TSTP Solution File: SEU360+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU360+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 12:11:05 EDT 2022
% Result : Theorem 0.51s 0.78s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 57
% Syntax : Number of formulae : 657 ( 230 unt; 30 typ; 0 def)
% Number of atoms : 6253 (1659 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 12876 (2262 ~;2213 |; 99 &;8250 @)
% ( 8 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 10 con; 0-3 aty)
% Number of variables : 1402 ( 0 ^1382 !; 20 ?;1402 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
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_ex_inf_of_relstr_set,type,
ex_inf_of_relstr_set: $i > $i > $o ).
thf(tp_ex_sup_of_relstr_set,type,
ex_sup_of_relstr_set: $i > $i > $o ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_lower_bounded_relstr,type,
lower_bounded_relstr: $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_related,type,
related: $i > $i > $i > $o ).
thf(tp_relstr_element_smaller,type,
relstr_element_smaller: $i > $i > $i > $o ).
thf(tp_relstr_set_smaller,type,
relstr_set_smaller: $i > $i > $i > $o ).
thf(tp_sK10_B,type,
sK10_B: $i > $i ).
thf(tp_sK11_A,type,
sK11_A: $i ).
thf(tp_sK12_A,type,
sK12_A: $i ).
thf(tp_sK13_D,type,
sK13_D: $i > $i > $i > $i ).
thf(tp_sK14_B,type,
sK14_B: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_C,type,
sK2_C: $i > $i > $i ).
thf(tp_sK3_D,type,
sK3_D: $i > $i > $i > $i ).
thf(tp_sK4_C,type,
sK4_C: $i > $i > $i ).
thf(tp_sK5_D,type,
sK5_D: $i > $i > $i > $i ).
thf(tp_sK6_A,type,
sK6_A: $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_A,type,
sK9_A: $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ empty_set @ B )
& ( relstr_element_smaller @ A @ empty_set @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).
thf(4,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(7,axiom,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ex_inf_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ D )
=> ( related @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_yellow_0) ).
thf(8,axiom,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ex_sup_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow_0) ).
thf(9,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(10,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(11,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(12,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(13,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(14,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(15,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(16,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(17,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(18,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(19,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(21,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(23,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ C @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice3) ).
thf(24,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( ( lower_bounded_relstr @ A )
<=> ? [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ ( the_carrier @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_yellow_0) ).
thf(25,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(27,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ( ex_sup_of_relstr_set @ A @ empty_set )
& ( ex_inf_of_relstr_set @ A @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_yellow_0) ).
thf(28,negated_conjecture,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ( ex_sup_of_relstr_set @ A @ empty_set )
& ( ex_inf_of_relstr_set @ A @ ( the_carrier @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[27]) ).
thf(29,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( antisymmetric_relstr @ A )
& ( lower_bounded_relstr @ A )
& ( rel_str @ A ) )
=> ( ( ex_sup_of_relstr_set @ A @ empty_set )
& ( ex_inf_of_relstr_set @ A @ ( the_carrier @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[28]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(32,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ empty_set @ B )
& ( relstr_element_smaller @ A @ empty_set @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(36,plain,
( ( ! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ex_inf_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ D )
=> ( related @ A @ D @ C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( ex_sup_of_relstr_set @ A @ B )
<=> ? [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ C )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( relstr_set_smaller @ A @ B @ D )
=> ( related @ A @ C @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(38,plain,
( ( ? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(39,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(40,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(41,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(42,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(44,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(45,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(46,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(47,plain,
$true = $true,
inference(unfold_def,[status(thm)],[18]) ).
thf(48,plain,
$true = $true,
inference(unfold_def,[status(thm)],[19]) ).
thf(49,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(51,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(52,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i,C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ C )
<=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( in @ D @ B )
=> ( related @ A @ C @ D ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(53,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( ( lower_bounded_relstr @ A )
<=> ? [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ ( the_carrier @ A ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(54,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(55,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(56,plain,
( ( ( ~ ( empty_carrier @ sK1_A )
& ( antisymmetric_relstr @ sK1_A )
& ( lower_bounded_relstr @ sK1_A )
& ( rel_str @ sK1_A ) )
=> ( ( ex_sup_of_relstr_set @ sK1_A @ empty_set )
& ( ex_inf_of_relstr_set @ sK1_A @ ( the_carrier @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(57,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(58,plain,
( ( antisymmetric_relstr @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(59,plain,
( ( lower_bounded_relstr @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(60,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(61,plain,
( ( ( ex_sup_of_relstr_set @ sK1_A @ empty_set )
& ( ex_inf_of_relstr_set @ sK1_A @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[56]) ).
thf(62,plain,
( ( ex_sup_of_relstr_set @ sK1_A @ empty_set )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[61]) ).
thf(63,plain,
( ( ex_inf_of_relstr_set @ sK1_A @ ( the_carrier @ sK1_A ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[61]) ).
thf(64,plain,
( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[62]) ).
thf(65,plain,
( ( ~ ( ex_inf_of_relstr_set @ sK1_A @ ( the_carrier @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[63]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(68,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ( relstr_element_smaller @ A @ empty_set @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ( relstr_set_smaller @ A @ empty_set @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(69,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(70,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(71,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(72,plain,
( ( ! [A: $i] :
( ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( ! [B: $i] :
( ! [C: $i] :
( ( ( element @ ( sK3_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK3_D @ C @ B @ A ) )
& ~ ( related @ A @ ( sK3_D @ C @ B @ A ) @ C ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ C ) )
| ( ex_inf_of_relstr_set @ A @ B ) )
& ! [B: $i] :
( ~ ( ex_inf_of_relstr_set @ A @ B )
| ( ! [SY39: $i] :
( ~ ( element @ SY39 @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ SY39 )
| ( related @ A @ SY39 @ ( sK2_C @ B @ A ) ) )
& ( element @ ( sK2_C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK2_C @ B @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(73,plain,
( ( ! [A: $i] :
( ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( ! [B: $i] :
( ! [C: $i] :
( ( ( element @ ( sK5_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ ( sK5_D @ C @ B @ A ) )
& ~ ( related @ A @ C @ ( sK5_D @ C @ B @ A ) ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_set_smaller @ A @ B @ C ) )
| ( ex_sup_of_relstr_set @ A @ B ) )
& ! [B: $i] :
( ~ ( ex_sup_of_relstr_set @ A @ B )
| ( ! [SY40: $i] :
( ~ ( element @ SY40 @ ( the_carrier @ A ) )
| ~ ( relstr_set_smaller @ A @ B @ SY40 )
| ( related @ A @ ( sK4_C @ B @ A ) @ SY40 ) )
& ( element @ ( sK4_C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ ( sK4_C @ B @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(74,plain,
( ( ( one_sorted_str @ sK6_A )
& ~ ( empty_carrier @ sK6_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(75,plain,
( ( ~ ( empty @ sK7_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(76,plain,
( ( empty @ sK8_A )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(77,plain,
( ( ~ ( empty @ sK9_A )
& ( finite @ sK9_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(78,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(79,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(80,plain,
( ( one_sorted_str @ sK11_A )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(81,plain,
( ( rel_str @ sK12_A )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(82,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(83,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ( ( element @ ( sK13_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( in @ ( sK13_D @ C @ B @ A ) @ B )
& ~ ( related @ A @ C @ ( sK13_D @ C @ B @ A ) ) )
| ( relstr_element_smaller @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ C )
| ! [D: $i] :
( ~ ( element @ D @ ( the_carrier @ A ) )
| ~ ( in @ D @ B )
| ( related @ A @ C @ D ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(84,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ ( the_carrier @ A ) @ B ) )
| ( lower_bounded_relstr @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( lower_bounded_relstr @ A )
| ( ( element @ ( sK14_B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ ( the_carrier @ A ) @ ( sK14_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(85,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(86,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(88,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(89,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ ( the_carrier @ A ) @ B ) )
| ( lower_bounded_relstr @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( lower_bounded_relstr @ A )
| ( ( element @ ( sK14_B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ ( the_carrier @ A ) @ ( sK14_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(90,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ( ( element @ ( sK13_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( in @ ( sK13_D @ C @ B @ A ) @ B )
& ~ ( related @ A @ C @ ( sK13_D @ C @ B @ A ) ) )
| ( relstr_element_smaller @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ C )
| ! [D: $i] :
( ~ ( element @ D @ ( the_carrier @ A ) )
| ~ ( in @ D @ B )
| ( related @ A @ C @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(91,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(92,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(93,plain,
$true = $true,
inference(copy,[status(thm)],[49]) ).
