric_relstr @ SV70 ) )
= $true )
| ( ( ~ ( rel_str @ SV70 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(524,plain,
! [SV50: $i] :
( ( ( reflexive_relstr @ SV50 )
= $false )
| ( ( ~ ( transitive_relstr @ SV50 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV50 ) )
= $true )
| ( ( ~ ( rel_str @ SV50 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV50 ) @ ( the_carrier @ SV50 ) @ ( the_carrier @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(525,plain,
( ( ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(526,plain,
( ( ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(527,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(528,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(529,plain,
! [SV75: $i,SV41: $i,SV25: $i] :
( ( ( ! [SY120: $i] :
( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SV75 @ SY120 ) ) )
= $true )
| ( ( SV25 = SV75 )
= $true )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(530,plain,
! [SV78: $i,SV76: $i,SV41: $i,SV25: $i] :
( ( ( ( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SV76 @ SV78 ) )
| ( SV41 = SV78 ) )
= $true )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(531,plain,
( ( ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(532,plain,
( ( ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(533,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(534,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(535,plain,
! [SV74: $i,SV77: $i] :
( ( ( ~ ( antisymmetric @ SV77 )
| ~ ( reflexive @ SV77 )
| ~ ( transitive @ SV77 )
| ~ ( v1_partfun1 @ SV77 @ SV74 @ SV74 )
| ~ ( relation_of2 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV74 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(536,plain,
! [SV58: $i,SV67: $i] :
( ( ( ~ ( antisymmetric @ SV67 )
| ~ ( reflexive @ SV67 ) )
= $true )
| ( ( ~ ( transitive @ SV67 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV58 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(537,plain,
( ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(538,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(539,plain,
! [SV79: $i] :
( ( ~ ( reflexive_relstr @ SV79 )
| ~ ( transitive_relstr @ SV79 )
| ~ ( antisymmetric_relstr @ SV79 )
| ~ ( rel_str @ SV79 )
| ( antisymmetric @ ( the_InternalRel @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(540,plain,
! [SV70: $i] :
( ( ( ~ ( reflexive_relstr @ SV70 )
| ~ ( transitive_relstr @ SV70 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV70 ) )
= $true )
| ( ( ~ ( rel_str @ SV70 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(541,plain,
! [SV50: $i] :
( ( ( transitive_relstr @ SV50 )
= $false )
| ( ( reflexive_relstr @ SV50 )
= $false )
| ( ( ~ ( antisymmetric_relstr @ SV50 ) )
= $true )
| ( ( ~ ( rel_str @ SV50 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV50 ) @ ( the_carrier @ SV50 ) @ ( the_carrier @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(542,plain,
! [SV80: $i] :
( ( reflexive_relstr @ ( incl_POSet @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(543,plain,
! [SV81: $i] :
( ( strict_rel_str @ ( incl_POSet @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(544,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(545,plain,
! [SV82: $i] :
( ( ( empty @ SV82 )
| ( reflexive_relstr @ ( incl_POSet @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(546,plain,
! [SV83: $i,SV75: $i,SV41: $i,SV25: $i] :
( ( ( ( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SV75 @ SV83 ) ) )
= $true )
| ( ( SV25 = SV75 )
= $true )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(547,plain,
! [SV78: $i,SV76: $i,SV41: $i,SV25: $i] :
( ( ( ( ( rel_str_of @ SV25 @ SV41 )
!= ( rel_str_of @ SV76 @ SV78 ) ) )
= $true )
| ( ( SV41 = SV78 )
= $true )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(548,plain,
( ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(549,plain,
! [SV84: $i] :
( ( transitive @ ( inclusion_order @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(550,plain,
! [SV85: $i] :
( ( ! [SY122: $i] :
( ~ ( antisymmetric @ SY122 )
| ~ ( reflexive @ SY122 )
| ~ ( transitive @ SY122 )
| ~ ( v1_partfun1 @ SY122 @ SV85 @ SV85 )
| ~ ( relation_of2 @ SY122 @ SV85 @ SV85 )
| ( reflexive_relstr @ ( rel_str_of @ SV85 @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(551,plain,
! [SV86: $i] :
( ( ! [SY123: $i] :
( ~ ( antisymmetric @ SY123 )
| ~ ( reflexive @ SY123 )
| ~ ( transitive @ SY123 )
| ~ ( v1_partfun1 @ SY123 @ SV86 @ SV86 )
| ~ ( relation_of2 @ SY123 @ SV86 @ SV86 )
| ( strict_rel_str @ ( rel_str_of @ SV86 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(552,plain,
! [SV74: $i,SV77: $i] :
( ( ( ~ ( antisymmetric @ SV77 )
| ~ ( reflexive @ SV77 )
| ~ ( transitive @ SV77 )
| ~ ( v1_partfun1 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV74 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(553,plain,
! [SV58: $i,SV67: $i] :
( ( ( ~ ( antisymmetric @ SV67 ) )
= $true )
| ( ( ~ ( reflexive @ SV67 ) )
= $true )
| ( ( ~ ( transitive @ SV67 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV58 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(554,plain,
( ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(555,plain,
( ( ~ ( strict_rel_str @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(556,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(557,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(558,plain,
! [SV79: $i] :
( ( ( ~ ( reflexive_relstr @ SV79 )
| ~ ( transitive_relstr @ SV79 )
| ~ ( antisymmetric_relstr @ SV79 )
| ~ ( rel_str @ SV79 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(559,plain,
! [SV70: $i] :
( ( ( ~ ( reflexive_relstr @ SV70 ) )
= $true )
| ( ( ~ ( transitive_relstr @ SV70 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV70 ) )
= $true )
| ( ( ~ ( rel_str @ SV70 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(560,plain,
! [SV50: $i] :
( ( ( antisymmetric_relstr @ SV50 )
= $false )
| ( ( reflexive_relstr @ SV50 )
= $false )
| ( ( transitive_relstr @ SV50 )
= $false )
| ( ( ~ ( rel_str @ SV50 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV50 ) @ ( the_carrier @ SV50 ) @ ( the_carrier @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(561,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(562,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[544]) ).
thf(563,plain,
! [SV82: $i] :
( ( ( empty @ SV82 )
= $true )
| ( ( reflexive_relstr @ ( incl_POSet @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(564,plain,
! [SV83: $i,SV75: $i,SV41: $i,SV25: $i] :
( ( ( ( rel_str_of @ SV25 @ SV41 )
= ( rel_str_of @ SV75 @ SV83 ) )
= $false )
| ( ( SV25 = SV75 )
= $true )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(565,plain,
! [SV78: $i,SV76: $i,SV41: $i,SV25: $i] :
( ( ( ( rel_str_of @ SV25 @ SV41 )
= ( rel_str_of @ SV76 @ SV78 ) )
= $false )
| ( ( SV41 = SV78 )
= $true )
| ( ( relation_of2 @ SV41 @ SV25 @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(566,plain,
( ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(567,plain,
( ( ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[548]) ).
thf(568,plain,
! [SV85: $i,SV87: $i] :
( ( ~ ( antisymmetric @ SV87 )
| ~ ( reflexive @ SV87 )
| ~ ( transitive @ SV87 )
| ~ ( v1_partfun1 @ SV87 @ SV85 @ SV85 )
| ~ ( relation_of2 @ SV87 @ SV85 @ SV85 )
| ( reflexive_relstr @ ( rel_str_of @ SV85 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(569,plain,
! [SV86: $i,SV88: $i] :
( ( ~ ( antisymmetric @ SV88 )
| ~ ( reflexive @ SV88 )
| ~ ( transitive @ SV88 )
| ~ ( v1_partfun1 @ SV88 @ SV86 @ SV86 )
| ~ ( relation_of2 @ SV88 @ SV86 @ SV86 )
| ( strict_rel_str @ ( rel_str_of @ SV86 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(570,plain,
! [SV74: $i,SV77: $i] :
( ( ( ~ ( antisymmetric @ SV77 )
| ~ ( reflexive @ SV77 )
| ~ ( transitive @ SV77 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV74 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(571,plain,
! [SV58: $i,SV67: $i] :
( ( ( antisymmetric @ SV67 )
= $false )
| ( ( ~ ( reflexive @ SV67 ) )
= $true )
| ( ( ~ ( transitive @ SV67 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV58 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(572,plain,
( ( ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(573,plain,
( ( strict_rel_str @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(574,plain,
( ( ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(575,plain,
( ( ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(576,plain,
! [SV79: $i] :
( ( ( ~ ( reflexive_relstr @ SV79 )
| ~ ( transitive_relstr @ SV79 )
| ~ ( antisymmetric_relstr @ SV79 ) )
= $true )
| ( ( ~ ( rel_str @ SV79 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(577,plain,
! [SV70: $i] :
( ( ( reflexive_relstr @ SV70 )
= $false )
| ( ( ~ ( transitive_relstr @ SV70 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV70 ) )
= $true )
| ( ( ~ ( rel_str @ SV70 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(578,plain,
! [SV50: $i] :
( ( ( rel_str @ SV50 )
= $false )
| ( ( transitive_relstr @ SV50 )
= $false )
| ( ( reflexive_relstr @ SV50 )
= $false )
| ( ( antisymmetric_relstr @ SV50 )
= $false )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV50 ) @ ( the_carrier @ SV50 ) @ ( the_carrier @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(579,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(580,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(581,plain,
( ( ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[566]) ).
thf(582,plain,
( ( ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[567]) ).
thf(583,plain,
! [SV85: $i,SV87: $i] :
( ( ( ~ ( antisymmetric @ SV87 )
| ~ ( reflexive @ SV87 )
| ~ ( transitive @ SV87 )
| ~ ( v1_partfun1 @ SV87 @ SV85 @ SV85 )
| ~ ( relation_of2 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV85 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(584,plain,
! [SV86: $i,SV88: $i] :
( ( ( ~ ( antisymmetric @ SV88 )
| ~ ( reflexive @ SV88 )
| ~ ( transitive @ SV88 )
| ~ ( v1_partfun1 @ SV88 @ SV86 @ SV86 )
| ~ ( relation_of2 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV86 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(585,plain,
! [SV74: $i,SV77: $i] :
( ( ( ~ ( antisymmetric @ SV77 )
| ~ ( reflexive @ SV77 ) )
= $true )
| ( ( ~ ( transitive @ SV77 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV74 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(586,plain,
! [SV58: $i,SV67: $i] :
( ( ( reflexive @ SV67 )
= $false )
| ( ( antisymmetric @ SV67 )
= $false )
| ( ( ~ ( transitive @ SV67 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV58 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(587,plain,
( ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(588,plain,
! [SV89: $i] :
( ( ~ ( reflexive_relstr @ SV89 )
| ~ ( transitive_relstr @ SV89 )
| ~ ( antisymmetric_relstr @ SV89 )
| ~ ( rel_str @ SV89 )
| ( reflexive @ ( the_InternalRel @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(589,plain,
! [SV90: $i] :
( ( ~ ( reflexive_relstr @ SV90 )
| ~ ( transitive_relstr @ SV90 )
| ~ ( antisymmetric_relstr @ SV90 )
| ~ ( rel_str @ SV90 )
| ( relation @ ( the_InternalRel @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(590,plain,
! [SV79: $i] :
( ( ( ~ ( reflexive_relstr @ SV79 )
| ~ ( transitive_relstr @ SV79 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV79 ) )
= $true )
| ( ( ~ ( rel_str @ SV79 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(591,plain,
! [SV70: $i] :
( ( ( transitive_relstr @ SV70 )
= $false )
| ( ( reflexive_relstr @ SV70 )
= $false )
| ( ( ~ ( antisymmetric_relstr @ SV70 ) )
= $true )
| ( ( ~ ( rel_str @ SV70 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(592,plain,
! [SV91: $i] :
( ( ( empty @ SV91 )
| ~ ( empty_carrier @ ( incl_POSet @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(593,plain,
! [SV92: $i] :
( ( ( empty @ SV92 )
| ( strict_rel_str @ ( incl_POSet @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(594,plain,
! [SV93: $i] :
( ( antisymmetric @ ( inclusion_order @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(595,plain,
! [SV94: $i] :
( ( reflexive @ ( inclusion_order @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(596,plain,
! [SV85: $i,SV87: $i] :
( ( ( ~ ( antisymmetric @ SV87 )
| ~ ( reflexive @ SV87 )
| ~ ( transitive @ SV87 )
| ~ ( v1_partfun1 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV85 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(597,plain,
! [SV86: $i,SV88: $i] :
( ( ( ~ ( antisymmetric @ SV88 )
| ~ ( reflexive @ SV88 )
| ~ ( transitive @ SV88 )
| ~ ( v1_partfun1 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV86 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(598,plain,
! [SV74: $i,SV77: $i] :
( ( ( ~ ( antisymmetric @ SV77 ) )
= $true )
| ( ( ~ ( reflexive @ SV77 ) )
= $true )
| ( ( ~ ( transitive @ SV77 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV74 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(599,plain,
! [SV58: $i,SV67: $i] :
( ( ( transitive @ SV67 )
= $false )
| ( ( antisymmetric @ SV67 )
= $false )
| ( ( reflexive @ SV67 )
= $false )
| ( ( ~ ( v1_partfun1 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV58 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(600,plain,
( ( ~ ( rel_str @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[587]) ).
thf(601,plain,
( ( ~ ~ ( empty_carrier @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[587]) ).