thf(94,plain,
$true = $true,
inference(copy,[status(thm)],[48]) ).
thf(95,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(96,plain,
( ( rel_str @ sK12_A )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(97,plain,
( ( one_sorted_str @ sK11_A )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(98,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(99,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(100,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(101,plain,
( ( ~ ( empty @ sK9_A )
& ( finite @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(102,plain,
( ( empty @ sK8_A )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(103,plain,
( ( ~ ( empty @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(104,plain,
( ( ( one_sorted_str @ sK6_A )
& ~ ( empty_carrier @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(105,plain,
( ( ! [A: $i] :
( ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( ! [B: $i] :
( ! [C: $i] :
( ( ( element @ ( sK5_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ ( sK5_D @ C @ B @ A ) )
& ~ ( related @ A @ C @ ( sK5_D @ C @ B @ A ) ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_set_smaller @ A @ B @ C ) )
| ( ex_sup_of_relstr_set @ A @ B ) )
& ! [B: $i] :
( ~ ( ex_sup_of_relstr_set @ A @ B )
| ( ! [SY40: $i] :
( ~ ( element @ SY40 @ ( the_carrier @ A ) )
| ~ ( relstr_set_smaller @ A @ B @ SY40 )
| ( related @ A @ ( sK4_C @ B @ A ) @ SY40 ) )
& ( element @ ( sK4_C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ ( sK4_C @ B @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(106,plain,
( ( ! [A: $i] :
( ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( ! [B: $i] :
( ! [C: $i] :
( ( ( element @ ( sK3_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK3_D @ C @ B @ A ) )
& ~ ( related @ A @ ( sK3_D @ C @ B @ A ) @ C ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ C ) )
| ( ex_inf_of_relstr_set @ A @ B ) )
& ! [B: $i] :
( ~ ( ex_inf_of_relstr_set @ A @ B )
| ( ! [SY39: $i] :
( ~ ( element @ SY39 @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ SY39 )
| ( related @ A @ SY39 @ ( sK2_C @ B @ A ) ) )
& ( element @ ( sK2_C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK2_C @ B @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(109,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(110,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ( relstr_element_smaller @ A @ empty_set @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ( relstr_set_smaller @ A @ empty_set @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(113,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(114,plain,
( ( lower_bounded_relstr @ sK1_A )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(115,plain,
( ( antisymmetric_relstr @ sK1_A )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(116,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(117,plain,
( ( ~ ( ex_sup_of_relstr_set @ sK1_A @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(118,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ( relstr_element_smaller @ SX0 @ empty_set @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ( relstr_set_smaller @ SX0 @ empty_set @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(119,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( ~ ( element @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( related @ SX0 @ SX2 @ ( sK13_D @ SX2 @ SX1 @ SX0 ) ) ) )
| ( relstr_element_smaller @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( related @ SX0 @ SX2 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(120,plain,
( ( ! [SX0: $i] :
( ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SX0 @ SX1 @ ( sK5_D @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( related @ SX0 @ SX2 @ ( sK5_D @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 ) )
| ( ex_sup_of_relstr_set @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ex_sup_of_relstr_set @ SX0 @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 )
| ( related @ SX0 @ ( sK4_C @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ ( sK4_C @ SX1 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(121,plain,
( ( ~ ( ~ ~ ( empty @ sK9_A )
| ~ ( finite @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(122,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ SX1 ) )
| ( lower_bounded_relstr @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( ~ ( element @ ( sK14_B @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ ( sK14_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(123,plain,
( ( ! [SX0: $i] :
( ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SX0 @ SX1 @ ( sK3_D @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( related @ SX0 @ ( sK3_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX2 ) )
| ( ex_inf_of_relstr_set @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ex_inf_of_relstr_set @ SX0 @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX2 )
| ( related @ SX0 @ SX2 @ ( sK2_C @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ ( sK2_C @ SX1 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(124,plain,
( ( ~ ( ~ ( one_sorted_str @ sK6_A )
| ~ ~ ( empty_carrier @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(125,plain,
! [SV1: $i] :
( ( ! [SY41: $i] :
( ~ ( in @ SV1 @ SY41 )
| ~ ( in @ SY41 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(126,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( finite @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(127,plain,
! [SV3: $i] :
( ( ~ ( rel_str @ SV3 )
| ( one_sorted_str @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(128,plain,
! [SV4: $i] :
( ( element @ ( sK10_B @ SV4 ) @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(129,plain,
! [SV5: $i] :
( ( ( empty_carrier @ SV5 )
| ~ ( one_sorted_str @ SV5 )
| ~ ( empty @ ( the_carrier @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(130,plain,
( ( empty @ sK7_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(131,plain,
! [SV6: $i] :
( ( ! [SY42: $i] :
( ~ ( in @ SV6 @ SY42 )
| ( element @ SV6 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(132,plain,
! [SV7: $i] :
( ( ! [SY43: $i] :
( ~ ( element @ SV7 @ SY43 )
| ( empty @ SY43 )
| ( in @ SV7 @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(133,plain,
! [SV8: $i] :
( ( ~ ( empty @ SV8 )
| ( SV8 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(134,plain,
! [SV9: $i] :
( ( ! [SY44: $i] :
( ~ ( empty @ SY44 )
| ~ ( in @ SV9 @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(135,plain,
! [SV10: $i] :
( ( ! [SY45: $i] :
( ( SV10 = SY45 )
| ~ ( empty @ SV10 )
| ~ ( empty @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(136,plain,
( ( empty_carrier @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(137,plain,
( ( ex_sup_of_relstr_set @ sK1_A @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(138,plain,
! [SV11: $i] :
( ( ~ ( rel_str @ SV11 )
| ~ ( ~ ! [SY46: $i] :
( ~ ( element @ SY46 @ ( the_carrier @ SV11 ) )
| ( relstr_element_smaller @ SV11 @ empty_set @ SY46 ) )
| ~ ! [SY47: $i] :
( ~ ( element @ SY47 @ ( the_carrier @ SV11 ) )
| ( relstr_set_smaller @ SV11 @ empty_set @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(139,plain,
! [SV12: $i] :
( ( ~ ( rel_str @ SV12 )
| ~ ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV12 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY49 @ SY48 @ SV12 ) @ ( the_carrier @ SV12 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY49 @ SY48 @ SV12 ) @ SY48 )
| ~ ~ ( related @ SV12 @ SY49 @ ( sK13_D @ SY49 @ SY48 @ SV12 ) ) ) )
| ( relstr_element_smaller @ SV12 @ SY48 @ SY49 ) )
| ~ ! [SY50: $i,SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV12 ) )
| ~ ( relstr_element_smaller @ SV12 @ SY50 @ SY51 )
| ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SY52 @ SY50 )
| ( related @ SV12 @ SY51 @ SY52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(140,plain,
! [SV13: $i] :
( ( ~ ( antisymmetric_relstr @ SV13 )
| ~ ( rel_str @ SV13 )
| ~ ( ~ ! [SY53: $i] :
( ! [SY54: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY54 @ SY53 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SY53 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SY54 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) ) ) )
| ~ ( element @ SY54 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY53 @ SY54 ) )
| ( ex_sup_of_relstr_set @ SV13 @ SY53 ) )
| ~ ! [SY55: $i] :
( ~ ( ex_sup_of_relstr_set @ SV13 @ SY55 )
| ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ SY56 )
| ( related @ SV13 @ ( sK4_C @ SY55 @ SV13 ) @ SY56 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY55 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ ( sK4_C @ SY55 @ SV13 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(141,plain,
( ( ~ ~ ( empty @ sK9_A )
| ~ ( finite @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(142,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ SX1 ) )
| ( lower_bounded_relstr @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( ~ ( element @ ( sK14_B @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ ( sK14_B @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(143,plain,
! [SV14: $i] :
( ( ~ ( antisymmetric_relstr @ SV14 )
| ~ ( rel_str @ SV14 )
| ~ ( ~ ! [SY57: $i] :
( ! [SY58: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SY57 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ SY58 ) ) )
| ~ ( element @ SY58 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY57 @ SY58 ) )
| ( ex_inf_of_relstr_set @ SV14 @ SY57 ) )
| ~ ! [SY59: $i] :
( ~ ( ex_inf_of_relstr_set @ SV14 @ SY59 )
| ~ ( ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ SY60 )
| ( related @ SV14 @ SY60 @ ( sK2_C @ SY59 @ SV14 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY59 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ ( sK2_C @ SY59 @ SV14 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(144,plain,
( ( ~ ( one_sorted_str @ sK6_A )
| ~ ~ ( empty_carrier @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(145,plain,
! [SV15: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV15 )
| ~ ( in @ SV15 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(146,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( finite @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(147,plain,
! [SV3: $i] :
( ( ( ~ ( rel_str @ SV3 ) )
= $true )
| ( ( one_sorted_str @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(148,plain,
! [SV5: $i] :
( ( ( ( empty_carrier @ SV5 )
| ~ ( one_sorted_str @ SV5 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(149,plain,
! [SV16: $i,SV6: $i] :
( ( ~ ( in @ SV6 @ SV16 )
| ( element @ SV6 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(150,plain,
! [SV17: $i,SV7: $i] :
( ( ~ ( element @ SV7 @ SV17 )
| ( empty @ SV17 )
| ( in @ SV7 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(151,plain,
! [SV8: $i] :
( ( ( ~ ( empty @ SV8 ) )
= $true )
| ( ( SV8 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(152,plain,
! [SV9: $i,SV18: $i] :
( ( ~ ( empty @ SV18 )
| ~ ( in @ SV9 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(153,plain,
! [SV19: $i,SV10: $i] :
( ( ( SV10 = SV19 )
| ~ ( empty @ SV10 )
| ~ ( empty @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(154,plain,
! [SV11: $i] :
( ( ( ~ ( rel_str @ SV11 ) )
= $true )
| ( ( ~ ( ~ ! [SY46: $i] :
( ~ ( element @ SY46 @ ( the_carrier @ SV11 ) )
| ( relstr_element_smaller @ SV11 @ empty_set @ SY46 ) )
| ~ ! [SY47: $i] :
( ~ ( element @ SY47 @ ( the_carrier @ SV11 ) )
| ( relstr_set_smaller @ SV11 @ empty_set @ SY47 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(155,plain,
! [SV12: $i] :
( ( ( ~ ( rel_str @ SV12 ) )
= $true )
| ( ( ~ ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV12 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY49 @ SY48 @ SV12 ) @ ( the_carrier @ SV12 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY49 @ SY48 @ SV12 ) @ SY48 )
| ~ ~ ( related @ SV12 @ SY49 @ ( sK13_D @ SY49 @ SY48 @ SV12 ) ) ) )
| ( relstr_element_smaller @ SV12 @ SY48 @ SY49 ) )
| ~ ! [SY50: $i,SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV12 ) )
| ~ ( relstr_element_smaller @ SV12 @ SY50 @ SY51 )
| ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SY52 @ SY50 )
| ( related @ SV12 @ SY51 @ SY52 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV13: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV13 )
| ~ ( rel_str @ SV13 ) )
= $true )
| ( ( ~ ( ~ ! [SY53: $i] :
( ! [SY54: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY54 @ SY53 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SY53 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SY54 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) ) ) )
| ~ ( element @ SY54 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY53 @ SY54 ) )
| ( ex_sup_of_relstr_set @ SV13 @ SY53 ) )
| ~ ! [SY55: $i] :
( ~ ( ex_sup_of_relstr_set @ SV13 @ SY55 )
| ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ SY56 )
| ( related @ SV13 @ ( sK4_C @ SY55 @ SV13 ) @ SY56 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY55 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ ( sK4_C @ SY55 @ SV13 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(157,plain,
( ( ~ ~ ( empty @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(158,plain,
( ( ~ ( finite @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(159,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ SX1 ) )
| ( lower_bounded_relstr @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(160,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( ~ ( element @ ( sK14_B @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ ( sK14_B @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(161,plain,
! [SV14: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV14 )
| ~ ( rel_str @ SV14 ) )
= $true )
| ( ( ~ ( ~ ! [SY57: $i] :
( ! [SY58: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SY57 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ SY58 ) ) )
| ~ ( element @ SY58 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY57 @ SY58 ) )
| ( ex_inf_of_relstr_set @ SV14 @ SY57 ) )
| ~ ! [SY59: $i] :
( ~ ( ex_inf_of_relstr_set @ SV14 @ SY59 )
| ~ ( ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ SY60 )
| ( related @ SV14 @ SY60 @ ( sK2_C @ SY59 @ SV14 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY59 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ ( sK2_C @ SY59 @ SV14 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(162,plain,
( ( ~ ( one_sorted_str @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(163,plain,
( ( ~ ~ ( empty_carrier @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(164,plain,
! [SV15: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV15 ) )
= $true )
| ( ( ~ ( in @ SV15 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(165,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( finite @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(166,plain,
! [SV3: $i] :
( ( ( rel_str @ SV3 )
= $false )
| ( ( one_sorted_str @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(167,plain,
! [SV5: $i] :
( ( ( empty_carrier @ SV5 )
= $true )
| ( ( ~ ( one_sorted_str @ SV5 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(168,plain,
! [SV16: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV16 ) )
= $true )
| ( ( element @ SV6 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(169,plain,
! [SV17: $i,SV7: $i] :
( ( ( ~ ( element @ SV7 @ SV17 ) )
= $true )
| ( ( ( empty @ SV17 )
| ( in @ SV7 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(170,plain,
! [SV8: $i] :
( ( ( empty @ SV8 )
= $false )
| ( ( SV8 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(171,plain,
! [SV9: $i,SV18: $i] :
( ( ( ~ ( empty @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV9 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(172,plain,
! [SV19: $i,SV10: $i] :
( ( ( ( SV10 = SV19 )
| ~ ( empty @ SV10 ) )
= $true )
| ( ( ~ ( empty @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(173,plain,
! [SV11: $i] :
( ( ( rel_str @ SV11 )
= $false )
| ( ( ~ ( ~ ! [SY46: $i] :
( ~ ( element @ SY46 @ ( the_carrier @ SV11 ) )
| ( relstr_element_smaller @ SV11 @ empty_set @ SY46 ) )
| ~ ! [SY47: $i] :
( ~ ( element @ SY47 @ ( the_carrier @ SV11 ) )
| ( relstr_set_smaller @ SV11 @ empty_set @ SY47 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(174,plain,
! [SV12: $i] :
( ( ( rel_str @ SV12 )
= $false )
| ( ( ~ ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV12 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY49 @ SY48 @ SV12 ) @ ( the_carrier @ SV12 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY49 @ SY48 @ SV12 ) @ SY48 )
| ~ ~ ( related @ SV12 @ SY49 @ ( sK13_D @ SY49 @ SY48 @ SV12 ) ) ) )
| ( relstr_element_smaller @ SV12 @ SY48 @ SY49 ) )
| ~ ! [SY50: $i,SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV12 ) )
| ~ ( relstr_element_smaller @ SV12 @ SY50 @ SY51 )
| ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SY52 @ SY50 )
| ( related @ SV12 @ SY51 @ SY52 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(175,plain,
! [SV13: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV13 ) )
= $true )
| ( ( ~ ( rel_str @ SV13 ) )
= $true )
| ( ( ~ ( ~ ! [SY53: $i] :
( ! [SY54: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY54 @ SY53 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SY53 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SY54 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) ) ) )