thf(602,plain,
! [SV89: $i] :
( ( ( ~ ( reflexive_relstr @ SV89 )
| ~ ( transitive_relstr @ SV89 )
| ~ ( antisymmetric_relstr @ SV89 )
| ~ ( rel_str @ SV89 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(603,plain,
! [SV90: $i] :
( ( ( ~ ( reflexive_relstr @ SV90 )
| ~ ( transitive_relstr @ SV90 )
| ~ ( antisymmetric_relstr @ SV90 )
| ~ ( rel_str @ SV90 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(604,plain,
! [SV79: $i] :
( ( ( ~ ( reflexive_relstr @ SV79 ) )
= $true )
| ( ( ~ ( transitive_relstr @ SV79 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV79 ) )
= $true )
| ( ( ~ ( rel_str @ SV79 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(605,plain,
! [SV70: $i] :
( ( ( antisymmetric_relstr @ SV70 )
= $false )
| ( ( reflexive_relstr @ SV70 )
= $false )
| ( ( transitive_relstr @ SV70 )
= $false )
| ( ( ~ ( rel_str @ SV70 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(606,plain,
! [SV91: $i] :
( ( ( empty @ SV91 )
= $true )
| ( ( ~ ( empty_carrier @ ( incl_POSet @ SV91 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(607,plain,
! [SV92: $i] :
( ( ( empty @ SV92 )
= $true )
| ( ( strict_rel_str @ ( incl_POSet @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(608,plain,
! [SV85: $i,SV87: $i] :
( ( ( ~ ( antisymmetric @ SV87 )
| ~ ( reflexive @ SV87 )
| ~ ( transitive @ SV87 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV85 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(609,plain,
! [SV86: $i,SV88: $i] :
( ( ( ~ ( antisymmetric @ SV88 )
| ~ ( reflexive @ SV88 )
| ~ ( transitive @ SV88 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV86 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(610,plain,
! [SV74: $i,SV77: $i] :
( ( ( antisymmetric @ SV77 )
= $false )
| ( ( ~ ( reflexive @ SV77 ) )
= $true )
| ( ( ~ ( transitive @ SV77 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV74 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(611,plain,
! [SV58: $i,SV67: $i] :
( ( ( v1_partfun1 @ SV67 @ SV58 @ SV58 )
= $false )
| ( ( reflexive @ SV67 )
= $false )
| ( ( antisymmetric @ SV67 )
= $false )
| ( ( transitive @ SV67 )
= $false )
| ( ( ~ ( relation_of2 @ SV67 @ SV58 @ SV58 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV58 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(612,plain,
( ( rel_str @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(613,plain,
( ( ~ ( empty_carrier @ sK12_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(614,plain,
! [SV89: $i] :
( ( ( ~ ( reflexive_relstr @ SV89 )
| ~ ( transitive_relstr @ SV89 )
| ~ ( antisymmetric_relstr @ SV89 ) )
= $true )
| ( ( ~ ( rel_str @ SV89 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(615,plain,
! [SV90: $i] :
( ( ( ~ ( reflexive_relstr @ SV90 )
| ~ ( transitive_relstr @ SV90 )
| ~ ( antisymmetric_relstr @ SV90 ) )
= $true )
| ( ( ~ ( rel_str @ SV90 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(616,plain,
! [SV79: $i] :
( ( ( reflexive_relstr @ SV79 )
= $false )
| ( ( ~ ( transitive_relstr @ SV79 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV79 ) )
= $true )
| ( ( ~ ( rel_str @ SV79 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(617,plain,
! [SV70: $i] :
( ( ( rel_str @ SV70 )
= $false )
| ( ( transitive_relstr @ SV70 )
= $false )
| ( ( reflexive_relstr @ SV70 )
= $false )
| ( ( antisymmetric_relstr @ SV70 )
= $false )
| ( ( transitive @ ( the_InternalRel @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(618,plain,
! [SV91: $i] :
( ( ( empty_carrier @ ( incl_POSet @ SV91 ) )
= $false )
| ( ( empty @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(619,plain,
! [SV85: $i,SV87: $i] :
( ( ( ~ ( antisymmetric @ SV87 )
| ~ ( reflexive @ SV87 ) )
= $true )
| ( ( ~ ( transitive @ SV87 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV85 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(620,plain,
! [SV86: $i,SV88: $i] :
( ( ( ~ ( antisymmetric @ SV88 )
| ~ ( reflexive @ SV88 ) )
= $true )
| ( ( ~ ( transitive @ SV88 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV86 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(621,plain,
! [SV74: $i,SV77: $i] :
( ( ( reflexive @ SV77 )
= $false )
| ( ( antisymmetric @ SV77 )
= $false )
| ( ( ~ ( transitive @ SV77 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV74 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(622,plain,
! [SV58: $i,SV67: $i] :
( ( ( relation_of2 @ SV67 @ SV58 @ SV58 )
= $false )
| ( ( transitive @ SV67 )
= $false )
| ( ( antisymmetric @ SV67 )
= $false )
| ( ( reflexive @ SV67 )
= $false )
| ( ( v1_partfun1 @ SV67 @ SV58 @ SV58 )
= $false )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV58 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(623,plain,
( ( empty_carrier @ sK12_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(624,plain,
! [SV89: $i] :
( ( ( ~ ( reflexive_relstr @ SV89 )
| ~ ( transitive_relstr @ SV89 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV89 ) )
= $true )
| ( ( ~ ( rel_str @ SV89 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(625,plain,
! [SV90: $i] :
( ( ( ~ ( reflexive_relstr @ SV90 )
| ~ ( transitive_relstr @ SV90 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV90 ) )
= $true )
| ( ( ~ ( rel_str @ SV90 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(626,plain,
! [SV79: $i] :
( ( ( transitive_relstr @ SV79 )
= $false )
| ( ( reflexive_relstr @ SV79 )
= $false )
| ( ( ~ ( antisymmetric_relstr @ SV79 ) )
= $true )
| ( ( ~ ( rel_str @ SV79 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(627,plain,
! [SV85: $i,SV87: $i] :
( ( ( ~ ( antisymmetric @ SV87 ) )
= $true )
| ( ( ~ ( reflexive @ SV87 ) )
= $true )
| ( ( ~ ( transitive @ SV87 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV85 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(628,plain,
! [SV86: $i,SV88: $i] :
( ( ( ~ ( antisymmetric @ SV88 ) )
= $true )
| ( ( ~ ( reflexive @ SV88 ) )
= $true )
| ( ( ~ ( transitive @ SV88 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV86 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(629,plain,
! [SV74: $i,SV77: $i] :
( ( ( transitive @ SV77 )
= $false )
| ( ( antisymmetric @ SV77 )
= $false )
| ( ( reflexive @ SV77 )
= $false )
| ( ( ~ ( v1_partfun1 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV74 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(630,plain,
! [SV89: $i] :
( ( ( ~ ( reflexive_relstr @ SV89 ) )
= $true )
| ( ( ~ ( transitive_relstr @ SV89 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV89 ) )
= $true )
| ( ( ~ ( rel_str @ SV89 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(631,plain,
! [SV90: $i] :
( ( ( ~ ( reflexive_relstr @ SV90 ) )
= $true )
| ( ( ~ ( transitive_relstr @ SV90 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV90 ) )
= $true )
| ( ( ~ ( rel_str @ SV90 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(632,plain,
! [SV79: $i] :
( ( ( antisymmetric_relstr @ SV79 )
= $false )
| ( ( reflexive_relstr @ SV79 )
= $false )
| ( ( transitive_relstr @ SV79 )
= $false )
| ( ( ~ ( rel_str @ SV79 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(633,plain,
! [SV85: $i,SV87: $i] :
( ( ( antisymmetric @ SV87 )
= $false )
| ( ( ~ ( reflexive @ SV87 ) )
= $true )
| ( ( ~ ( transitive @ SV87 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV85 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(634,plain,
! [SV86: $i,SV88: $i] :
( ( ( antisymmetric @ SV88 )
= $false )
| ( ( ~ ( reflexive @ SV88 ) )
= $true )
| ( ( ~ ( transitive @ SV88 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV86 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(635,plain,
! [SV74: $i,SV77: $i] :
( ( ( v1_partfun1 @ SV77 @ SV74 @ SV74 )
= $false )
| ( ( reflexive @ SV77 )
= $false )
| ( ( antisymmetric @ SV77 )
= $false )
| ( ( transitive @ SV77 )
= $false )
| ( ( ~ ( relation_of2 @ SV77 @ SV74 @ SV74 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV74 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(636,plain,
! [SV89: $i] :
( ( ( reflexive_relstr @ SV89 )
= $false )
| ( ( ~ ( transitive_relstr @ SV89 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV89 ) )
= $true )
| ( ( ~ ( rel_str @ SV89 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(637,plain,
! [SV90: $i] :
( ( ( reflexive_relstr @ SV90 )
= $false )
| ( ( ~ ( transitive_relstr @ SV90 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV90 ) )
= $true )
| ( ( ~ ( rel_str @ SV90 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(638,plain,
! [SV79: $i] :
( ( ( rel_str @ SV79 )
= $false )
| ( ( transitive_relstr @ SV79 )
= $false )
| ( ( reflexive_relstr @ SV79 )
= $false )
| ( ( antisymmetric_relstr @ SV79 )
= $false )
| ( ( antisymmetric @ ( the_InternalRel @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(639,plain,
! [SV85: $i,SV87: $i] :
( ( ( reflexive @ SV87 )
= $false )
| ( ( antisymmetric @ SV87 )
= $false )
| ( ( ~ ( transitive @ SV87 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV85 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(640,plain,
! [SV86: $i,SV88: $i] :
( ( ( reflexive @ SV88 )
= $false )
| ( ( antisymmetric @ SV88 )
= $false )
| ( ( ~ ( transitive @ SV88 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV86 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(641,plain,
! [SV74: $i,SV77: $i] :
( ( ( relation_of2 @ SV77 @ SV74 @ SV74 )
= $false )
| ( ( transitive @ SV77 )
= $false )
| ( ( antisymmetric @ SV77 )
= $false )
| ( ( reflexive @ SV77 )
= $false )
| ( ( v1_partfun1 @ SV77 @ SV74 @ SV74 )
= $false )
| ( ( transitive_relstr @ ( rel_str_of @ SV74 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(642,plain,
! [SV89: $i] :
( ( ( transitive_relstr @ SV89 )
= $false )
| ( ( reflexive_relstr @ SV89 )
= $false )
| ( ( ~ ( antisymmetric_relstr @ SV89 ) )
= $true )
| ( ( ~ ( rel_str @ SV89 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(643,plain,
! [SV90: $i] :
( ( ( transitive_relstr @ SV90 )
= $false )
| ( ( reflexive_relstr @ SV90 )
= $false )
| ( ( ~ ( antisymmetric_relstr @ SV90 ) )
= $true )
| ( ( ~ ( rel_str @ SV90 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(644,plain,
! [SV85: $i,SV87: $i] :
( ( ( transitive @ SV87 )
= $false )
| ( ( antisymmetric @ SV87 )
= $false )
| ( ( reflexive @ SV87 )
= $false )
| ( ( ~ ( v1_partfun1 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV85 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(645,plain,
! [SV86: $i,SV88: $i] :
( ( ( transitive @ SV88 )
= $false )
| ( ( antisymmetric @ SV88 )
= $false )
| ( ( reflexive @ SV88 )
= $false )
| ( ( ~ ( v1_partfun1 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV86 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(646,plain,
! [SV89: $i] :
( ( ( antisymmetric_relstr @ SV89 )
= $false )
| ( ( reflexive_relstr @ SV89 )
= $false )
| ( ( transitive_relstr @ SV89 )
= $false )
| ( ( ~ ( rel_str @ SV89 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(647,plain,
! [SV90: $i] :
( ( ( antisymmetric_relstr @ SV90 )
= $false )
| ( ( reflexive_relstr @ SV90 )
= $false )
| ( ( transitive_relstr @ SV90 )
= $false )
| ( ( ~ ( rel_str @ SV90 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(648,plain,
! [SV85: $i,SV87: $i] :
( ( ( v1_partfun1 @ SV87 @ SV85 @ SV85 )
= $false )
| ( ( reflexive @ SV87 )
= $false )
| ( ( antisymmetric @ SV87 )
= $false )
| ( ( transitive @ SV87 )
= $false )
| ( ( ~ ( relation_of2 @ SV87 @ SV85 @ SV85 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV85 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(649,plain,
! [SV86: $i,SV88: $i] :
( ( ( v1_partfun1 @ SV88 @ SV86 @ SV86 )
= $false )
| ( ( reflexive @ SV88 )
= $false )
| ( ( antisymmetric @ SV88 )
= $false )
| ( ( transitive @ SV88 )
= $false )
| ( ( ~ ( relation_of2 @ SV88 @ SV86 @ SV86 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV86 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(650,plain,
! [SV89: $i] :
( ( ( rel_str @ SV89 )
= $false )
| ( ( transitive_relstr @ SV89 )
= $false )
| ( ( reflexive_relstr @ SV89 )
= $false )
| ( ( antisymmetric_relstr @ SV89 )
= $false )
| ( ( reflexive @ ( the_InternalRel @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[646]) ).
thf(651,plain,
! [SV90: $i] :
( ( ( rel_str @ SV90 )
= $false )
| ( ( transitive_relstr @ SV90 )
= $false )
| ( ( reflexive_relstr @ SV90 )
= $false )
| ( ( antisymmetric_relstr @ SV90 )
= $false )
| ( ( relation @ ( the_InternalRel @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(652,plain,
! [SV85: $i,SV87: $i] :
( ( ( relation_of2 @ SV87 @ SV85 @ SV85 )
= $false )
| ( ( transitive @ SV87 )
= $false )
| ( ( antisymmetric @ SV87 )
= $false )
| ( ( reflexive @ SV87 )
= $false )
| ( ( v1_partfun1 @ SV87 @ SV85 @ SV85 )
= $false )
| ( ( reflexive_relstr @ ( rel_str_of @ SV85 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(653,plain,
! [SV86: $i,SV88: $i] :
( ( ( relation_of2 @ SV88 @ SV86 @ SV86 )
= $false )
| ( ( transitive @ SV88 )
= $false )
| ( ( antisymmetric @ SV88 )
= $false )
| ( ( reflexive @ SV88 )
= $false )
| ( ( v1_partfun1 @ SV88 @ SV86 @ SV86 )
= $false )
| ( ( strict_rel_str @ ( rel_str_of @ SV86 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(654,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[154,653,652,651,650,641,638,623,622,618,617,612,607,595,594,578,573,565,564,563,549,543,542,520,519,511,508,503,502,497,493,489,486,485,484,479,469,468,466,456,442,438,426,424,408,407,406,404,403,402,399,398,397,396,393,386,385,381,373,360,334,333,331,330,326,324,319,279,277,275,247,246,244,241,236,230,228,202,194,188,187,180,179,178,177,169,159]) ).
thf(655,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(656,plain,
$true = $true,
inference(copy,[status(thm)],[106]) ).
thf(657,plain,
( ( ( one_sorted_str @ sK14_A )
& ~ ( empty_carrier @ sK14_A ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(658,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(659,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ( ( element @ ( sK13_B @ A ) @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ ( sK13_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(660,plain,
( ( ( rel_str @ sK12_A )
& ~ ( empty_carrier @ sK12_A )
& ( strict_rel_str @ sK12_A )
& ( reflexive_relstr @ sK12_A )
& ( transitive_relstr @ sK12_A )
& ( antisymmetric_relstr @ sK12_A ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(661,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(662,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(663,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(664,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(665,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(666,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ~ ( empty_carrier @ ( incl_POSet @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ( strict_rel_str @ ( incl_POSet @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ( reflexive_relstr @ ( incl_POSet @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ( transitive_relstr @ ( incl_POSet @ A ) ) )
& ! [A: $i] :
( ( empty @ A )
| ( antisymmetric_relstr @ ( incl_POSet @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(667,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ~ ( empty_carrier @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( empty @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(668,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK11_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK11_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(669,plain,
( ( ! [A: $i,B: $i] :
( ( empty @ A )
| ( empty @ B )
| ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(670,plain,
( ( ! [A: $i] :
( ( element @ ( sK10_B @ A ) @ ( powerset @ A ) )
& ( empty @ ( sK10_B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(671,plain,
( ( empty @ sK9_A )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(672,plain,
( ( ~ ( empty @ sK8_A ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(673,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(674,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(675,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(676,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(677,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK7_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(678,plain,
( ( ! [A: $i] : ( element @ ( sK6_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(679,plain,
$true = $true,
inference(copy,[status(thm)],[83]) ).
thf(680,plain,
$true = $true,
inference(copy,[status(thm)],[82]) ).
thf(681,plain,
$true = $true,
inference(copy,[status(thm)],[81]) ).
thf(682,plain,
$true = $true,
inference(copy,[status(thm)],[80]) ).
thf(683,plain,
( ( ! [A: $i,B: $i] :
( ~ ( antisymmetric @ B )
| ~ ( reflexive @ B )
| ~ ( transitive @ B )
| ~ ( v1_partfun1 @ B @ A @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( reflexive_relstr @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( antisymmetric @ B )
| ~ ( reflexive @ B )
| ~ ( transitive @ B )
| ~ ( v1_partfun1 @ B @ A @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( strict_rel_str @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( antisymmetric @ B )
| ~ ( reflexive @ B )
| ~ ( transitive @ B )
| ~ ( v1_partfun1 @ B @ A @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( transitive_relstr @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( antisymmetric @ B )
| ~ ( reflexive @ B )
| ~ ( transitive @ B )
| ~ ( v1_partfun1 @ B @ A @ A )
| ~ ( relation_of2 @ B @ A @ A )
| ( antisymmetric_relstr @ ( rel_str_of @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(684,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(685,plain,
( ( ! [A: $i] :
~ ( empty @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(686,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)],[128]) ).
thf(687,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( ! [C: $i] :
( ! [D: $i] :
( ( rel_str_of @ A @ B )
!= ( rel_str_of @ C @ D ) )
| ( A = C ) )
& ! [C: $i,D: $i] :
( ( ( rel_str_of @ A @ B )
!= ( rel_str_of @ C @ D ) )
| ( B = D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(688,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( strict_rel_str @ A )
| ( A
= ( rel_str_of @ ( the_carrier @ A ) @ ( the_InternalRel @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(689,plain,
( ( rel_str @ sK5_A )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(690,plain,
( ( one_sorted_str @ sK4_A )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(691,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK3_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(692,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(693,plain,
( ( ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( rel_str @ ( rel_str_of @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ~ ( relation_of2 @ B @ A @ A )
| ( strict_rel_str @ ( rel_str_of @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(694,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(695,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(696,plain,
$true = $true,
inference(copy,[status(thm)],[66]) ).
thf(697,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(698,plain,
( ( ( rel_str @ sK2_A )
& ( strict_rel_str @ sK2_A ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(699,plain,
( ( ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( reflexive @ ( the_InternalRel @ A ) ) )
& ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( relation @ ( the_InternalRel @ A ) ) )
& ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( antisymmetric @ ( the_InternalRel @ A ) ) )
& ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( transitive @ ( the_InternalRel @ A ) ) )
& ! [A: $i] :
( ~ ( reflexive_relstr @ A )
| ~ ( transitive_relstr @ A )
| ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( v1_partfun1 @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(700,plain,
( ( ! [A: $i] :
( ( inclusion_order @ A )
= ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(701,plain,
( ( ! [A: $i] : ( antisymmetric @ ( inclusion_order @ A ) )
& ! [A: $i] : ( reflexive @ ( inclusion_order @ A ) )
& ! [A: $i] : ( transitive @ ( inclusion_order @ A ) )
& ! [A: $i] : ( v1_partfun1 @ ( inclusion_order @ A ) @ A @ A )
& ! [A: $i] : ( relation_of2_as_subset @ ( inclusion_order @ A ) @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(702,plain,
( ( ! [A: $i] : ( rel_str @ ( incl_POSet @ A ) )
& ! [A: $i] : ( strict_rel_str @ ( incl_POSet @ A ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(703,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(704,plain,
$true = $true,
inference(copy,[status(thm)],[58]) ).
thf(705,plain,
( ( ! [A: $i] : ( reflexive_relstr @ ( incl_POSet @ A ) )
& ! [A: $i] : ( strict_rel_str @ ( incl_POSet @ A ) )
& ! [A: $i] : ( transitive_relstr @ ( incl_POSet @ A ) )
& ! [A: $i] : ( antisymmetric_relstr @ ( incl_POSet @ A ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(706,plain,
( ( ! [A: $i] :
( ( incl_POSet @ A )
= ( rel_str_of @ A @ ( inclusion_order @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(707,plain,
( ( ( ( the_InternalRel @ ( incl_POSet @ sK1_A ) )
!= ( inclusion_order @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(708,plain,
( ( ! [SX0: $i] :
~ ( ~ ( element @ ( sK10_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ( empty @ ( sK10_B @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(709,plain,
( ( ! [SX0: $i] :
( ( empty_carrier @ SX0 )
| ~ ( one_sorted_str @ SX0 )
| ~ ( ~ ( element @ ( sK13_B @ SX0 ) @ ( powerset @ ( the_carrier @ SX0 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(710,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[692]) ).
thf(711,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[705]) ).
thf(712,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( antisymmetric_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[683]) ).
thf(713,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) )
| ~ ( transitive_relstr @ sK12_A ) )
| ~ ( antisymmetric_relstr @ sK12_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(714,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[693]) ).
thf(715,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( v1_partfun1 @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(716,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(717,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ( rel_str_of @ SX0 @ SX1 )
!= ( rel_str_of @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( ( rel_str_of @ SX0 @ SX1 )
!= ( rel_str_of @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(718,plain,
( ( ~ ( ~ ( rel_str @ sK2_A )
| ~ ( strict_rel_str @ sK2_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(719,plain,
( ( ~ ( ~ ( one_sorted_str @ sK14_A )
| ~ ~ ( empty_carrier @ sK14_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(720,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
| ~ ! [SX0: $i] : ( relation_of2_as_subset @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[701]) ).
thf(721,plain,
( ( ~ ( ~ ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[702]) ).
thf(722,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( empty_carrier @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[667]) ).
thf(723,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)],[686]) ).
thf(724,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ( element @ ( sK11_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK11_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[668]) ).
thf(725,plain,
! [SV95: $i] :
( ( ! [SY124: $i] :
( ~ ( in @ SV95 @ SY124 )
| ~ ( in @ SY124 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(726,plain,
! [SV96: $i] :
( ( ( empty_carrier @ SV96 )
| ~ ( one_sorted_str @ SV96 )
| ~ ( empty @ ( the_carrier @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(727,plain,
! [SV97: $i] :
( ( ! [SY125: $i] :
( ~ ( in @ SV97 @ SY125 )
| ( element @ SV97 @ SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(728,plain,
! [SV98: $i] :
( ( ! [SY126: $i,SY127: $i] :
( ~ ( element @ SY126 @ ( powerset @ SY127 ) )
| ~ ( in @ SV98 @ SY126 )
| ( element @ SV98 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(729,plain,
! [SV99: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ( element @ SY128 @ ( powerset @ SY129 ) )
| ~ ( in @ SV99 @ SY128 )
| ~ ( empty @ SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(730,plain,
! [SV100: $i] :
( ( subset @ SV100 @ SV100 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(731,plain,
! [SV101: $i] :
( ( ! [SY130: $i] :
( ( empty @ SV101 )
| ( empty @ SY130 )
| ~ ( empty @ ( cartesian_product2 @ SV101 @ SY130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(732,plain,
( ( empty @ sK8_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(733,plain,
! [SV102: $i] :
( ( ! [SY131: $i] :
( ~ ( element @ SV102 @ SY131 )
| ( empty @ SY131 )
| ( in @ SV102 @ SY131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(734,plain,
! [SV103: $i] :
( ( ~ ( empty @ SV103 )
| ( SV103 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(735,plain,
! [SV104: $i] :
( ( ! [SY132: $i] :
( ~ ( empty @ SY132 )
| ~ ( in @ SV104 @ SY132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(736,plain,
! [SV105: $i] :
( ( ! [SY133: $i] :
( ( SV105 = SY133 )
| ~ ( empty @ SV105 )
| ~ ( empty @ SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(737,plain,
! [SV106: $i] :
( ( ! [SY134: $i] : ( relation_of2 @ ( sK7_C @ SY134 @ SV106 ) @ SV106 @ SY134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(738,plain,
! [SV107: $i] :
( ( element @ ( sK6_B @ SV107 ) @ SV107 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(739,plain,
! [SV108: $i] :
( ( ! [SY135: $i,SY136: $i] :
( ~ ( element @ SY136 @ ( powerset @ ( cartesian_product2 @ SV108 @ SY135 ) ) )
| ( relation @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(740,plain,
! [SV109: $i] :
( ( ~ ( empty @ ( powerset @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(741,plain,
! [SV110: $i] :
( ( ~ ( rel_str @ SV110 )
| ~ ( strict_rel_str @ SV110 )
| ( SV110
= ( rel_str_of @ ( the_carrier @ SV110 ) @ ( the_InternalRel @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(742,plain,
! [SV111: $i] :
( ( ! [SY137: $i] : ( relation_of2_as_subset @ ( sK3_C @ SY137 @ SV111 ) @ SV111 @ SY137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(743,plain,
! [SV112: $i] :
( ( relation @ ( inclusion_relation @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(744,plain,
! [SV113: $i] :
( ( ~ ( rel_str @ SV113 )
| ( one_sorted_str @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(745,plain,
! [SV114: $i] :
( ( ! [SY138: $i,SY139: $i] :
( ~ ( relation_of2_as_subset @ SY139 @ SV114 @ SY138 )
| ( element @ SY139 @ ( powerset @ ( cartesian_product2 @ SV114 @ SY138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(746,plain,
! [SV115: $i] :
( ( ( inclusion_order @ SV115 )
= ( inclusion_relation @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(747,plain,
! [SV116: $i] :
( ( ~ ( rel_str @ SV116 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SV116 ) @ ( the_carrier @ SV116 ) @ ( the_carrier @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(748,plain,
! [SV117: $i] :
( ( ( incl_POSet @ SV117 )
= ( rel_str_of @ SV117 @ ( inclusion_order @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(749,plain,
( ( ( the_InternalRel @ ( incl_POSet @ sK1_A ) )
= ( inclusion_order @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(750,plain,
! [SV118: $i] :
( ( ~ ( ~ ( element @ ( sK10_B @ SV118 ) @ ( powerset @ SV118 ) )
| ~ ( empty @ ( sK10_B @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(751,plain,
! [SV119: $i] :
( ( ( empty_carrier @ SV119 )
| ~ ( one_sorted_str @ SV119 )
| ~ ( ~ ( element @ ( sK13_B @ SV119 ) @ ( powerset @ ( the_carrier @ SV119 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(752,plain,
! [SV120: $i] :
( ( ~ ( ~ ! [SY140: $i,SY141: $i] :
( ~ ( relation_of2 @ SY141 @ SV120 @ SY140 )
| ( relation_of2_as_subset @ SY141 @ SV120 @ SY140 ) )
| ~ ! [SY142: $i,SY143: $i] :
( ~ ( relation_of2_as_subset @ SY143 @ SV120 @ SY142 )
| ( relation_of2 @ SY143 @ SV120 @ SY142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(753,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(754,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( antisymmetric_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(755,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) )
| ~ ( transitive_relstr @ sK12_A ) )
| ~ ( antisymmetric_relstr @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(756,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(757,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( v1_partfun1 @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(758,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(759,plain,
! [SV121: $i] :
( ( ! [SY144: $i] :
( ~ ( relation_of2 @ SY144 @ SV121 @ SV121 )
| ~ ( ~ ! [SY145: $i] :
( ! [SY146: $i] :
( ( rel_str_of @ SV121 @ SY144 )
!= ( rel_str_of @ SY145 @ SY146 ) )
| ( SV121 = SY145 ) )
| ~ ! [SY147: $i,SY148: $i] :
( ( ( rel_str_of @ SV121 @ SY144 )
!= ( rel_str_of @ SY147 @ SY148 ) )
| ( SY144 = SY148 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(760,plain,
( ( ~ ( rel_str @ sK2_A )
| ~ ( strict_rel_str @ sK2_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(761,plain,
( ( ~ ( one_sorted_str @ sK14_A )
| ~ ~ ( empty_carrier @ sK14_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(762,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
| ~ ! [SX0: $i] : ( relation_of2_as_subset @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(763,plain,
( ( ~ ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(764,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( empty_carrier @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(765,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)],[723]) ).