| ~ ( element @ SY54 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY53 @ SY54 ) )
| ( ex_sup_of_relstr_set @ SV13 @ SY53 ) )
| ~ ! [SY55: $i] :
( ~ ( ex_sup_of_relstr_set @ SV13 @ SY55 )
| ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ SY56 )
| ( related @ SV13 @ ( sK4_C @ SY55 @ SV13 ) @ SY56 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY55 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ ( sK4_C @ SY55 @ SV13 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(176,plain,
( ( ~ ( empty @ sK9_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(177,plain,
( ( finite @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(178,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ SX1 ) )
| ( lower_bounded_relstr @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(179,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( ~ ( element @ ( sK14_B @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ ( sK14_B @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(180,plain,
! [SV14: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV14 ) )
= $true )
| ( ( ~ ( rel_str @ SV14 ) )
= $true )
| ( ( ~ ( ~ ! [SY57: $i] :
( ! [SY58: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SY57 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ SY58 ) ) )
| ~ ( element @ SY58 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY57 @ SY58 ) )
| ( ex_inf_of_relstr_set @ SV14 @ SY57 ) )
| ~ ! [SY59: $i] :
( ~ ( ex_inf_of_relstr_set @ SV14 @ SY59 )
| ~ ( ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ SY60 )
| ( related @ SV14 @ SY60 @ ( sK2_C @ SY59 @ SV14 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY59 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ ( sK2_C @ SY59 @ SV14 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(181,plain,
( ( one_sorted_str @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(182,plain,
( ( ~ ( empty_carrier @ sK6_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(183,plain,
! [SV15: $i,SV1: $i] :
( ( ( in @ SV1 @ SV15 )
= $false )
| ( ( ~ ( in @ SV15 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(184,plain,
! [SV5: $i] :
( ( ( one_sorted_str @ SV5 )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(185,plain,
! [SV16: $i,SV6: $i] :
( ( ( in @ SV6 @ SV16 )
= $false )
| ( ( element @ SV6 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(186,plain,
! [SV17: $i,SV7: $i] :
( ( ( element @ SV7 @ SV17 )
= $false )
| ( ( ( empty @ SV17 )
| ( in @ SV7 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(187,plain,
! [SV9: $i,SV18: $i] :
( ( ( empty @ SV18 )
= $false )
| ( ( ~ ( in @ SV9 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(188,plain,
! [SV19: $i,SV10: $i] :
( ( ( SV10 = SV19 )
= $true )
| ( ( ~ ( empty @ SV10 ) )
= $true )
| ( ( ~ ( empty @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(189,plain,
! [SV11: $i] :
( ( ( ~ ! [SY46: $i] :
( ~ ( element @ SY46 @ ( the_carrier @ SV11 ) )
| ( relstr_element_smaller @ SV11 @ empty_set @ SY46 ) )
| ~ ! [SY47: $i] :
( ~ ( element @ SY47 @ ( the_carrier @ SV11 ) )
| ( relstr_set_smaller @ SV11 @ empty_set @ SY47 ) ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(190,plain,
! [SV12: $i] :
( ( ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV12 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY49 @ SY48 @ SV12 ) @ ( the_carrier @ SV12 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY49 @ SY48 @ SV12 ) @ SY48 )
| ~ ~ ( related @ SV12 @ SY49 @ ( sK13_D @ SY49 @ SY48 @ SV12 ) ) ) )
| ( relstr_element_smaller @ SV12 @ SY48 @ SY49 ) )
| ~ ! [SY50: $i,SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV12 ) )
| ~ ( relstr_element_smaller @ SV12 @ SY50 @ SY51 )
| ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SY52 @ SY50 )
| ( related @ SV12 @ SY51 @ SY52 ) ) ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(191,plain,
! [SV13: $i] :
( ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( ~ ( rel_str @ SV13 ) )
= $true )
| ( ( ~ ( ~ ! [SY53: $i] :
( ! [SY54: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY54 @ SY53 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SY53 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SY54 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) ) ) )
| ~ ( element @ SY54 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY53 @ SY54 ) )
| ( ex_sup_of_relstr_set @ SV13 @ SY53 ) )
| ~ ! [SY55: $i] :
( ~ ( ex_sup_of_relstr_set @ SV13 @ SY55 )
| ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ SY56 )
| ( related @ SV13 @ ( sK4_C @ SY55 @ SV13 ) @ SY56 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY55 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ ( sK4_C @ SY55 @ SV13 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(192,plain,
( ( empty @ sK9_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(193,plain,
! [SV20: $i] :
( ( ~ ( rel_str @ SV20 )
| ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SV20 ) )
| ~ ( relstr_element_smaller @ SV20 @ ( the_carrier @ SV20 ) @ SY61 ) )
| ( lower_bounded_relstr @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(194,plain,
! [SV21: $i] :
( ( ~ ( rel_str @ SV21 )
| ~ ( lower_bounded_relstr @ SV21 )
| ~ ( ~ ( element @ ( sK14_B @ SV21 ) @ ( the_carrier @ SV21 ) )
| ~ ( relstr_element_smaller @ SV21 @ ( the_carrier @ SV21 ) @ ( sK14_B @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(195,plain,
! [SV14: $i] :
( ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( ~ ( rel_str @ SV14 ) )
= $true )
| ( ( ~ ( ~ ! [SY57: $i] :
( ! [SY58: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SY57 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ SY58 ) ) )
| ~ ( element @ SY58 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY57 @ SY58 ) )
| ( ex_inf_of_relstr_set @ SV14 @ SY57 ) )
| ~ ! [SY59: $i] :
( ~ ( ex_inf_of_relstr_set @ SV14 @ SY59 )
| ~ ( ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ SY60 )
| ( related @ SV14 @ SY60 @ ( sK2_C @ SY59 @ SV14 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY59 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ ( sK2_C @ SY59 @ SV14 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(196,plain,
( ( empty_carrier @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(197,plain,
! [SV1: $i,SV15: $i] :
( ( ( in @ SV15 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(198,plain,
! [SV5: $i] :
( ( ( empty @ ( the_carrier @ SV5 ) )
= $false )
| ( ( empty_carrier @ SV5 )
= $true )
| ( ( one_sorted_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(199,plain,
! [SV7: $i,SV17: $i] :
( ( ( empty @ SV17 )
= $true )
| ( ( in @ SV7 @ SV17 )
= $true )
| ( ( element @ SV7 @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(200,plain,
! [SV18: $i,SV9: $i] :
( ( ( in @ SV9 @ SV18 )
= $false )
| ( ( empty @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(201,plain,
! [SV19: $i,SV10: $i] :
( ( ( empty @ SV10 )
= $false )
| ( ( SV10 = SV19 )
= $true )
| ( ( ~ ( empty @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(202,plain,
! [SV11: $i] :
( ( ( ~ ! [SY46: $i] :
( ~ ( element @ SY46 @ ( the_carrier @ SV11 ) )
| ( relstr_element_smaller @ SV11 @ empty_set @ SY46 ) ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(203,plain,
! [SV11: $i] :
( ( ( ~ ! [SY47: $i] :
( ~ ( element @ SY47 @ ( the_carrier @ SV11 ) )
| ( relstr_set_smaller @ SV11 @ empty_set @ SY47 ) ) )
= $false )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(204,plain,
! [SV12: $i] :
( ( ( ~ ! [SY48: $i,SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV12 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY49 @ SY48 @ SV12 ) @ ( the_carrier @ SV12 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY49 @ SY48 @ SV12 ) @ SY48 )
| ~ ~ ( related @ SV12 @ SY49 @ ( sK13_D @ SY49 @ SY48 @ SV12 ) ) ) )
| ( relstr_element_smaller @ SV12 @ SY48 @ SY49 ) ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(205,plain,
! [SV12: $i] :
( ( ( ~ ! [SY50: $i,SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV12 ) )
| ~ ( relstr_element_smaller @ SV12 @ SY50 @ SY51 )
| ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SY52 @ SY50 )
| ( related @ SV12 @ SY51 @ SY52 ) ) ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(206,plain,
! [SV13: $i] :
( ( ( rel_str @ SV13 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( ~ ( ~ ! [SY53: $i] :
( ! [SY54: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY54 @ SY53 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SY53 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SY54 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) ) ) )