thf(766,plain,
! [SV122: $i] :
( ( ( empty @ SV122 )
| ~ ( ~ ( element @ ( sK11_B @ SV122 ) @ ( powerset @ SV122 ) )
| ~ ~ ( empty @ ( sK11_B @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(767,plain,
! [SV123: $i,SV95: $i] :
( ( ~ ( in @ SV95 @ SV123 )
| ~ ( in @ SV123 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(768,plain,
! [SV96: $i] :
( ( ( ( empty_carrier @ SV96 )
| ~ ( one_sorted_str @ SV96 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(769,plain,
! [SV124: $i,SV97: $i] :
( ( ~ ( in @ SV97 @ SV124 )
| ( element @ SV97 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(770,plain,
! [SV98: $i,SV125: $i] :
( ( ! [SY149: $i] :
( ~ ( element @ SV125 @ ( powerset @ SY149 ) )
| ~ ( in @ SV98 @ SV125 )
| ( element @ SV98 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(771,plain,
! [SV99: $i,SV126: $i] :
( ( ! [SY150: $i] :
( ~ ( element @ SV126 @ ( powerset @ SY150 ) )
| ~ ( in @ SV99 @ SV126 )
| ~ ( empty @ SY150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(772,plain,
! [SV127: $i,SV101: $i] :
( ( ( empty @ SV101 )
| ( empty @ SV127 )
| ~ ( empty @ ( cartesian_product2 @ SV101 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(773,plain,
! [SV128: $i,SV102: $i] :
( ( ~ ( element @ SV102 @ SV128 )
| ( empty @ SV128 )
| ( in @ SV102 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(774,plain,
! [SV103: $i] :
( ( ( ~ ( empty @ SV103 ) )
= $true )
| ( ( SV103 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(775,plain,
! [SV104: $i,SV129: $i] :
( ( ~ ( empty @ SV129 )
| ~ ( in @ SV104 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(776,plain,
! [SV130: $i,SV105: $i] :
( ( ( SV105 = SV130 )
| ~ ( empty @ SV105 )
| ~ ( empty @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(777,plain,
! [SV106: $i,SV131: $i] :
( ( relation_of2 @ ( sK7_C @ SV131 @ SV106 ) @ SV106 @ SV131 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(778,plain,
! [SV132: $i,SV108: $i] :
( ( ! [SY151: $i] :
( ~ ( element @ SY151 @ ( powerset @ ( cartesian_product2 @ SV108 @ SV132 ) ) )
| ( relation @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(779,plain,
! [SV109: $i] :
( ( empty @ ( powerset @ SV109 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(780,plain,
! [SV110: $i] :
( ( ( ~ ( rel_str @ SV110 ) )
= $true )
| ( ( ~ ( strict_rel_str @ SV110 )
| ( SV110
= ( rel_str_of @ ( the_carrier @ SV110 ) @ ( the_InternalRel @ SV110 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(781,plain,
! [SV111: $i,SV133: $i] :
( ( relation_of2_as_subset @ ( sK3_C @ SV133 @ SV111 ) @ SV111 @ SV133 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(782,plain,
! [SV113: $i] :
( ( ( ~ ( rel_str @ SV113 ) )
= $true )
| ( ( one_sorted_str @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(783,plain,
! [SV134: $i,SV114: $i] :
( ( ! [SY152: $i] :
( ~ ( relation_of2_as_subset @ SY152 @ SV114 @ SV134 )
| ( element @ SY152 @ ( powerset @ ( cartesian_product2 @ SV114 @ SV134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(784,plain,
! [SV116: $i] :
( ( ( ~ ( rel_str @ SV116 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV116 ) @ ( the_carrier @ SV116 ) @ ( the_carrier @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(785,plain,
! [SV118: $i] :
( ( ~ ( element @ ( sK10_B @ SV118 ) @ ( powerset @ SV118 ) )
| ~ ( empty @ ( sK10_B @ SV118 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(786,plain,
! [SV119: $i] :
( ( ( ( empty_carrier @ SV119 )
| ~ ( one_sorted_str @ SV119 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK13_B @ SV119 ) @ ( powerset @ ( the_carrier @ SV119 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(787,plain,
! [SV120: $i] :
( ( ~ ! [SY140: $i,SY141: $i] :
( ~ ( relation_of2 @ SY141 @ SV120 @ SY140 )
| ( relation_of2_as_subset @ SY141 @ SV120 @ SY140 ) )
| ~ ! [SY142: $i,SY143: $i] :
( ~ ( relation_of2_as_subset @ SY143 @ SV120 @ SY142 )
| ( relation_of2 @ SY143 @ SV120 @ SY142 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(788,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[753]) ).
thf(789,plain,
( ( ~ ! [SX0: $i] : ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[753]) ).
thf(790,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(791,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( antisymmetric_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[754]) ).
thf(792,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) )
| ~ ( transitive_relstr @ sK12_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[755]) ).
thf(793,plain,
( ( ~ ( antisymmetric_relstr @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[755]) ).
thf(794,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(795,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[756]) ).
thf(796,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(797,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( v1_partfun1 @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[757]) ).
thf(798,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(799,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(800,plain,
! [SV121: $i,SV135: $i] :
( ( ~ ( relation_of2 @ SV135 @ SV121 @ SV121 )
| ~ ( ~ ! [SY153: $i] :
( ! [SY154: $i] :
( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SY153 @ SY154 ) )
| ( SV121 = SY153 ) )
| ~ ! [SY155: $i,SY156: $i] :
( ( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SY155 @ SY156 ) )
| ( SV135 = SY156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(801,plain,
( ( ~ ( rel_str @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[760]) ).
thf(802,plain,
( ( ~ ( strict_rel_str @ sK2_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[760]) ).
thf(803,plain,
( ( ~ ( one_sorted_str @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[761]) ).
thf(804,plain,
( ( ~ ~ ( empty_carrier @ sK14_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[761]) ).
thf(805,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(806,plain,
( ( ~ ! [SX0: $i] : ( relation_of2_as_subset @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[762]) ).
thf(807,plain,
( ( ~ ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[763]) ).
thf(808,plain,
( ( ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[763]) ).
thf(809,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( empty_carrier @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[764]) ).
thf(810,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[764]) ).
thf(811,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(812,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[765]) ).
thf(813,plain,
! [SV122: $i] :
( ( ( empty @ SV122 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_B @ SV122 ) @ ( powerset @ SV122 ) )
| ~ ~ ( empty @ ( sK11_B @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(814,plain,
! [SV123: $i,SV95: $i] :
( ( ( ~ ( in @ SV95 @ SV123 ) )
= $true )
| ( ( ~ ( in @ SV123 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(815,plain,
! [SV96: $i] :
( ( ( empty_carrier @ SV96 )
= $true )
| ( ( ~ ( one_sorted_str @ SV96 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV96 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(816,plain,
! [SV124: $i,SV97: $i] :
( ( ( ~ ( in @ SV97 @ SV124 ) )
= $true )
| ( ( element @ SV97 @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(817,plain,
! [SV98: $i,SV136: $i,SV125: $i] :
( ( ~ ( element @ SV125 @ ( powerset @ SV136 ) )
| ~ ( in @ SV98 @ SV125 )
| ( element @ SV98 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(818,plain,
! [SV99: $i,SV137: $i,SV126: $i] :
( ( ~ ( element @ SV126 @ ( powerset @ SV137 ) )
| ~ ( in @ SV99 @ SV126 )
| ~ ( empty @ SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(819,plain,
! [SV127: $i,SV101: $i] :
( ( ( ( empty @ SV101 )
| ( empty @ SV127 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV101 @ SV127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(820,plain,
! [SV128: $i,SV102: $i] :
( ( ( ~ ( element @ SV102 @ SV128 ) )
= $true )
| ( ( ( empty @ SV128 )
| ( in @ SV102 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(821,plain,
! [SV103: $i] :
( ( ( empty @ SV103 )
= $false )
| ( ( SV103 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(822,plain,
! [SV104: $i,SV129: $i] :
( ( ( ~ ( empty @ SV129 ) )
= $true )
| ( ( ~ ( in @ SV104 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(823,plain,
! [SV130: $i,SV105: $i] :
( ( ( ( SV105 = SV130 )
| ~ ( empty @ SV105 ) )
= $true )
| ( ( ~ ( empty @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[776]) ).
thf(824,plain,
! [SV132: $i,SV108: $i,SV138: $i] :
( ( ~ ( element @ SV138 @ ( powerset @ ( cartesian_product2 @ SV108 @ SV132 ) ) )
| ( relation @ SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(825,plain,
! [SV110: $i] :
( ( ( rel_str @ SV110 )
= $false )
| ( ( ~ ( strict_rel_str @ SV110 )
| ( SV110
= ( rel_str_of @ ( the_carrier @ SV110 ) @ ( the_InternalRel @ SV110 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(826,plain,
! [SV113: $i] :
( ( ( rel_str @ SV113 )
= $false )
| ( ( one_sorted_str @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(827,plain,
! [SV134: $i,SV114: $i,SV139: $i] :
( ( ~ ( relation_of2_as_subset @ SV139 @ SV114 @ SV134 )
| ( element @ SV139 @ ( powerset @ ( cartesian_product2 @ SV114 @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(828,plain,
! [SV116: $i] :
( ( ( rel_str @ SV116 )
= $false )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV116 ) @ ( the_carrier @ SV116 ) @ ( the_carrier @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[784]) ).
thf(829,plain,
! [SV118: $i] :
( ( ~ ( element @ ( sK10_B @ SV118 ) @ ( powerset @ SV118 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(830,plain,
! [SV118: $i] :
( ( ~ ( empty @ ( sK10_B @ SV118 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(831,plain,
! [SV119: $i] :
( ( ( empty_carrier @ SV119 )
= $true )
| ( ( ~ ( one_sorted_str @ SV119 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK13_B @ SV119 ) @ ( powerset @ ( the_carrier @ SV119 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(832,plain,
! [SV120: $i] :
( ( ~ ! [SY140: $i,SY141: $i] :
( ~ ( relation_of2 @ SY141 @ SV120 @ SY140 )
| ( relation_of2_as_subset @ SY141 @ SV120 @ SY140 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[787]) ).
thf(833,plain,
! [SV120: $i] :
( ( ~ ! [SY142: $i,SY143: $i] :
( ~ ( relation_of2_as_subset @ SY143 @ SV120 @ SY142 )
| ( relation_of2 @ SY143 @ SV120 @ SY142 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[787]) ).
thf(834,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[788]) ).
thf(835,plain,
( ( ! [SX0: $i] : ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(836,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(837,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( antisymmetric_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(838,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) )
| ~ ( transitive_relstr @ sK12_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(839,plain,
( ( antisymmetric_relstr @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(840,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(841,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(842,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(843,plain,
( ( ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( v1_partfun1 @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(844,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(845,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ( antisymmetric_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(846,plain,
! [SV121: $i,SV135: $i] :
( ( ( ~ ( relation_of2 @ SV135 @ SV121 @ SV121 ) )
= $true )
| ( ( ~ ( ~ ! [SY153: $i] :
( ! [SY154: $i] :
( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SY153 @ SY154 ) )
| ( SV121 = SY153 ) )
| ~ ! [SY155: $i,SY156: $i] :
( ( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SY155 @ SY156 ) )
| ( SV135 = SY156 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(847,plain,
( ( rel_str @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(848,plain,
( ( strict_rel_str @ sK2_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(849,plain,
( ( one_sorted_str @ sK14_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(850,plain,
( ( ~ ( empty_carrier @ sK14_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(851,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[805]) ).
thf(852,plain,
( ( ! [SX0: $i] : ( relation_of2_as_subset @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(853,plain,
( ( ! [SX0: $i] : ( rel_str @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(854,plain,
( ( ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(855,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ~ ( empty_carrier @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(856,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( empty @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(857,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(858,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(859,plain,
! [SV122: $i] :
( ( ( ~ ( element @ ( sK11_B @ SV122 ) @ ( powerset @ SV122 ) )
| ~ ~ ( empty @ ( sK11_B @ SV122 ) ) )
= $false )
| ( ( empty @ SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(860,plain,
! [SV123: $i,SV95: $i] :
( ( ( in @ SV95 @ SV123 )
= $false )
| ( ( ~ ( in @ SV123 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(861,plain,
! [SV96: $i] :
( ( ( one_sorted_str @ SV96 )
= $false )
| ( ( empty_carrier @ SV96 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV96 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[815]) ).
thf(862,plain,
! [SV124: $i,SV97: $i] :
( ( ( in @ SV97 @ SV124 )
= $false )
| ( ( element @ SV97 @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(863,plain,
! [SV98: $i,SV136: $i,SV125: $i] :
( ( ( ~ ( element @ SV125 @ ( powerset @ SV136 ) )
| ~ ( in @ SV98 @ SV125 ) )
= $true )
| ( ( element @ SV98 @ SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(864,plain,
! [SV99: $i,SV137: $i,SV126: $i] :
( ( ( ~ ( element @ SV126 @ ( powerset @ SV137 ) )
| ~ ( in @ SV99 @ SV126 ) )
= $true )
| ( ( ~ ( empty @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(865,plain,
! [SV127: $i,SV101: $i] :
( ( ( empty @ SV101 )
= $true )
| ( ( empty @ SV127 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product2 @ SV101 @ SV127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(866,plain,
! [SV128: $i,SV102: $i] :
( ( ( element @ SV102 @ SV128 )
= $false )
| ( ( ( empty @ SV128 )
| ( in @ SV102 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(867,plain,
! [SV104: $i,SV129: $i] :
( ( ( empty @ SV129 )
= $false )
| ( ( ~ ( in @ SV104 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(868,plain,
! [SV130: $i,SV105: $i] :
( ( ( SV105 = SV130 )
= $true )
| ( ( ~ ( empty @ SV105 ) )
= $true )
| ( ( ~ ( empty @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(869,plain,
! [SV132: $i,SV108: $i,SV138: $i] :
( ( ( ~ ( element @ SV138 @ ( powerset @ ( cartesian_product2 @ SV108 @ SV132 ) ) ) )
= $true )
| ( ( relation @ SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(870,plain,
! [SV110: $i] :
( ( ( ~ ( strict_rel_str @ SV110 ) )
= $true )
| ( ( SV110
= ( rel_str_of @ ( the_carrier @ SV110 ) @ ( the_InternalRel @ SV110 ) ) )
= $true )
| ( ( rel_str @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(871,plain,
! [SV134: $i,SV114: $i,SV139: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV139 @ SV114 @ SV134 ) )
= $true )
| ( ( element @ SV139 @ ( powerset @ ( cartesian_product2 @ SV114 @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[827]) ).
thf(872,plain,
! [SV118: $i] :
( ( element @ ( sK10_B @ SV118 ) @ ( powerset @ SV118 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(873,plain,
! [SV118: $i] :
( ( empty @ ( sK10_B @ SV118 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(874,plain,
! [SV119: $i] :
( ( ( one_sorted_str @ SV119 )
= $false )
| ( ( empty_carrier @ SV119 )
= $true )
| ( ( ~ ( ~ ( element @ ( sK13_B @ SV119 ) @ ( powerset @ ( the_carrier @ SV119 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(875,plain,
! [SV120: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ~ ( relation_of2 @ SY141 @ SV120 @ SY140 )
| ( relation_of2_as_subset @ SY141 @ SV120 @ SY140 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(876,plain,
! [SV120: $i] :
( ( ! [SY142: $i,SY143: $i] :
( ~ ( relation_of2_as_subset @ SY143 @ SV120 @ SY142 )
| ( relation_of2 @ SY143 @ SV120 @ SY142 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[833]) ).