| ~ ( element @ SY54 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY53 @ SY54 ) )
| ( ex_sup_of_relstr_set @ SV13 @ SY53 ) )
| ~ ! [SY55: $i] :
( ~ ( ex_sup_of_relstr_set @ SV13 @ SY55 )
| ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ SY56 )
| ( related @ SV13 @ ( sK4_C @ SY55 @ SV13 ) @ SY56 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY55 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ ( sK4_C @ SY55 @ SV13 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(207,plain,
! [SV20: $i] :
( ( ( ~ ( rel_str @ SV20 ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SV20 ) )
| ~ ( relstr_element_smaller @ SV20 @ ( the_carrier @ SV20 ) @ SY61 ) )
| ( lower_bounded_relstr @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(208,plain,
! [SV21: $i] :
( ( ( ~ ( rel_str @ SV21 ) )
= $true )
| ( ( ~ ( lower_bounded_relstr @ SV21 )
| ~ ( ~ ( element @ ( sK14_B @ SV21 ) @ ( the_carrier @ SV21 ) )
| ~ ( relstr_element_smaller @ SV21 @ ( the_carrier @ SV21 ) @ ( sK14_B @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(209,plain,
! [SV14: $i] :
( ( ( rel_str @ SV14 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( ~ ( ~ ! [SY57: $i] :
( ! [SY58: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SY57 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ SY58 ) ) )
| ~ ( element @ SY58 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY57 @ SY58 ) )
| ( ex_inf_of_relstr_set @ SV14 @ SY57 ) )
| ~ ! [SY59: $i] :
( ~ ( ex_inf_of_relstr_set @ SV14 @ SY59 )
| ~ ( ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ SY60 )
| ( related @ SV14 @ SY60 @ ( sK2_C @ SY59 @ SV14 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY59 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ ( sK2_C @ SY59 @ SV14 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(210,plain,
! [SV10: $i,SV19: $i] :
( ( ( empty @ SV19 )
= $false )
| ( ( SV10 = SV19 )
= $true )
| ( ( empty @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(211,plain,
! [SV11: $i] :
( ( ( ! [SY46: $i] :
( ~ ( element @ SY46 @ ( the_carrier @ SV11 ) )
| ( relstr_element_smaller @ SV11 @ empty_set @ SY46 ) ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(212,plain,
! [SV11: $i] :
( ( ( ! [SY47: $i] :
( ~ ( element @ SY47 @ ( the_carrier @ SV11 ) )
| ( relstr_set_smaller @ SV11 @ empty_set @ SY47 ) ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(213,plain,
! [SV12: $i] :
( ( ( ! [SY48: $i,SY49: $i] :
( ~ ( element @ SY49 @ ( the_carrier @ SV12 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY49 @ SY48 @ SV12 ) @ ( the_carrier @ SV12 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY49 @ SY48 @ SV12 ) @ SY48 )
| ~ ~ ( related @ SV12 @ SY49 @ ( sK13_D @ SY49 @ SY48 @ SV12 ) ) ) )
| ( relstr_element_smaller @ SV12 @ SY48 @ SY49 ) ) )
= $true )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(214,plain,
! [SV12: $i] :
( ( ( ! [SY50: $i,SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV12 ) )
| ~ ( relstr_element_smaller @ SV12 @ SY50 @ SY51 )
| ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SY52 @ SY50 )
| ( related @ SV12 @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(215,plain,
! [SV13: $i] :
( ( ( ~ ! [SY53: $i] :
( ! [SY54: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY54 @ SY53 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SY53 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SY54 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) ) ) )
| ~ ( element @ SY54 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY53 @ SY54 ) )
| ( ex_sup_of_relstr_set @ SV13 @ SY53 ) )
| ~ ! [SY55: $i] :
( ~ ( ex_sup_of_relstr_set @ SV13 @ SY55 )
| ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ SY56 )
| ( related @ SV13 @ ( sK4_C @ SY55 @ SV13 ) @ SY56 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY55 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ ( sK4_C @ SY55 @ SV13 ) ) ) ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(216,plain,
! [SV20: $i] :
( ( ( rel_str @ SV20 )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SV20 ) )
| ~ ( relstr_element_smaller @ SV20 @ ( the_carrier @ SV20 ) @ SY61 ) )
| ( lower_bounded_relstr @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(217,plain,
! [SV21: $i] :
( ( ( rel_str @ SV21 )
= $false )
| ( ( ~ ( lower_bounded_relstr @ SV21 )
| ~ ( ~ ( element @ ( sK14_B @ SV21 ) @ ( the_carrier @ SV21 ) )
| ~ ( relstr_element_smaller @ SV21 @ ( the_carrier @ SV21 ) @ ( sK14_B @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(218,plain,
! [SV14: $i] :
( ( ( ~ ! [SY57: $i] :
( ! [SY58: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SY57 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ SY58 ) ) )
| ~ ( element @ SY58 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY57 @ SY58 ) )
| ( ex_inf_of_relstr_set @ SV14 @ SY57 ) )
| ~ ! [SY59: $i] :
( ~ ( ex_inf_of_relstr_set @ SV14 @ SY59 )
| ~ ( ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ SY60 )
| ( related @ SV14 @ SY60 @ ( sK2_C @ SY59 @ SV14 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY59 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ ( sK2_C @ SY59 @ SV14 ) ) ) ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(219,plain,
! [SV11: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( the_carrier @ SV11 ) )
| ( relstr_element_smaller @ SV11 @ empty_set @ SV22 ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(220,plain,
! [SV11: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV11 ) )
| ( relstr_set_smaller @ SV11 @ empty_set @ SV23 ) )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(221,plain,
! [SV24: $i,SV12: $i] :
( ( ( ! [SY62: $i] :
( ~ ( element @ SY62 @ ( the_carrier @ SV12 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY62 @ SV24 @ SV12 ) @ ( the_carrier @ SV12 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY62 @ SV24 @ SV12 ) @ SV24 )
| ~ ~ ( related @ SV12 @ SY62 @ ( sK13_D @ SY62 @ SV24 @ SV12 ) ) ) )
| ( relstr_element_smaller @ SV12 @ SV24 @ SY62 ) ) )
= $true )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(222,plain,
! [SV25: $i,SV12: $i] :
( ( ( ! [SY63: $i] :
( ~ ( element @ SY63 @ ( the_carrier @ SV12 ) )
| ~ ( relstr_element_smaller @ SV12 @ SV25 @ SY63 )
| ! [SY64: $i] :
( ~ ( element @ SY64 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SY64 @ SV25 )
| ( related @ SV12 @ SY63 @ SY64 ) ) ) )
= $true )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(223,plain,
! [SV13: $i] :
( ( ( ~ ! [SY53: $i] :
( ! [SY54: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY54 @ SY53 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SY53 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SY54 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) ) ) )
| ~ ( element @ SY54 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY53 @ SY54 ) )
| ( ex_sup_of_relstr_set @ SV13 @ SY53 ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(224,plain,
! [SV13: $i] :
( ( ( ~ ! [SY55: $i] :
( ~ ( ex_sup_of_relstr_set @ SV13 @ SY55 )
| ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ SY56 )
| ( related @ SV13 @ ( sK4_C @ SY55 @ SV13 ) @ SY56 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY55 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ ( sK4_C @ SY55 @ SV13 ) ) ) ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(225,plain,
! [SV20: $i] :
( ( ( ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SV20 ) )
| ~ ( relstr_element_smaller @ SV20 @ ( the_carrier @ SV20 ) @ SY61 ) ) )
= $true )
| ( ( lower_bounded_relstr @ SV20 )
= $true )
| ( ( rel_str @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(226,plain,
! [SV21: $i] :
( ( ( ~ ( lower_bounded_relstr @ SV21 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK14_B @ SV21 ) @ ( the_carrier @ SV21 ) )
| ~ ( relstr_element_smaller @ SV21 @ ( the_carrier @ SV21 ) @ ( sK14_B @ SV21 ) ) ) )
= $true )
| ( ( rel_str @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(227,plain,
! [SV14: $i] :
( ( ( ~ ! [SY57: $i] :
( ! [SY58: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SY57 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ SY58 ) ) )
| ~ ( element @ SY58 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY57 @ SY58 ) )
| ( ex_inf_of_relstr_set @ SV14 @ SY57 ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(228,plain,
! [SV14: $i] :
( ( ( ~ ! [SY59: $i] :
( ~ ( ex_inf_of_relstr_set @ SV14 @ SY59 )
| ~ ( ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ SY60 )
| ( related @ SV14 @ SY60 @ ( sK2_C @ SY59 @ SV14 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY59 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ ( sK2_C @ SY59 @ SV14 ) ) ) ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[218]) ).