thf(877,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(878,plain,
! [SV140: $i] :
( ( antisymmetric_relstr @ ( incl_POSet @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(879,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(880,plain,
! [SV141: $i] :
( ( ! [SY157: $i] :
( ~ ( antisymmetric @ SY157 )
| ~ ( reflexive @ SY157 )
| ~ ( transitive @ SY157 )
| ~ ( v1_partfun1 @ SY157 @ SV141 @ SV141 )
| ~ ( relation_of2 @ SY157 @ SV141 @ SV141 )
| ( antisymmetric_relstr @ ( rel_str_of @ SV141 @ SY157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(881,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) )
| ~ ( transitive_relstr @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(882,plain,
! [SV142: $i] :
( ( ! [SY158: $i] :
( ~ ( relation_of2 @ SY158 @ SV142 @ SV142 )
| ( rel_str @ ( rel_str_of @ SV142 @ SY158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(883,plain,
! [SV143: $i] :
( ( ! [SY159: $i] :
( ~ ( relation_of2 @ SY159 @ SV143 @ SV143 )
| ( strict_rel_str @ ( rel_str_of @ SV143 @ SY159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(884,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(885,plain,
! [SV144: $i] :
( ( ~ ( reflexive_relstr @ SV144 )
| ~ ( transitive_relstr @ SV144 )
| ~ ( antisymmetric_relstr @ SV144 )
| ~ ( rel_str @ SV144 )
| ( v1_partfun1 @ ( the_InternalRel @ SV144 ) @ ( the_carrier @ SV144 ) @ ( the_carrier @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(886,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(887,plain,
! [SV145: $i] :
( ( ( empty @ SV145 )
| ( antisymmetric_relstr @ ( incl_POSet @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(888,plain,
! [SV121: $i,SV135: $i] :
( ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false )
| ( ( ~ ( ~ ! [SY153: $i] :
( ! [SY154: $i] :
( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SY153 @ SY154 ) )
| ( SV121 = SY153 ) )
| ~ ! [SY155: $i,SY156: $i] :
( ( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SY155 @ SY156 ) )
| ( SV135 = SY156 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(889,plain,
( ( empty_carrier @ sK14_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[850]) ).
thf(890,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(891,plain,
! [SV146: $i] :
( ( relation_of2_as_subset @ ( inclusion_order @ SV146 ) @ SV146 @ SV146 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(892,plain,
! [SV147: $i] :
( ( rel_str @ ( incl_POSet @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(893,plain,
! [SV148: $i] :
( ( strict_rel_str @ ( incl_POSet @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(894,plain,
! [SV149: $i] :
( ( ! [SY160: $i] :
( ( empty @ SV149 )
| ~ ( relation_of2 @ SY160 @ SV149 @ SV149 )
| ~ ( empty_carrier @ ( rel_str_of @ SV149 @ SY160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(895,plain,
! [SV150: $i] :
( ( ! [SY161: $i] :
( ( empty @ SV150 )
| ~ ( relation_of2 @ SY161 @ SV150 @ SV150 )
| ( strict_rel_str @ ( rel_str_of @ SV150 @ SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(896,plain,
! [SV151: $i] :
( ( ! [SY162: $i] :
( ~ ( element @ SV151 @ ( powerset @ SY162 ) )
| ( subset @ SV151 @ SY162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(897,plain,
! [SV152: $i] :
( ( ! [SY163: $i] :
( ~ ( subset @ SV152 @ SY163 )
| ( element @ SV152 @ ( powerset @ SY163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(898,plain,
! [SV122: $i] :
( ( ( ~ ( element @ ( sK11_B @ SV122 ) @ ( powerset @ SV122 ) ) )
= $false )
| ( ( empty @ SV122 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[859]) ).
thf(899,plain,
! [SV122: $i] :
( ( ( ~ ~ ( empty @ ( sK11_B @ SV122 ) ) )
= $false )
| ( ( empty @ SV122 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[859]) ).
thf(900,plain,
! [SV95: $i,SV123: $i] :
( ( ( in @ SV123 @ SV95 )
= $false )
| ( ( in @ SV95 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(901,plain,
! [SV96: $i] :
( ( ( empty @ ( the_carrier @ SV96 ) )
= $false )
| ( ( empty_carrier @ SV96 )
= $true )
| ( ( one_sorted_str @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(902,plain,
! [SV98: $i,SV136: $i,SV125: $i] :
( ( ( ~ ( element @ SV125 @ ( powerset @ SV136 ) ) )
= $true )
| ( ( ~ ( in @ SV98 @ SV125 ) )
= $true )
| ( ( element @ SV98 @ SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(903,plain,
! [SV99: $i,SV137: $i,SV126: $i] :
( ( ( ~ ( element @ SV126 @ ( powerset @ SV137 ) ) )
= $true )
| ( ( ~ ( in @ SV99 @ SV126 ) )
= $true )
| ( ( ~ ( empty @ SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(904,plain,
! [SV127: $i,SV101: $i] :
( ( ( empty @ ( cartesian_product2 @ SV101 @ SV127 ) )
= $false )
| ( ( empty @ SV127 )
= $true )
| ( ( empty @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(905,plain,
! [SV102: $i,SV128: $i] :
( ( ( empty @ SV128 )
= $true )
| ( ( in @ SV102 @ SV128 )
= $true )
| ( ( element @ SV102 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(906,plain,
! [SV129: $i,SV104: $i] :
( ( ( in @ SV104 @ SV129 )
= $false )
| ( ( empty @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(907,plain,
! [SV130: $i,SV105: $i] :
( ( ( empty @ SV105 )
= $false )
| ( ( SV105 = SV130 )
= $true )
| ( ( ~ ( empty @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(908,plain,
! [SV132: $i,SV108: $i,SV138: $i] :
( ( ( element @ SV138 @ ( powerset @ ( cartesian_product2 @ SV108 @ SV132 ) ) )
= $false )
| ( ( relation @ SV138 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[869]) ).
thf(909,plain,
! [SV110: $i] :
( ( ( strict_rel_str @ SV110 )
= $false )
| ( ( SV110
= ( rel_str_of @ ( the_carrier @ SV110 ) @ ( the_InternalRel @ SV110 ) ) )
= $true )
| ( ( rel_str @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(910,plain,
! [SV134: $i,SV114: $i,SV139: $i] :
( ( ( relation_of2_as_subset @ SV139 @ SV114 @ SV134 )
= $false )
| ( ( element @ SV139 @ ( powerset @ ( cartesian_product2 @ SV114 @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(911,plain,
! [SV119: $i] :
( ( ( ~ ( element @ ( sK13_B @ SV119 ) @ ( powerset @ ( the_carrier @ SV119 ) ) )
| ~ ~ ( empty @ ( sK13_B @ SV119 ) ) )
= $false )
| ( ( empty_carrier @ SV119 )
= $true )
| ( ( one_sorted_str @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(912,plain,
! [SV153: $i,SV120: $i] :
( ( ! [SY164: $i] :
( ~ ( relation_of2 @ SY164 @ SV120 @ SV153 )
| ( relation_of2_as_subset @ SY164 @ SV120 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(913,plain,
! [SV154: $i,SV120: $i] :
( ( ! [SY165: $i] :
( ~ ( relation_of2_as_subset @ SY165 @ SV120 @ SV154 )
| ( relation_of2 @ SY165 @ SV120 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(914,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(915,plain,
( ( ~ ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[877]) ).
thf(916,plain,
( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[879]) ).
thf(917,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[879]) ).
thf(918,plain,
! [SV141: $i,SV155: $i] :
( ( ~ ( antisymmetric @ SV155 )
| ~ ( reflexive @ SV155 )
| ~ ( transitive @ SV155 )
| ~ ( v1_partfun1 @ SV155 @ SV141 @ SV141 )
| ~ ( relation_of2 @ SV155 @ SV141 @ SV141 )
| ( antisymmetric_relstr @ ( rel_str_of @ SV141 @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(919,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(920,plain,
( ( ~ ( transitive_relstr @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[881]) ).
thf(921,plain,
! [SV142: $i,SV156: $i] :
( ( ~ ( relation_of2 @ SV156 @ SV142 @ SV142 )
| ( rel_str @ ( rel_str_of @ SV142 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(922,plain,
! [SV143: $i,SV157: $i] :
( ( ~ ( relation_of2 @ SV157 @ SV143 @ SV143 )
| ( strict_rel_str @ ( rel_str_of @ SV143 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(923,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[884]) ).
thf(924,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[884]) ).
thf(925,plain,
! [SV144: $i] :
( ( ( ~ ( reflexive_relstr @ SV144 )
| ~ ( transitive_relstr @ SV144 )
| ~ ( antisymmetric_relstr @ SV144 )
| ~ ( rel_str @ SV144 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV144 ) @ ( the_carrier @ SV144 ) @ ( the_carrier @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(926,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[886]) ).
thf(927,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[886]) ).
thf(928,plain,
! [SV145: $i] :
( ( ( empty @ SV145 )
= $true )
| ( ( antisymmetric_relstr @ ( incl_POSet @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(929,plain,
! [SV135: $i,SV121: $i] :
( ( ( ~ ! [SY153: $i] :
( ! [SY154: $i] :
( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SY153 @ SY154 ) )
| ( SV121 = SY153 ) )
| ~ ! [SY155: $i,SY156: $i] :
( ( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SY155 @ SY156 ) )
| ( SV135 = SY156 ) ) )
= $false )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(930,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(931,plain,
( ( ~ ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[890]) ).
thf(932,plain,
! [SV158: $i,SV149: $i] :
( ( ( empty @ SV149 )
| ~ ( relation_of2 @ SV158 @ SV149 @ SV149 )
| ~ ( empty_carrier @ ( rel_str_of @ SV149 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(933,plain,
! [SV159: $i,SV150: $i] :
( ( ( empty @ SV150 )
| ~ ( relation_of2 @ SV159 @ SV150 @ SV150 )
| ( strict_rel_str @ ( rel_str_of @ SV150 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(934,plain,
! [SV160: $i,SV151: $i] :
( ( ~ ( element @ SV151 @ ( powerset @ SV160 ) )
| ( subset @ SV151 @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(935,plain,
! [SV161: $i,SV152: $i] :
( ( ~ ( subset @ SV152 @ SV161 )
| ( element @ SV152 @ ( powerset @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(936,plain,
! [SV122: $i] :
( ( ( element @ ( sK11_B @ SV122 ) @ ( powerset @ SV122 ) )
= $true )
| ( ( empty @ SV122 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[898]) ).
thf(937,plain,
! [SV122: $i] :
( ( ( ~ ( empty @ ( sK11_B @ SV122 ) ) )
= $true )
| ( ( empty @ SV122 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[899]) ).
thf(938,plain,
! [SV98: $i,SV136: $i,SV125: $i] :
( ( ( element @ SV125 @ ( powerset @ SV136 ) )
= $false )
| ( ( ~ ( in @ SV98 @ SV125 ) )
= $true )
| ( ( element @ SV98 @ SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(939,plain,
! [SV99: $i,SV137: $i,SV126: $i] :
( ( ( element @ SV126 @ ( powerset @ SV137 ) )
= $false )
| ( ( ~ ( in @ SV99 @ SV126 ) )
= $true )
| ( ( ~ ( empty @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(940,plain,
! [SV105: $i,SV130: $i] :
( ( ( empty @ SV130 )
= $false )
| ( ( SV105 = SV130 )
= $true )
| ( ( empty @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(941,plain,
! [SV119: $i] :
( ( ( ~ ( element @ ( sK13_B @ SV119 ) @ ( powerset @ ( the_carrier @ SV119 ) ) ) )
= $false )
| ( ( empty_carrier @ SV119 )
= $true )
| ( ( one_sorted_str @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(942,plain,
! [SV119: $i] :
( ( ( ~ ~ ( empty @ ( sK13_B @ SV119 ) ) )
= $false )
| ( ( empty_carrier @ SV119 )
= $true )
| ( ( one_sorted_str @ SV119 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(943,plain,
! [SV153: $i,SV120: $i,SV162: $i] :
( ( ~ ( relation_of2 @ SV162 @ SV120 @ SV153 )
| ( relation_of2_as_subset @ SV162 @ SV120 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(944,plain,
! [SV154: $i,SV120: $i,SV163: $i] :
( ( ~ ( relation_of2_as_subset @ SV163 @ SV120 @ SV154 )
| ( relation_of2 @ SV163 @ SV120 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(945,plain,
( ( ~ ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[914]) ).
thf(946,plain,
( ( ! [SX0: $i] : ( transitive_relstr @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[915]) ).
thf(947,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(948,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( transitive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(949,plain,
! [SV141: $i,SV155: $i] :
( ( ( ~ ( antisymmetric @ SV155 )
| ~ ( reflexive @ SV155 )
| ~ ( transitive @ SV155 )
| ~ ( v1_partfun1 @ SV155 @ SV141 @ SV141 )
| ~ ( relation_of2 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV141 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(950,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[919]) ).
thf(951,plain,
( ( transitive_relstr @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[920]) ).
thf(952,plain,
! [SV142: $i,SV156: $i] :
( ( ( ~ ( relation_of2 @ SV156 @ SV142 @ SV142 ) )
= $true )
| ( ( rel_str @ ( rel_str_of @ SV142 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(953,plain,
! [SV143: $i,SV157: $i] :
( ( ( ~ ( relation_of2 @ SV157 @ SV143 @ SV143 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV143 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(954,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[923]) ).
thf(955,plain,
( ( ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( transitive @ ( the_InternalRel @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[924]) ).
thf(956,plain,
! [SV144: $i] :
( ( ( ~ ( reflexive_relstr @ SV144 )
| ~ ( transitive_relstr @ SV144 )
| ~ ( antisymmetric_relstr @ SV144 ) )
= $true )
| ( ( ~ ( rel_str @ SV144 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV144 ) @ ( the_carrier @ SV144 ) @ ( the_carrier @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(957,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[926]) ).
thf(958,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ( transitive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[927]) ).
thf(959,plain,
! [SV135: $i,SV121: $i] :
( ( ( ~ ! [SY153: $i] :
( ! [SY154: $i] :
( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SY153 @ SY154 ) )
| ( SV121 = SY153 ) ) )
= $false )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[929]) ).
thf(960,plain,
! [SV135: $i,SV121: $i] :
( ( ( ~ ! [SY155: $i,SY156: $i] :
( ( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SY155 @ SY156 ) )
| ( SV135 = SY156 ) ) )
= $false )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[929]) ).
thf(961,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[930]) ).