thf(229,plain,
! [SV11: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( relstr_element_smaller @ SV11 @ empty_set @ SV22 )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(230,plain,
! [SV11: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV11 ) ) )
= $true )
| ( ( relstr_set_smaller @ SV11 @ empty_set @ SV23 )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(231,plain,
! [SV24: $i,SV12: $i,SV26: $i] :
( ( ( ~ ( element @ SV26 @ ( the_carrier @ SV12 ) )
| ~ ( ~ ( element @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ ( the_carrier @ SV12 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ SV24 )
| ~ ~ ( related @ SV12 @ SV26 @ ( sK13_D @ SV26 @ SV24 @ SV12 ) ) ) )
| ( relstr_element_smaller @ SV12 @ SV24 @ SV26 ) )
= $true )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(232,plain,
! [SV25: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( element @ SV27 @ ( the_carrier @ SV12 ) )
| ~ ( relstr_element_smaller @ SV12 @ SV25 @ SV27 )
| ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SY65 @ SV25 )
| ( related @ SV12 @ SV27 @ SY65 ) ) )
= $true )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(233,plain,
! [SV13: $i] :
( ( ( ! [SY53: $i] :
( ! [SY54: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY54 @ SY53 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SY53 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SY54 @ ( sK5_D @ SY54 @ SY53 @ SV13 ) ) ) )
| ~ ( element @ SY54 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY53 @ SY54 ) )
| ( ex_sup_of_relstr_set @ SV13 @ SY53 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(234,plain,
! [SV13: $i] :
( ( ( ! [SY55: $i] :
( ~ ( ex_sup_of_relstr_set @ SV13 @ SY55 )
| ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ SY56 )
| ( related @ SV13 @ ( sK4_C @ SY55 @ SV13 ) @ SY56 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY55 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SY55 @ ( sK4_C @ SY55 @ SV13 ) ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(235,plain,
! [SV20: $i,SV28: $i] :
( ( ( ~ ( element @ SV28 @ ( the_carrier @ SV20 ) )
| ~ ( relstr_element_smaller @ SV20 @ ( the_carrier @ SV20 ) @ SV28 ) )
= $true )
| ( ( lower_bounded_relstr @ SV20 )
= $true )
| ( ( rel_str @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(236,plain,
! [SV21: $i] :
( ( ( lower_bounded_relstr @ SV21 )
= $false )
| ( ( ~ ( ~ ( element @ ( sK14_B @ SV21 ) @ ( the_carrier @ SV21 ) )
| ~ ( relstr_element_smaller @ SV21 @ ( the_carrier @ SV21 ) @ ( sK14_B @ SV21 ) ) ) )
= $true )
| ( ( rel_str @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(237,plain,
! [SV14: $i] :
( ( ( ! [SY57: $i] :
( ! [SY58: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SY57 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SY58 @ SY57 @ SV14 ) @ SY58 ) ) )
| ~ ( element @ SY58 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY57 @ SY58 ) )
| ( ex_inf_of_relstr_set @ SV14 @ SY57 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(238,plain,
! [SV14: $i] :
( ( ( ! [SY59: $i] :
( ~ ( ex_inf_of_relstr_set @ SV14 @ SY59 )
| ~ ( ~ ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ SY60 )
| ( related @ SV14 @ SY60 @ ( sK2_C @ SY59 @ SV14 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY59 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SY59 @ ( sK2_C @ SY59 @ SV14 ) ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(239,plain,
! [SV11: $i,SV22: $i] :
( ( ( element @ SV22 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( relstr_element_smaller @ SV11 @ empty_set @ SV22 )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(240,plain,
! [SV11: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV11 ) )
= $false )
| ( ( relstr_set_smaller @ SV11 @ empty_set @ SV23 )
= $true )
| ( ( rel_str @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(241,plain,
! [SV24: $i,SV12: $i,SV26: $i] :
( ( ( ~ ( element @ SV26 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ ( the_carrier @ SV12 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ SV24 )
| ~ ~ ( related @ SV12 @ SV26 @ ( sK13_D @ SV26 @ SV24 @ SV12 ) ) ) )
| ( relstr_element_smaller @ SV12 @ SV24 @ SV26 ) )
= $true )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(242,plain,
! [SV25: $i,SV12: $i,SV27: $i] :
( ( ( ~ ( element @ SV27 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV12 @ SV25 @ SV27 )
| ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SY65 @ SV25 )
| ( related @ SV12 @ SV27 @ SY65 ) ) )
= $true )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(243,plain,
! [SV13: $i,SV29: $i] :
( ( ( ! [SY66: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY66 @ SV29 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SY66 @ SV29 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SY66 @ ( sK5_D @ SY66 @ SV29 @ SV13 ) ) ) )
| ~ ( element @ SY66 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SY66 ) )
| ( ex_sup_of_relstr_set @ SV13 @ SV29 ) )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(244,plain,
! [SV30: $i,SV13: $i] :
( ( ( ~ ( ex_sup_of_relstr_set @ SV13 @ SV30 )
| ~ ( ~ ! [SY67: $i] :
( ~ ( element @ SY67 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ SY67 )
| ( related @ SV13 @ ( sK4_C @ SV30 @ SV13 ) @ SY67 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SV30 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ ( sK4_C @ SV30 @ SV13 ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(245,plain,
! [SV20: $i,SV28: $i] :
( ( ( ~ ( element @ SV28 @ ( the_carrier @ SV20 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV20 @ ( the_carrier @ SV20 ) @ SV28 ) )
= $true )
| ( ( lower_bounded_relstr @ SV20 )
= $true )
| ( ( rel_str @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(246,plain,
! [SV21: $i] :
( ( ( ~ ( element @ ( sK14_B @ SV21 ) @ ( the_carrier @ SV21 ) )
| ~ ( relstr_element_smaller @ SV21 @ ( the_carrier @ SV21 ) @ ( sK14_B @ SV21 ) ) )
= $false )
| ( ( lower_bounded_relstr @ SV21 )
= $false )
| ( ( rel_str @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(247,plain,
! [SV14: $i,SV31: $i] :
( ( ( ! [SY68: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY68 @ SV31 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SY68 @ SV31 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SY68 @ SV31 @ SV14 ) @ SY68 ) ) )
| ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SY68 ) )
| ( ex_inf_of_relstr_set @ SV14 @ SV31 ) )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(248,plain,
! [SV32: $i,SV14: $i] :
( ( ( ~ ( ex_inf_of_relstr_set @ SV14 @ SV32 )
| ~ ( ~ ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ SY69 )
| ( related @ SV14 @ SY69 @ ( sK2_C @ SV32 @ SV14 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SV32 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ ( sK2_C @ SV32 @ SV14 ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(249,plain,
! [SV24: $i,SV12: $i,SV26: $i] :
( ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ ( the_carrier @ SV12 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ SV24 )
| ~ ~ ( related @ SV12 @ SV26 @ ( sK13_D @ SV26 @ SV24 @ SV12 ) ) ) )
| ( relstr_element_smaller @ SV12 @ SV24 @ SV26 ) )
= $true )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(250,plain,
! [SV25: $i,SV12: $i,SV27: $i] :
( ( ( element @ SV27 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV12 @ SV25 @ SV27 )
| ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SY65 @ SV25 )
| ( related @ SV12 @ SV27 @ SY65 ) ) )
= $true )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(251,plain,
! [SV13: $i,SV29: $i] :
( ( ( ! [SY66: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY66 @ SV29 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SY66 @ SV29 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SY66 @ ( sK5_D @ SY66 @ SV29 @ SV13 ) ) ) )
| ~ ( element @ SY66 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SY66 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(252,plain,
! [SV30: $i,SV13: $i] :
( ( ( ~ ( ex_sup_of_relstr_set @ SV13 @ SV30 ) )
= $true )
| ( ( ~ ( ~ ! [SY67: $i] :
( ~ ( element @ SY67 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ SY67 )
| ( related @ SV13 @ ( sK4_C @ SV30 @ SV13 ) @ SY67 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SV30 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ ( sK4_C @ SV30 @ SV13 ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(253,plain,
! [SV20: $i,SV28: $i] :
( ( ( element @ SV28 @ ( the_carrier @ SV20 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV20 @ ( the_carrier @ SV20 ) @ SV28 ) )
= $true )
| ( ( lower_bounded_relstr @ SV20 )
= $true )
| ( ( rel_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(254,plain,
! [SV21: $i] :
( ( ( ~ ( element @ ( sK14_B @ SV21 ) @ ( the_carrier @ SV21 ) ) )
= $false )
| ( ( lower_bounded_relstr @ SV21 )
= $false )
| ( ( rel_str @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(255,plain,
! [SV21: $i] :
( ( ( ~ ( relstr_element_smaller @ SV21 @ ( the_carrier @ SV21 ) @ ( sK14_B @ SV21 ) ) )
= $false )
| ( ( lower_bounded_relstr @ SV21 )
= $false )
| ( ( rel_str @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(256,plain,
! [SV14: $i,SV31: $i] :
( ( ( ! [SY68: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY68 @ SV31 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SY68 @ SV31 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SY68 @ SV31 @ SV14 ) @ SY68 ) ) )