thf(962,plain,
( ( ! [SX0: $i] : ( v1_partfun1 @ ( inclusion_order @ SX0 ) @ SX0 @ SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[931]) ).
thf(963,plain,
! [SV158: $i,SV149: $i] :
( ( ( ( empty @ SV149 )
| ~ ( relation_of2 @ SV158 @ SV149 @ SV149 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( rel_str_of @ SV149 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(964,plain,
! [SV159: $i,SV150: $i] :
( ( ( ( empty @ SV150 )
| ~ ( relation_of2 @ SV159 @ SV150 @ SV150 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV150 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(965,plain,
! [SV160: $i,SV151: $i] :
( ( ( ~ ( element @ SV151 @ ( powerset @ SV160 ) ) )
= $true )
| ( ( subset @ SV151 @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[934]) ).
thf(966,plain,
! [SV161: $i,SV152: $i] :
( ( ( ~ ( subset @ SV152 @ SV161 ) )
= $true )
| ( ( element @ SV152 @ ( powerset @ SV161 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(967,plain,
! [SV122: $i] :
( ( ( empty @ ( sK11_B @ SV122 ) )
= $false )
| ( ( empty @ SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(968,plain,
! [SV136: $i,SV125: $i,SV98: $i] :
( ( ( in @ SV98 @ SV125 )
= $false )
| ( ( element @ SV125 @ ( powerset @ SV136 ) )
= $false )
| ( ( element @ SV98 @ SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(969,plain,
! [SV137: $i,SV126: $i,SV99: $i] :
( ( ( in @ SV99 @ SV126 )
= $false )
| ( ( element @ SV126 @ ( powerset @ SV137 ) )
= $false )
| ( ( ~ ( empty @ SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(970,plain,
! [SV119: $i] :
( ( ( element @ ( sK13_B @ SV119 ) @ ( powerset @ ( the_carrier @ SV119 ) ) )
= $true )
| ( ( empty_carrier @ SV119 )
= $true )
| ( ( one_sorted_str @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[941]) ).
thf(971,plain,
! [SV119: $i] :
( ( ( ~ ( empty @ ( sK13_B @ SV119 ) ) )
= $true )
| ( ( empty_carrier @ SV119 )
= $true )
| ( ( one_sorted_str @ SV119 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[942]) ).
thf(972,plain,
! [SV153: $i,SV120: $i,SV162: $i] :
( ( ( ~ ( relation_of2 @ SV162 @ SV120 @ SV153 ) )
= $true )
| ( ( relation_of2_as_subset @ SV162 @ SV120 @ SV153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(973,plain,
! [SV154: $i,SV120: $i,SV163: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV163 @ SV120 @ SV154 ) )
= $true )
| ( ( relation_of2 @ SV163 @ SV120 @ SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(974,plain,
( ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) )
| ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(975,plain,
! [SV164: $i] :
( ( transitive_relstr @ ( incl_POSet @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(976,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(977,plain,
! [SV165: $i] :
( ( ! [SY166: $i] :
( ~ ( antisymmetric @ SY166 )
| ~ ( reflexive @ SY166 )
| ~ ( transitive @ SY166 )
| ~ ( v1_partfun1 @ SY166 @ SV165 @ SV165 )
| ~ ( relation_of2 @ SY166 @ SV165 @ SV165 )
| ( transitive_relstr @ ( rel_str_of @ SV165 @ SY166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(978,plain,
! [SV141: $i,SV155: $i] :
( ( ( ~ ( antisymmetric @ SV155 )
| ~ ( reflexive @ SV155 )
| ~ ( transitive @ SV155 )
| ~ ( v1_partfun1 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV141 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[949]) ).
thf(979,plain,
( ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
| ~ ( reflexive_relstr @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(980,plain,
! [SV142: $i,SV156: $i] :
( ( ( relation_of2 @ SV156 @ SV142 @ SV142 )
= $false )
| ( ( rel_str @ ( rel_str_of @ SV142 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(981,plain,
! [SV143: $i,SV157: $i] :
( ( ( relation_of2 @ SV157 @ SV143 @ SV143 )
= $false )
| ( ( strict_rel_str @ ( rel_str_of @ SV143 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(982,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(983,plain,
! [SV166: $i] :
( ( ~ ( reflexive_relstr @ SV166 )
| ~ ( transitive_relstr @ SV166 )
| ~ ( antisymmetric_relstr @ SV166 )
| ~ ( rel_str @ SV166 )
| ( transitive @ ( the_InternalRel @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(984,plain,
! [SV144: $i] :
( ( ( ~ ( reflexive_relstr @ SV144 )
| ~ ( transitive_relstr @ SV144 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV144 ) )
= $true )
| ( ( ~ ( rel_str @ SV144 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV144 ) @ ( the_carrier @ SV144 ) @ ( the_carrier @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(985,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(986,plain,
! [SV167: $i] :
( ( ( empty @ SV167 )
| ( transitive_relstr @ ( incl_POSet @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(987,plain,
! [SV135: $i,SV121: $i] :
( ( ( ! [SY153: $i] :
( ! [SY154: $i] :
( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SY153 @ SY154 ) )
| ( SV121 = SY153 ) ) )
= $true )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[959]) ).
thf(988,plain,
! [SV135: $i,SV121: $i] :
( ( ( ! [SY155: $i,SY156: $i] :
( ( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SY155 @ SY156 ) )
| ( SV135 = SY156 ) ) )
= $true )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[960]) ).
thf(989,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
| ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(990,plain,
! [SV168: $i] :
( ( v1_partfun1 @ ( inclusion_order @ SV168 ) @ SV168 @ SV168 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(991,plain,
! [SV158: $i,SV149: $i] :
( ( ( empty @ SV149 )
= $true )
| ( ( ~ ( relation_of2 @ SV158 @ SV149 @ SV149 ) )
= $true )
| ( ( ~ ( empty_carrier @ ( rel_str_of @ SV149 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(992,plain,
! [SV159: $i,SV150: $i] :
( ( ( empty @ SV150 )
= $true )
| ( ( ~ ( relation_of2 @ SV159 @ SV150 @ SV150 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV150 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(993,plain,
! [SV160: $i,SV151: $i] :
( ( ( element @ SV151 @ ( powerset @ SV160 ) )
= $false )
| ( ( subset @ SV151 @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(994,plain,
! [SV161: $i,SV152: $i] :
( ( ( subset @ SV152 @ SV161 )
= $false )
| ( ( element @ SV152 @ ( powerset @ SV161 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(995,plain,
! [SV99: $i,SV126: $i,SV137: $i] :
( ( ( empty @ SV137 )
= $false )
| ( ( element @ SV126 @ ( powerset @ SV137 ) )
= $false )
| ( ( in @ SV99 @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(996,plain,
! [SV119: $i] :
( ( ( empty @ ( sK13_B @ SV119 ) )
= $false )
| ( ( empty_carrier @ SV119 )
= $true )
| ( ( one_sorted_str @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(997,plain,
! [SV153: $i,SV120: $i,SV162: $i] :
( ( ( relation_of2 @ SV162 @ SV120 @ SV153 )
= $false )
| ( ( relation_of2_as_subset @ SV162 @ SV120 @ SV153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(998,plain,
! [SV154: $i,SV120: $i,SV163: $i] :
( ( ( relation_of2_as_subset @ SV163 @ SV120 @ SV154 )
= $false )
| ( ( relation_of2 @ SV163 @ SV120 @ SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(999,plain,
( ( ~ ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(1000,plain,
( ( ~ ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(1001,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1002,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[976]) ).
thf(1003,plain,
! [SV165: $i,SV169: $i] :
( ( ~ ( antisymmetric @ SV169 )
| ~ ( reflexive @ SV169 )
| ~ ( transitive @ SV169 )
| ~ ( v1_partfun1 @ SV169 @ SV165 @ SV165 )
| ~ ( relation_of2 @ SV169 @ SV165 @ SV165 )
| ( transitive_relstr @ ( rel_str_of @ SV165 @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1004,plain,
! [SV141: $i,SV155: $i] :
( ( ( ~ ( antisymmetric @ SV155 )
| ~ ( reflexive @ SV155 )
| ~ ( transitive @ SV155 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV141 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1005,plain,
( ( ~ ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1006,plain,
( ( ~ ( reflexive_relstr @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[979]) ).
thf(1007,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1008,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1009,plain,
! [SV166: $i] :
( ( ( ~ ( reflexive_relstr @ SV166 )
| ~ ( transitive_relstr @ SV166 )
| ~ ( antisymmetric_relstr @ SV166 )
| ~ ( rel_str @ SV166 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[983]) ).
thf(1010,plain,
! [SV144: $i] :
( ( ( ~ ( reflexive_relstr @ SV144 ) )
= $true )
| ( ( ~ ( transitive_relstr @ SV144 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV144 ) )
= $true )
| ( ( ~ ( rel_str @ SV144 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV144 ) @ ( the_carrier @ SV144 ) @ ( the_carrier @ SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1011,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1012,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[985]) ).
thf(1013,plain,
! [SV167: $i] :
( ( ( empty @ SV167 )
= $true )
| ( ( transitive_relstr @ ( incl_POSet @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1014,plain,
! [SV170: $i,SV135: $i,SV121: $i] :
( ( ( ! [SY167: $i] :
( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SV170 @ SY167 ) )
| ( SV121 = SV170 ) )
= $true )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1015,plain,
! [SV171: $i,SV135: $i,SV121: $i] :
( ( ( ! [SY168: $i] :
( ( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SV171 @ SY168 ) )
| ( SV135 = SY168 ) ) )
= $true )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1016,plain,
( ( ~ ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1017,plain,
( ( ~ ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[989]) ).
thf(1018,plain,
! [SV149: $i,SV158: $i] :
( ( ( relation_of2 @ SV158 @ SV149 @ SV149 )
= $false )
| ( ( empty @ SV149 )
= $true )
| ( ( ~ ( empty_carrier @ ( rel_str_of @ SV149 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1019,plain,
! [SV150: $i,SV159: $i] :
( ( ( relation_of2 @ SV159 @ SV150 @ SV150 )
= $false )
| ( ( empty @ SV150 )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV150 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1020,plain,
( ( ! [SX0: $i] : ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[999]) ).
thf(1021,plain,
( ( ! [SX0: $i] : ( strict_rel_str @ ( incl_POSet @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1000]) ).
thf(1022,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( reflexive_relstr @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1023,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( antisymmetric @ SX1 )
| ~ ( reflexive @ SX1 )
| ~ ( transitive @ SX1 )
| ~ ( v1_partfun1 @ SX1 @ SX0 @ SX0 )
| ~ ( relation_of2 @ SX1 @ SX0 @ SX0 )
| ( strict_rel_str @ ( rel_str_of @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1002]) ).
thf(1024,plain,
! [SV165: $i,SV169: $i] :
( ( ( ~ ( antisymmetric @ SV169 )
| ~ ( reflexive @ SV169 )
| ~ ( transitive @ SV169 )
| ~ ( v1_partfun1 @ SV169 @ SV165 @ SV165 )
| ~ ( relation_of2 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV165 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1025,plain,
! [SV141: $i,SV155: $i] :
( ( ( ~ ( antisymmetric @ SV155 )
| ~ ( reflexive @ SV155 ) )
= $true )
| ( ( ~ ( transitive @ SV155 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV141 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1026,plain,
( ( ~ ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1027,plain,
( ( reflexive_relstr @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1028,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1007]) ).
thf(1029,plain,
( ( ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( antisymmetric @ ( the_InternalRel @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1008]) ).
thf(1030,plain,
! [SV166: $i] :
( ( ( ~ ( reflexive_relstr @ SV166 )
| ~ ( transitive_relstr @ SV166 )
| ~ ( antisymmetric_relstr @ SV166 ) )
= $true )
| ( ( ~ ( rel_str @ SV166 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1031,plain,
! [SV144: $i] :
( ( ( reflexive_relstr @ SV144 )
= $false )
| ( ( ~ ( transitive_relstr @ SV144 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV144 ) )
= $true )
| ( ( ~ ( rel_str @ SV144 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV144 ) @ ( the_carrier @ SV144 ) @ ( the_carrier @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1032,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1011]) ).
thf(1033,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ( reflexive_relstr @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1012]) ).
thf(1034,plain,
! [SV170: $i,SV135: $i,SV121: $i] :
( ( ( ! [SY167: $i] :
( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SV170 @ SY167 ) ) )
= $true )
| ( ( SV121 = SV170 )
= $true )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1035,plain,
! [SV172: $i,SV171: $i,SV135: $i,SV121: $i] :
( ( ( ( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SV171 @ SV172 ) )
| ( SV135 = SV172 ) )
= $true )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1036,plain,
( ( ~ ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1037,plain,
( ( ! [SX0: $i] : ( transitive @ ( inclusion_order @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1017]) ).
thf(1038,plain,
! [SV158: $i,SV149: $i] :
( ( ( empty_carrier @ ( rel_str_of @ SV149 @ SV158 ) )
= $false )
| ( ( empty @ SV149 )
= $true )
| ( ( relation_of2 @ SV158 @ SV149 @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1039,plain,
! [SV173: $i] :
( ( reflexive_relstr @ ( incl_POSet @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1040,plain,
! [SV174: $i] :
( ( strict_rel_str @ ( incl_POSet @ SV174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1041,plain,
! [SV175: $i] :
( ( ! [SY169: $i] :
( ~ ( antisymmetric @ SY169 )
| ~ ( reflexive @ SY169 )
| ~ ( transitive @ SY169 )
| ~ ( v1_partfun1 @ SY169 @ SV175 @ SV175 )
| ~ ( relation_of2 @ SY169 @ SV175 @ SV175 )
| ( reflexive_relstr @ ( rel_str_of @ SV175 @ SY169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1042,plain,
! [SV176: $i] :
( ( ! [SY170: $i] :
( ~ ( antisymmetric @ SY170 )
| ~ ( reflexive @ SY170 )
| ~ ( transitive @ SY170 )
| ~ ( v1_partfun1 @ SY170 @ SV176 @ SV176 )
| ~ ( relation_of2 @ SY170 @ SV176 @ SV176 )
| ( strict_rel_str @ ( rel_str_of @ SV176 @ SY170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1043,plain,
! [SV165: $i,SV169: $i] :
( ( ( ~ ( antisymmetric @ SV169 )
| ~ ( reflexive @ SV169 )
| ~ ( transitive @ SV169 )
| ~ ( v1_partfun1 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV165 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1044,plain,
! [SV141: $i,SV155: $i] :
( ( ( ~ ( antisymmetric @ SV155 ) )
= $true )
| ( ( ~ ( reflexive @ SV155 ) )
= $true )
| ( ( ~ ( transitive @ SV155 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV141 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1045,plain,
( ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
| ~ ( strict_rel_str @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1046,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1047,plain,
! [SV177: $i] :
( ( ~ ( reflexive_relstr @ SV177 )
| ~ ( transitive_relstr @ SV177 )
| ~ ( antisymmetric_relstr @ SV177 )
| ~ ( rel_str @ SV177 )
| ( antisymmetric @ ( the_InternalRel @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1048,plain,
! [SV166: $i] :
( ( ( ~ ( reflexive_relstr @ SV166 )
| ~ ( transitive_relstr @ SV166 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV166 ) )
= $true )
| ( ( ~ ( rel_str @ SV166 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1049,plain,
! [SV144: $i] :
( ( ( transitive_relstr @ SV144 )
= $false )
| ( ( reflexive_relstr @ SV144 )
= $false )
| ( ( ~ ( antisymmetric_relstr @ SV144 ) )
= $true )
| ( ( ~ ( rel_str @ SV144 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV144 ) @ ( the_carrier @ SV144 ) @ ( the_carrier @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1050,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) )
| ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1032]) ).
thf(1051,plain,
! [SV178: $i] :
( ( ( empty @ SV178 )
| ( reflexive_relstr @ ( incl_POSet @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1052,plain,
! [SV179: $i,SV170: $i,SV135: $i,SV121: $i] :
( ( ( ( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SV170 @ SV179 ) ) )
= $true )
| ( ( SV121 = SV170 )
= $true )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1053,plain,
! [SV172: $i,SV171: $i,SV135: $i,SV121: $i] :
( ( ( ( ( rel_str_of @ SV121 @ SV135 )
!= ( rel_str_of @ SV171 @ SV172 ) ) )
= $true )
| ( ( SV135 = SV172 )
= $true )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1054,plain,
( ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) )
| ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1055,plain,
! [SV180: $i] :
( ( transitive @ ( inclusion_order @ SV180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1056,plain,
! [SV175: $i,SV181: $i] :
( ( ~ ( antisymmetric @ SV181 )
| ~ ( reflexive @ SV181 )
| ~ ( transitive @ SV181 )
| ~ ( v1_partfun1 @ SV181 @ SV175 @ SV175 )
| ~ ( relation_of2 @ SV181 @ SV175 @ SV175 )
| ( reflexive_relstr @ ( rel_str_of @ SV175 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1057,plain,
! [SV176: $i,SV182: $i] :
( ( ~ ( antisymmetric @ SV182 )
| ~ ( reflexive @ SV182 )
| ~ ( transitive @ SV182 )
| ~ ( v1_partfun1 @ SV182 @ SV176 @ SV176 )
| ~ ( relation_of2 @ SV182 @ SV176 @ SV176 )
| ( strict_rel_str @ ( rel_str_of @ SV176 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1058,plain,
! [SV165: $i,SV169: $i] :
( ( ( ~ ( antisymmetric @ SV169 )
| ~ ( reflexive @ SV169 )
| ~ ( transitive @ SV169 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV165 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1043]) ).
thf(1059,plain,
! [SV141: $i,SV155: $i] :
( ( ( antisymmetric @ SV155 )
= $false )
| ( ( ~ ( reflexive @ SV155 ) )
= $true )
| ( ( ~ ( transitive @ SV155 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV141 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1060,plain,
( ( ~ ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1045]) ).
thf(1061,plain,
( ( ~ ( strict_rel_str @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1045]) ).
thf(1062,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1063,plain,
( ( ~ ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1046]) ).
thf(1064,plain,
! [SV177: $i] :
( ( ( ~ ( reflexive_relstr @ SV177 )
| ~ ( transitive_relstr @ SV177 )
| ~ ( antisymmetric_relstr @ SV177 )
| ~ ( rel_str @ SV177 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1047]) ).
thf(1065,plain,
! [SV166: $i] :
( ( ( ~ ( reflexive_relstr @ SV166 ) )
= $true )
| ( ( ~ ( transitive_relstr @ SV166 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV166 ) )
= $true )
| ( ( ~ ( rel_str @ SV166 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1066,plain,
! [SV144: $i] :
( ( ( antisymmetric_relstr @ SV144 )
= $false )
| ( ( reflexive_relstr @ SV144 )
= $false )
| ( ( transitive_relstr @ SV144 )
= $false )
| ( ( ~ ( rel_str @ SV144 ) )
= $true )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV144 ) @ ( the_carrier @ SV144 ) @ ( the_carrier @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1067,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1068,plain,
( ( ~ ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1050]) ).
thf(1069,plain,
! [SV178: $i] :
( ( ( empty @ SV178 )
= $true )
| ( ( reflexive_relstr @ ( incl_POSet @ SV178 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1070,plain,
! [SV179: $i,SV170: $i,SV135: $i,SV121: $i] :
( ( ( ( rel_str_of @ SV121 @ SV135 )
= ( rel_str_of @ SV170 @ SV179 ) )
= $false )
| ( ( SV121 = SV170 )
= $true )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1071,plain,
! [SV172: $i,SV171: $i,SV135: $i,SV121: $i] :
( ( ( ( rel_str_of @ SV121 @ SV135 )
= ( rel_str_of @ SV171 @ SV172 ) )
= $false )
| ( ( SV135 = SV172 )
= $true )
| ( ( relation_of2 @ SV135 @ SV121 @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1072,plain,
( ( ~ ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1054]) ).
thf(1073,plain,
( ( ~ ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1054]) ).
thf(1074,plain,
! [SV175: $i,SV181: $i] :
( ( ( ~ ( antisymmetric @ SV181 )
| ~ ( reflexive @ SV181 )
| ~ ( transitive @ SV181 )
| ~ ( v1_partfun1 @ SV181 @ SV175 @ SV175 )
| ~ ( relation_of2 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV175 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1056]) ).
thf(1075,plain,
! [SV176: $i,SV182: $i] :
( ( ( ~ ( antisymmetric @ SV182 )
| ~ ( reflexive @ SV182 )
| ~ ( transitive @ SV182 )
| ~ ( v1_partfun1 @ SV182 @ SV176 @ SV176 )
| ~ ( relation_of2 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV176 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1076,plain,
! [SV165: $i,SV169: $i] :
( ( ( ~ ( antisymmetric @ SV169 )
| ~ ( reflexive @ SV169 ) )
= $true )
| ( ( ~ ( transitive @ SV169 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV165 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1077,plain,
! [SV141: $i,SV155: $i] :
( ( ( reflexive @ SV155 )
= $false )
| ( ( antisymmetric @ SV155 )
= $false )
| ( ( ~ ( transitive @ SV155 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV141 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1078,plain,
( ( ~ ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1060]) ).
thf(1079,plain,
( ( strict_rel_str @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1061]) ).
thf(1080,plain,
( ( ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( reflexive @ ( the_InternalRel @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1062]) ).
thf(1081,plain,
( ( ! [SX0: $i] :
( ~ ( reflexive_relstr @ SX0 )
| ~ ( transitive_relstr @ SX0 )
| ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ( relation @ ( the_InternalRel @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1063]) ).
thf(1082,plain,
! [SV177: $i] :
( ( ( ~ ( reflexive_relstr @ SV177 )
| ~ ( transitive_relstr @ SV177 )
| ~ ( antisymmetric_relstr @ SV177 ) )
= $true )
| ( ( ~ ( rel_str @ SV177 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1083,plain,
! [SV166: $i] :
( ( ( reflexive_relstr @ SV166 )
= $false )
| ( ( ~ ( transitive_relstr @ SV166 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV166 ) )
= $true )
| ( ( ~ ( rel_str @ SV166 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1084,plain,
! [SV144: $i] :
( ( ( rel_str @ SV144 )
= $false )
| ( ( transitive_relstr @ SV144 )
= $false )
| ( ( reflexive_relstr @ SV144 )
= $false )
| ( ( antisymmetric_relstr @ SV144 )
= $false )
| ( ( v1_partfun1 @ ( the_InternalRel @ SV144 ) @ ( the_carrier @ SV144 ) @ ( the_carrier @ SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1085,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( empty_carrier @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1086,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ( strict_rel_str @ ( incl_POSet @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1087,plain,
( ( ! [SX0: $i] : ( antisymmetric @ ( inclusion_order @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1072]) ).
thf(1088,plain,
( ( ! [SX0: $i] : ( reflexive @ ( inclusion_order @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1073]) ).
thf(1089,plain,
! [SV175: $i,SV181: $i] :
( ( ( ~ ( antisymmetric @ SV181 )
| ~ ( reflexive @ SV181 )
| ~ ( transitive @ SV181 )
| ~ ( v1_partfun1 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV175 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1090,plain,
! [SV176: $i,SV182: $i] :
( ( ( ~ ( antisymmetric @ SV182 )
| ~ ( reflexive @ SV182 )
| ~ ( transitive @ SV182 )
| ~ ( v1_partfun1 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV176 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1091,plain,
! [SV165: $i,SV169: $i] :
( ( ( ~ ( antisymmetric @ SV169 ) )
= $true )
| ( ( ~ ( reflexive @ SV169 ) )
= $true )
| ( ( ~ ( transitive @ SV169 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV165 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1092,plain,
! [SV141: $i,SV155: $i] :
( ( ( transitive @ SV155 )
= $false )
| ( ( antisymmetric @ SV155 )
= $false )
| ( ( reflexive @ SV155 )
= $false )
| ( ( ~ ( v1_partfun1 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV141 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1093,plain,
( ( ~ ( rel_str @ sK12_A )
| ~ ~ ( empty_carrier @ sK12_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1094,plain,
! [SV183: $i] :
( ( ~ ( reflexive_relstr @ SV183 )
| ~ ( transitive_relstr @ SV183 )
| ~ ( antisymmetric_relstr @ SV183 )
| ~ ( rel_str @ SV183 )
| ( reflexive @ ( the_InternalRel @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1095,plain,
! [SV184: $i] :
( ( ~ ( reflexive_relstr @ SV184 )
| ~ ( transitive_relstr @ SV184 )
| ~ ( antisymmetric_relstr @ SV184 )
| ~ ( rel_str @ SV184 )
| ( relation @ ( the_InternalRel @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1096,plain,
! [SV177: $i] :
( ( ( ~ ( reflexive_relstr @ SV177 )
| ~ ( transitive_relstr @ SV177 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV177 ) )
= $true )
| ( ( ~ ( rel_str @ SV177 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1082]) ).
thf(1097,plain,
! [SV166: $i] :
( ( ( transitive_relstr @ SV166 )
= $false )
| ( ( reflexive_relstr @ SV166 )
= $false )
| ( ( ~ ( antisymmetric_relstr @ SV166 ) )
= $true )
| ( ( ~ ( rel_str @ SV166 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1098,plain,
! [SV185: $i] :
( ( ( empty @ SV185 )
| ~ ( empty_carrier @ ( incl_POSet @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1099,plain,
! [SV186: $i] :
( ( ( empty @ SV186 )
| ( strict_rel_str @ ( incl_POSet @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1100,plain,
! [SV187: $i] :
( ( antisymmetric @ ( inclusion_order @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1101,plain,
! [SV188: $i] :
( ( reflexive @ ( inclusion_order @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1102,plain,
! [SV175: $i,SV181: $i] :
( ( ( ~ ( antisymmetric @ SV181 )
| ~ ( reflexive @ SV181 )
| ~ ( transitive @ SV181 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV175 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1103,plain,
! [SV176: $i,SV182: $i] :
( ( ( ~ ( antisymmetric @ SV182 )
| ~ ( reflexive @ SV182 )
| ~ ( transitive @ SV182 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV176 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1090]) ).
thf(1104,plain,
! [SV165: $i,SV169: $i] :
( ( ( antisymmetric @ SV169 )
= $false )
| ( ( ~ ( reflexive @ SV169 ) )
= $true )
| ( ( ~ ( transitive @ SV169 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV165 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1091]) ).
thf(1105,plain,
! [SV141: $i,SV155: $i] :
( ( ( v1_partfun1 @ SV155 @ SV141 @ SV141 )
= $false )
| ( ( reflexive @ SV155 )
= $false )
| ( ( antisymmetric @ SV155 )
= $false )
| ( ( transitive @ SV155 )
= $false )
| ( ( ~ ( relation_of2 @ SV155 @ SV141 @ SV141 ) )
= $true )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV141 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1106,plain,
( ( ~ ( rel_str @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1093]) ).
thf(1107,plain,
( ( ~ ~ ( empty_carrier @ sK12_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1093]) ).
thf(1108,plain,
! [SV183: $i] :
( ( ( ~ ( reflexive_relstr @ SV183 )
| ~ ( transitive_relstr @ SV183 )
| ~ ( antisymmetric_relstr @ SV183 )
| ~ ( rel_str @ SV183 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1094]) ).
thf(1109,plain,
! [SV184: $i] :
( ( ( ~ ( reflexive_relstr @ SV184 )
| ~ ( transitive_relstr @ SV184 )
| ~ ( antisymmetric_relstr @ SV184 )
| ~ ( rel_str @ SV184 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1095]) ).
thf(1110,plain,
! [SV177: $i] :
( ( ( ~ ( reflexive_relstr @ SV177 ) )
= $true )
| ( ( ~ ( transitive_relstr @ SV177 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV177 ) )
= $true )
| ( ( ~ ( rel_str @ SV177 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1096]) ).
thf(1111,plain,
! [SV166: $i] :
( ( ( antisymmetric_relstr @ SV166 )
= $false )
| ( ( reflexive_relstr @ SV166 )
= $false )
| ( ( transitive_relstr @ SV166 )
= $false )
| ( ( ~ ( rel_str @ SV166 ) )
= $true )
| ( ( transitive @ ( the_InternalRel @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1112,plain,
! [SV185: $i] :
( ( ( empty @ SV185 )
= $true )
| ( ( ~ ( empty_carrier @ ( incl_POSet @ SV185 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1098]) ).
thf(1113,plain,
! [SV186: $i] :
( ( ( empty @ SV186 )
= $true )
| ( ( strict_rel_str @ ( incl_POSet @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1099]) ).
thf(1114,plain,
! [SV175: $i,SV181: $i] :
( ( ( ~ ( antisymmetric @ SV181 )
| ~ ( reflexive @ SV181 ) )
= $true )
| ( ( ~ ( transitive @ SV181 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV175 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1102]) ).