| ~ ( element @ SY68 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SY68 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(257,plain,
! [SV32: $i,SV14: $i] :
( ( ( ~ ( ex_inf_of_relstr_set @ SV14 @ SV32 ) )
= $true )
| ( ( ~ ( ~ ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ SY69 )
| ( related @ SV14 @ SY69 @ ( sK2_C @ SV32 @ SV14 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SV32 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ ( sK2_C @ SV32 @ SV14 ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(258,plain,
! [SV12: $i,SV24: $i,SV26: $i] :
( ( ( ~ ( ~ ( element @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ ( the_carrier @ SV12 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ SV24 )
| ~ ~ ( related @ SV12 @ SV26 @ ( sK13_D @ SV26 @ SV24 @ SV12 ) ) ) ) )
= $true )
| ( ( relstr_element_smaller @ SV12 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(259,plain,
! [SV27: $i,SV25: $i,SV12: $i] :
( ( ( ~ ( relstr_element_smaller @ SV12 @ SV25 @ SV27 ) )
= $true )
| ( ( ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SY65 @ SV25 )
| ( related @ SV12 @ SV27 @ SY65 ) ) )
= $true )
| ( ( element @ SV27 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(260,plain,
! [SV13: $i,SV29: $i,SV33: $i] :
( ( ( ~ ( ~ ( element @ ( sK5_D @ SV33 @ SV29 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SV33 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) ) ) )
| ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(261,plain,
! [SV30: $i,SV13: $i] :
( ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( ~ ( ~ ! [SY67: $i] :
( ~ ( element @ SY67 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ SY67 )
| ( related @ SV13 @ ( sK4_C @ SV30 @ SV13 ) @ SY67 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SV30 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ ( sK4_C @ SV30 @ SV13 ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(262,plain,
! [SV28: $i,SV20: $i] :
( ( ( relstr_element_smaller @ SV20 @ ( the_carrier @ SV20 ) @ SV28 )
= $false )
| ( ( element @ SV28 @ ( the_carrier @ SV20 ) )
= $false )
| ( ( lower_bounded_relstr @ SV20 )
= $true )
| ( ( rel_str @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(263,plain,
! [SV21: $i] :
( ( ( element @ ( sK14_B @ SV21 ) @ ( the_carrier @ SV21 ) )
= $true )
| ( ( lower_bounded_relstr @ SV21 )
= $false )
| ( ( rel_str @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(264,plain,
! [SV21: $i] :
( ( ( relstr_element_smaller @ SV21 @ ( the_carrier @ SV21 ) @ ( sK14_B @ SV21 ) )
= $true )
| ( ( lower_bounded_relstr @ SV21 )
= $false )
| ( ( rel_str @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(265,plain,
! [SV14: $i,SV31: $i,SV34: $i] :
( ( ( ~ ( ~ ( element @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ SV34 ) ) )
| ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(266,plain,
! [SV32: $i,SV14: $i] :
( ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( ~ ( ~ ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ SY69 )
| ( related @ SV14 @ SY69 @ ( sK2_C @ SV32 @ SV14 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SV32 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ ( sK2_C @ SV32 @ SV14 ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(267,plain,
! [SV12: $i,SV24: $i,SV26: $i] :
( ( ( ~ ( element @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ ( the_carrier @ SV12 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ SV24 )
| ~ ~ ( related @ SV12 @ SV26 @ ( sK13_D @ SV26 @ SV24 @ SV12 ) ) ) )
= $false )
| ( ( relstr_element_smaller @ SV12 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(268,plain,
! [SV27: $i,SV25: $i,SV12: $i] :
( ( ( relstr_element_smaller @ SV12 @ SV25 @ SV27 )
= $false )
| ( ( ! [SY65: $i] :
( ~ ( element @ SY65 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SY65 @ SV25 )
| ( related @ SV12 @ SV27 @ SY65 ) ) )
= $true )
| ( ( element @ SV27 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(269,plain,
! [SV13: $i,SV29: $i,SV33: $i] :
( ( ( ~ ( ~ ( element @ ( sK5_D @ SV33 @ SV29 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SV33 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) ) ) ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(270,plain,
! [SV30: $i,SV13: $i] :
( ( ( ~ ! [SY67: $i] :
( ~ ( element @ SY67 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ SY67 )
| ( related @ SV13 @ ( sK4_C @ SV30 @ SV13 ) @ SY67 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SV30 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ ( sK4_C @ SV30 @ SV13 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(271,plain,
! [SV14: $i,SV31: $i,SV34: $i] :
( ( ( ~ ( ~ ( element @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ SV34 ) ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(272,plain,
! [SV32: $i,SV14: $i] :
( ( ( ~ ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ SY69 )
| ( related @ SV14 @ SY69 @ ( sK2_C @ SV32 @ SV14 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SV32 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ ( sK2_C @ SV32 @ SV14 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(273,plain,
! [SV12: $i,SV24: $i,SV26: $i] :
( ( ( ~ ( element @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ ( the_carrier @ SV12 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV12 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(274,plain,
! [SV12: $i,SV24: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ SV24 )
| ~ ~ ( related @ SV12 @ SV26 @ ( sK13_D @ SV26 @ SV24 @ SV12 ) ) ) )
= $false )
| ( ( relstr_element_smaller @ SV12 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(275,plain,
! [SV27: $i,SV25: $i,SV12: $i,SV35: $i] :
( ( ( ~ ( element @ SV35 @ ( the_carrier @ SV12 ) )
| ~ ( in @ SV35 @ SV25 )
| ( related @ SV12 @ SV27 @ SV35 ) )
= $true )
| ( ( relstr_element_smaller @ SV12 @ SV25 @ SV27 )
= $false )
| ( ( element @ SV27 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(276,plain,
! [SV13: $i,SV29: $i,SV33: $i] :
( ( ( ~ ( element @ ( sK5_D @ SV33 @ SV29 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SV33 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) ) ) )
= $false )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(277,plain,
! [SV30: $i,SV13: $i] :
( ( ( ~ ! [SY67: $i] :
( ~ ( element @ SY67 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ SY67 )
| ( related @ SV13 @ ( sK4_C @ SV30 @ SV13 ) @ SY67 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(278,plain,
! [SV13: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK4_C @ SV30 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ ( sK4_C @ SV30 @ SV13 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[270]) ).
thf(279,plain,
! [SV14: $i,SV31: $i,SV34: $i] :
( ( ( ~ ( element @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ SV34 ) ) )
= $false )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(280,plain,
! [SV32: $i,SV14: $i] :
( ( ( ~ ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ SY69 )
| ( related @ SV14 @ SY69 @ ( sK2_C @ SV32 @ SV14 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(281,plain,
! [SV14: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK2_C @ SV32 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ ( sK2_C @ SV32 @ SV14 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[272]) ).
thf(282,plain,
! [SV12: $i,SV24: $i,SV26: $i] :
( ( ( element @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ ( the_carrier @ SV12 ) )
= $true )
| ( ( relstr_element_smaller @ SV12 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(283,plain,
! [SV12: $i,SV24: $i,SV26: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ SV24 )
| ~ ~ ( related @ SV12 @ SV26 @ ( sK13_D @ SV26 @ SV24 @ SV12 ) ) ) )
= $true )
| ( ( relstr_element_smaller @ SV12 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(284,plain,
! [SV27: $i,SV25: $i,SV12: $i,SV35: $i] :
( ( ( ~ ( element @ SV35 @ ( the_carrier @ SV12 ) ) )
= $true )
| ( ( ~ ( in @ SV35 @ SV25 )
| ( related @ SV12 @ SV27 @ SV35 ) )
= $true )
| ( ( relstr_element_smaller @ SV12 @ SV25 @ SV27 )
= $false )
| ( ( element @ SV27 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(285,plain,
! [SV13: $i,SV29: $i,SV33: $i] :
( ( ( ~ ( element @ ( sK5_D @ SV33 @ SV29 @ SV13 ) @ ( the_carrier @ SV13 ) ) )
= $false )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(286,plain,
! [SV33: $i,SV29: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SV33 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) ) ) )
= $false )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[276]) ).
thf(287,plain,
! [SV30: $i,SV13: $i] :
( ( ( ! [SY67: $i] :
( ~ ( element @ SY67 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ SY67 )
| ( related @ SV13 @ ( sK4_C @ SV30 @ SV13 ) @ SY67 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(288,plain,
! [SV13: $i,SV30: $i] :
( ( ( ~ ( ~ ( element @ ( sK4_C @ SV30 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ ( sK4_C @ SV30 @ SV13 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(289,plain,
! [SV14: $i,SV31: $i,SV34: $i] :
( ( ( ~ ( element @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ ( the_carrier @ SV14 ) ) )
= $false )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(290,plain,
! [SV34: $i,SV31: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ SV34 ) ) )
= $false )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[279]) ).