thf(1115,plain,
! [SV176: $i,SV182: $i] :
( ( ( ~ ( antisymmetric @ SV182 )
| ~ ( reflexive @ SV182 ) )
= $true )
| ( ( ~ ( transitive @ SV182 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV176 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1103]) ).
thf(1116,plain,
! [SV165: $i,SV169: $i] :
( ( ( reflexive @ SV169 )
= $false )
| ( ( antisymmetric @ SV169 )
= $false )
| ( ( ~ ( transitive @ SV169 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV165 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1117,plain,
! [SV141: $i,SV155: $i] :
( ( ( relation_of2 @ SV155 @ SV141 @ SV141 )
= $false )
| ( ( transitive @ SV155 )
= $false )
| ( ( antisymmetric @ SV155 )
= $false )
| ( ( reflexive @ SV155 )
= $false )
| ( ( v1_partfun1 @ SV155 @ SV141 @ SV141 )
= $false )
| ( ( antisymmetric_relstr @ ( rel_str_of @ SV141 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1118,plain,
( ( rel_str @ sK12_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1119,plain,
( ( ~ ( empty_carrier @ sK12_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1120,plain,
! [SV183: $i] :
( ( ( ~ ( reflexive_relstr @ SV183 )
| ~ ( transitive_relstr @ SV183 )
| ~ ( antisymmetric_relstr @ SV183 ) )
= $true )
| ( ( ~ ( rel_str @ SV183 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1121,plain,
! [SV184: $i] :
( ( ( ~ ( reflexive_relstr @ SV184 )
| ~ ( transitive_relstr @ SV184 )
| ~ ( antisymmetric_relstr @ SV184 ) )
= $true )
| ( ( ~ ( rel_str @ SV184 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1122,plain,
! [SV177: $i] :
( ( ( reflexive_relstr @ SV177 )
= $false )
| ( ( ~ ( transitive_relstr @ SV177 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV177 ) )
= $true )
| ( ( ~ ( rel_str @ SV177 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1123,plain,
! [SV166: $i] :
( ( ( rel_str @ SV166 )
= $false )
| ( ( transitive_relstr @ SV166 )
= $false )
| ( ( reflexive_relstr @ SV166 )
= $false )
| ( ( antisymmetric_relstr @ SV166 )
= $false )
| ( ( transitive @ ( the_InternalRel @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1111]) ).
thf(1124,plain,
! [SV185: $i] :
( ( ( empty_carrier @ ( incl_POSet @ SV185 ) )
= $false )
| ( ( empty @ SV185 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1112]) ).
thf(1125,plain,
! [SV175: $i,SV181: $i] :
( ( ( ~ ( antisymmetric @ SV181 ) )
= $true )
| ( ( ~ ( reflexive @ SV181 ) )
= $true )
| ( ( ~ ( transitive @ SV181 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV175 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1126,plain,
! [SV176: $i,SV182: $i] :
( ( ( ~ ( antisymmetric @ SV182 ) )
= $true )
| ( ( ~ ( reflexive @ SV182 ) )
= $true )
| ( ( ~ ( transitive @ SV182 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV176 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1127,plain,
! [SV165: $i,SV169: $i] :
( ( ( transitive @ SV169 )
= $false )
| ( ( antisymmetric @ SV169 )
= $false )
| ( ( reflexive @ SV169 )
= $false )
| ( ( ~ ( v1_partfun1 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV165 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1116]) ).
thf(1128,plain,
( ( empty_carrier @ sK12_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1129,plain,
! [SV183: $i] :
( ( ( ~ ( reflexive_relstr @ SV183 )
| ~ ( transitive_relstr @ SV183 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV183 ) )
= $true )
| ( ( ~ ( rel_str @ SV183 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1130,plain,
! [SV184: $i] :
( ( ( ~ ( reflexive_relstr @ SV184 )
| ~ ( transitive_relstr @ SV184 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV184 ) )
= $true )
| ( ( ~ ( rel_str @ SV184 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1121]) ).
thf(1131,plain,
! [SV177: $i] :
( ( ( transitive_relstr @ SV177 )
= $false )
| ( ( reflexive_relstr @ SV177 )
= $false )
| ( ( ~ ( antisymmetric_relstr @ SV177 ) )
= $true )
| ( ( ~ ( rel_str @ SV177 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1132,plain,
! [SV175: $i,SV181: $i] :
( ( ( antisymmetric @ SV181 )
= $false )
| ( ( ~ ( reflexive @ SV181 ) )
= $true )
| ( ( ~ ( transitive @ SV181 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV175 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1133,plain,
! [SV176: $i,SV182: $i] :
( ( ( antisymmetric @ SV182 )
= $false )
| ( ( ~ ( reflexive @ SV182 ) )
= $true )
| ( ( ~ ( transitive @ SV182 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV176 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1126]) ).
thf(1134,plain,
! [SV165: $i,SV169: $i] :
( ( ( v1_partfun1 @ SV169 @ SV165 @ SV165 )
= $false )
| ( ( reflexive @ SV169 )
= $false )
| ( ( antisymmetric @ SV169 )
= $false )
| ( ( transitive @ SV169 )
= $false )
| ( ( ~ ( relation_of2 @ SV169 @ SV165 @ SV165 ) )
= $true )
| ( ( transitive_relstr @ ( rel_str_of @ SV165 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1127]) ).
thf(1135,plain,
! [SV183: $i] :
( ( ( ~ ( reflexive_relstr @ SV183 ) )
= $true )
| ( ( ~ ( transitive_relstr @ SV183 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV183 ) )
= $true )
| ( ( ~ ( rel_str @ SV183 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1136,plain,
! [SV184: $i] :
( ( ( ~ ( reflexive_relstr @ SV184 ) )
= $true )
| ( ( ~ ( transitive_relstr @ SV184 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV184 ) )
= $true )
| ( ( ~ ( rel_str @ SV184 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1137,plain,
! [SV177: $i] :
( ( ( antisymmetric_relstr @ SV177 )
= $false )
| ( ( reflexive_relstr @ SV177 )
= $false )
| ( ( transitive_relstr @ SV177 )
= $false )
| ( ( ~ ( rel_str @ SV177 ) )
= $true )
| ( ( antisymmetric @ ( the_InternalRel @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1138,plain,
! [SV175: $i,SV181: $i] :
( ( ( reflexive @ SV181 )
= $false )
| ( ( antisymmetric @ SV181 )
= $false )
| ( ( ~ ( transitive @ SV181 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV175 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1139,plain,
! [SV176: $i,SV182: $i] :
( ( ( reflexive @ SV182 )
= $false )
| ( ( antisymmetric @ SV182 )
= $false )
| ( ( ~ ( transitive @ SV182 ) )
= $true )
| ( ( ~ ( v1_partfun1 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV176 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1133]) ).
thf(1140,plain,
! [SV165: $i,SV169: $i] :
( ( ( relation_of2 @ SV169 @ SV165 @ SV165 )
= $false )
| ( ( transitive @ SV169 )
= $false )
| ( ( antisymmetric @ SV169 )
= $false )
| ( ( reflexive @ SV169 )
= $false )
| ( ( v1_partfun1 @ SV169 @ SV165 @ SV165 )
= $false )
| ( ( transitive_relstr @ ( rel_str_of @ SV165 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1141,plain,
! [SV183: $i] :
( ( ( reflexive_relstr @ SV183 )
= $false )
| ( ( ~ ( transitive_relstr @ SV183 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV183 ) )
= $true )
| ( ( ~ ( rel_str @ SV183 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1142,plain,
! [SV184: $i] :
( ( ( reflexive_relstr @ SV184 )
= $false )
| ( ( ~ ( transitive_relstr @ SV184 ) )
= $true )
| ( ( ~ ( antisymmetric_relstr @ SV184 ) )
= $true )
| ( ( ~ ( rel_str @ SV184 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1143,plain,
! [SV177: $i] :
( ( ( rel_str @ SV177 )
= $false )
| ( ( transitive_relstr @ SV177 )
= $false )
| ( ( reflexive_relstr @ SV177 )
= $false )
| ( ( antisymmetric_relstr @ SV177 )
= $false )
| ( ( antisymmetric @ ( the_InternalRel @ SV177 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1144,plain,
! [SV175: $i,SV181: $i] :
( ( ( transitive @ SV181 )
= $false )
| ( ( antisymmetric @ SV181 )
= $false )
| ( ( reflexive @ SV181 )
= $false )
| ( ( ~ ( v1_partfun1 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV175 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1145,plain,
! [SV176: $i,SV182: $i] :
( ( ( transitive @ SV182 )
= $false )
| ( ( antisymmetric @ SV182 )
= $false )
| ( ( reflexive @ SV182 )
= $false )
| ( ( ~ ( v1_partfun1 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( ~ ( relation_of2 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV176 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1146,plain,
! [SV183: $i] :
( ( ( transitive_relstr @ SV183 )
= $false )
| ( ( reflexive_relstr @ SV183 )
= $false )
| ( ( ~ ( antisymmetric_relstr @ SV183 ) )
= $true )
| ( ( ~ ( rel_str @ SV183 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1141]) ).
thf(1147,plain,
! [SV184: $i] :
( ( ( transitive_relstr @ SV184 )
= $false )
| ( ( reflexive_relstr @ SV184 )
= $false )
| ( ( ~ ( antisymmetric_relstr @ SV184 ) )
= $true )
| ( ( ~ ( rel_str @ SV184 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1148,plain,
! [SV175: $i,SV181: $i] :
( ( ( v1_partfun1 @ SV181 @ SV175 @ SV175 )
= $false )
| ( ( reflexive @ SV181 )
= $false )
| ( ( antisymmetric @ SV181 )
= $false )
| ( ( transitive @ SV181 )
= $false )
| ( ( ~ ( relation_of2 @ SV181 @ SV175 @ SV175 ) )
= $true )
| ( ( reflexive_relstr @ ( rel_str_of @ SV175 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1149,plain,
! [SV176: $i,SV182: $i] :
( ( ( v1_partfun1 @ SV182 @ SV176 @ SV176 )
= $false )
| ( ( reflexive @ SV182 )
= $false )
| ( ( antisymmetric @ SV182 )
= $false )
| ( ( transitive @ SV182 )
= $false )
| ( ( ~ ( relation_of2 @ SV182 @ SV176 @ SV176 ) )
= $true )
| ( ( strict_rel_str @ ( rel_str_of @ SV176 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1150,plain,
! [SV183: $i] :
( ( ( antisymmetric_relstr @ SV183 )
= $false )
| ( ( reflexive_relstr @ SV183 )
= $false )
| ( ( transitive_relstr @ SV183 )
= $false )
| ( ( ~ ( rel_str @ SV183 ) )
= $true )
| ( ( reflexive @ ( the_InternalRel @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1146]) ).
thf(1151,plain,
! [SV184: $i] :
( ( ( antisymmetric_relstr @ SV184 )
= $false )
| ( ( reflexive_relstr @ SV184 )
= $false )
| ( ( transitive_relstr @ SV184 )
= $false )
| ( ( ~ ( rel_str @ SV184 ) )
= $true )
| ( ( relation @ ( the_InternalRel @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1152,plain,
! [SV175: $i,SV181: $i] :
( ( ( relation_of2 @ SV181 @ SV175 @ SV175 )
= $false )
| ( ( transitive @ SV181 )
= $false )
| ( ( antisymmetric @ SV181 )
= $false )
| ( ( reflexive @ SV181 )
= $false )
| ( ( v1_partfun1 @ SV181 @ SV175 @ SV175 )
= $false )
| ( ( reflexive_relstr @ ( rel_str_of @ SV175 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1153,plain,
! [SV176: $i,SV182: $i] :
( ( ( relation_of2 @ SV182 @ SV176 @ SV176 )
= $false )
| ( ( transitive @ SV182 )
= $false )
| ( ( antisymmetric @ SV182 )
= $false )
| ( ( reflexive @ SV182 )
= $false )
| ( ( v1_partfun1 @ SV182 @ SV176 @ SV176 )
= $false )
| ( ( strict_rel_str @ ( rel_str_of @ SV176 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1154,plain,
! [SV183: $i] :
( ( ( rel_str @ SV183 )
= $false )
| ( ( transitive_relstr @ SV183 )
= $false )
| ( ( reflexive_relstr @ SV183 )
= $false )
| ( ( antisymmetric_relstr @ SV183 )
= $false )
| ( ( reflexive @ ( the_InternalRel @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1155,plain,
! [SV184: $i] :
( ( ( rel_str @ SV184 )
= $false )
| ( ( transitive_relstr @ SV184 )
= $false )
| ( ( reflexive_relstr @ SV184 )
= $false )
| ( ( antisymmetric_relstr @ SV184 )
= $false )
| ( ( relation @ ( the_InternalRel @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1151]) ).
thf(1156,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[656,1155,1154,1153,1152,1143,1140,1128,1124,1123,1118,1117,1113,1101,1100,1084,1079,1071,1070,1069,1055,1040,1039,1038,1027,1019,1013,998,997,996,995,994,993,990,981,980,975,970,968,967,951,940,936,928,910,909,908,906,905,904,901,900,893,892,891,889,878,873,872,862,849,848,847,839,828,826,821,781,779,777,749,748,746,743,738,732,730,704,696,690,689,682,681,680,679,671,661]) ).
thf(1157,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1156,654]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU368+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 20:09:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.36 .
% 0.18/0.36
% 0.18/0.36 No.of.Axioms: 52
% 0.18/0.36
% 0.18/0.36 Length.of.Defs: 0
% 0.18/0.36
% 0.18/0.36 Contains.Choice.Funs: false
% 0.18/0.39 .
% 0.18/0.39 (rf:0,axioms:52,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:54,loop_count:0,foatp_calls:0,translation:fof_full).......................................................
% 0.58/0.86
% 0.58/0.86 ********************************
% 0.58/0.86 * All subproblems solved! *
% 0.58/0.86 ********************************
% 0.58/0.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:52,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:1156,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.05/1.30
% 1.05/1.30 %**** Beginning of derivation protocol ****
% 1.05/1.30 % SZS output start CNFRefutation
% See solution above
% 1.05/1.31
% 1.05/1.31 %**** End of derivation protocol ****
% 1.05/1.31 %**** no. of clauses in derivation: 1157 ****
% 1.05/1.31 %**** clause counter: 1156 ****
% 1.05/1.31
% 1.05/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:52,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:1156,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------