thf(291,plain,
! [SV32: $i,SV14: $i] :
( ( ( ! [SY69: $i] :
( ~ ( element @ SY69 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ SY69 )
| ( related @ SV14 @ SY69 @ ( sK2_C @ SV32 @ SV14 ) ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(292,plain,
! [SV14: $i,SV32: $i] :
( ( ( ~ ( ~ ( element @ ( sK2_C @ SV32 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ ( sK2_C @ SV32 @ SV14 ) ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(293,plain,
! [SV12: $i,SV24: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ SV24 )
| ~ ~ ( related @ SV12 @ SV26 @ ( sK13_D @ SV26 @ SV24 @ SV12 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV12 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(294,plain,
! [SV27: $i,SV25: $i,SV12: $i,SV35: $i] :
( ( ( element @ SV35 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( ~ ( in @ SV35 @ SV25 )
| ( related @ SV12 @ SV27 @ SV35 ) )
= $true )
| ( ( relstr_element_smaller @ SV12 @ SV25 @ SV27 )
= $false )
| ( ( element @ SV27 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(295,plain,
! [SV13: $i,SV29: $i,SV33: $i] :
( ( ( element @ ( sK5_D @ SV33 @ SV29 @ SV13 ) @ ( the_carrier @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(296,plain,
! [SV33: $i,SV29: $i,SV13: $i] :
( ( ( ~ ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SV33 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) ) ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(297,plain,
! [SV30: $i,SV13: $i,SV36: $i] :
( ( ( ~ ( element @ SV36 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ SV36 )
| ( related @ SV13 @ ( sK4_C @ SV30 @ SV13 ) @ SV36 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(298,plain,
! [SV13: $i,SV30: $i] :
( ( ( ~ ( element @ ( sK4_C @ SV30 @ SV13 ) @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV30 @ ( sK4_C @ SV30 @ SV13 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(299,plain,
! [SV14: $i,SV31: $i,SV34: $i] :
( ( ( element @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ ( the_carrier @ SV14 ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[289]) ).
thf(300,plain,
! [SV34: $i,SV31: $i,SV14: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ SV34 ) ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(301,plain,
! [SV32: $i,SV14: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ SV37 )
| ( related @ SV14 @ SV37 @ ( sK2_C @ SV32 @ SV14 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(302,plain,
! [SV14: $i,SV32: $i] :
( ( ( ~ ( element @ ( sK2_C @ SV32 @ SV14 ) @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV32 @ ( sK2_C @ SV32 @ SV14 ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(303,plain,
! [SV12: $i,SV24: $i,SV26: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ SV24 ) )
= $false )
| ( ( relstr_element_smaller @ SV12 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(304,plain,
! [SV24: $i,SV26: $i,SV12: $i] :
( ( ( ~ ~ ( related @ SV12 @ SV26 @ ( sK13_D @ SV26 @ SV24 @ SV12 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV12 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(305,plain,
! [SV27: $i,SV12: $i,SV25: $i,SV35: $i] :
( ( ( ~ ( in @ SV35 @ SV25 ) )
= $true )
| ( ( related @ SV12 @ SV27 @ SV35 )
= $true )
| ( ( element @ SV35 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( relstr_element_smaller @ SV12 @ SV25 @ SV27 )
= $false )
| ( ( element @ SV27 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(306,plain,
! [SV29: $i,SV13: $i,SV33: $i] :
( ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( element @ ( sK5_D @ SV33 @ SV29 @ SV13 ) @ ( the_carrier @ SV13 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(307,plain,
! [SV33: $i,SV29: $i,SV13: $i] :
( ( ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
| ~ ~ ( related @ SV13 @ SV33 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) ) )
= $false )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(308,plain,
! [SV30: $i,SV13: $i,SV36: $i] :
( ( ( ~ ( element @ SV36 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV13 @ SV30 @ SV36 )
| ( related @ SV13 @ ( sK4_C @ SV30 @ SV13 ) @ SV36 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(309,plain,
! [SV13: $i,SV30: $i] :
( ( ( ~ ( element @ ( sK4_C @ SV30 @ SV13 ) @ ( the_carrier @ SV13 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(310,plain,
! [SV30: $i,SV13: $i] :
( ( ( ~ ( relstr_set_smaller @ SV13 @ SV30 @ ( sK4_C @ SV30 @ SV13 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(311,plain,
! [SV31: $i,SV14: $i,SV34: $i] :
( ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( element @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ ( the_carrier @ SV14 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(312,plain,
! [SV34: $i,SV31: $i,SV14: $i] :
( ( ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) )
| ~ ~ ( related @ SV14 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ SV34 ) )
= $false )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(313,plain,
! [SV32: $i,SV14: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV14 @ SV32 @ SV37 )
| ( related @ SV14 @ SV37 @ ( sK2_C @ SV32 @ SV14 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(314,plain,
! [SV14: $i,SV32: $i] :
( ( ( ~ ( element @ ( sK2_C @ SV32 @ SV14 ) @ ( the_carrier @ SV14 ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(315,plain,
! [SV32: $i,SV14: $i] :
( ( ( ~ ( relstr_element_smaller @ SV14 @ SV32 @ ( sK2_C @ SV32 @ SV14 ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(316,plain,
! [SV12: $i,SV24: $i,SV26: $i] :
( ( ( in @ ( sK13_D @ SV26 @ SV24 @ SV12 ) @ SV24 )
= $true )
| ( ( relstr_element_smaller @ SV12 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(317,plain,
! [SV24: $i,SV26: $i,SV12: $i] :
( ( ( ~ ( related @ SV12 @ SV26 @ ( sK13_D @ SV26 @ SV24 @ SV12 ) ) )
= $true )
| ( ( relstr_element_smaller @ SV12 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(318,plain,
! [SV27: $i,SV12: $i,SV25: $i,SV35: $i] :
( ( ( in @ SV35 @ SV25 )
= $false )
| ( ( related @ SV12 @ SV27 @ SV35 )
= $true )
| ( ( element @ SV35 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( relstr_element_smaller @ SV12 @ SV25 @ SV27 )
= $false )
| ( ( element @ SV27 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(319,plain,
! [SV29: $i,SV13: $i,SV33: $i] :
( ( ( element @ SV33 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( element @ ( sK5_D @ SV33 @ SV29 @ SV13 ) @ ( the_carrier @ SV13 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(320,plain,
! [SV33: $i,SV29: $i,SV13: $i] :
( ( ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) ) )
= $false )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(321,plain,
! [SV29: $i,SV33: $i,SV13: $i] :
( ( ( ~ ~ ( related @ SV13 @ SV33 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) ) )
= $false )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(322,plain,
! [SV30: $i,SV13: $i,SV36: $i] :
( ( ( element @ SV36 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV13 @ SV30 @ SV36 )
| ( related @ SV13 @ ( sK4_C @ SV30 @ SV13 ) @ SV36 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(323,plain,
! [SV13: $i,SV30: $i] :
( ( ( element @ ( sK4_C @ SV30 @ SV13 ) @ ( the_carrier @ SV13 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(324,plain,
! [SV30: $i,SV13: $i] :
( ( ( relstr_set_smaller @ SV13 @ SV30 @ ( sK4_C @ SV30 @ SV13 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(325,plain,
! [SV31: $i,SV14: $i,SV34: $i] :
( ( ( element @ SV34 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( element @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ ( the_carrier @ SV14 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(326,plain,
! [SV34: $i,SV31: $i,SV14: $i] :
( ( ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) ) )
= $false )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(327,plain,
! [SV31: $i,SV34: $i,SV14: $i] :
( ( ( ~ ~ ( related @ SV14 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ SV34 ) )
= $false )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[312]) ).
thf(328,plain,
! [SV32: $i,SV14: $i,SV37: $i] :
( ( ( element @ SV37 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV14 @ SV32 @ SV37 )
| ( related @ SV14 @ SV37 @ ( sK2_C @ SV32 @ SV14 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(329,plain,
! [SV14: $i,SV32: $i] :
( ( ( element @ ( sK2_C @ SV32 @ SV14 ) @ ( the_carrier @ SV14 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(330,plain,
! [SV32: $i,SV14: $i] :
( ( ( relstr_element_smaller @ SV14 @ SV32 @ ( sK2_C @ SV32 @ SV14 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(331,plain,
! [SV24: $i,SV26: $i,SV12: $i] :
( ( ( related @ SV12 @ SV26 @ ( sK13_D @ SV26 @ SV24 @ SV12 ) )
= $false )
| ( ( relstr_element_smaller @ SV12 @ SV24 @ SV26 )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV12 ) )
= $false )
| ( ( rel_str @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(332,plain,
! [SV33: $i,SV29: $i,SV13: $i] :
( ( ( relstr_set_smaller @ SV13 @ SV29 @ SV33 )
= $false )
| ( ( element @ SV33 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( element @ ( sK5_D @ SV33 @ SV29 @ SV13 ) @ ( the_carrier @ SV13 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(333,plain,
! [SV33: $i,SV29: $i,SV13: $i] :
( ( ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[320]) ).
thf(334,plain,
! [SV29: $i,SV33: $i,SV13: $i] :
( ( ( ~ ( related @ SV13 @ SV33 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) ) )
= $true )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(335,plain,
! [SV36: $i,SV30: $i,SV13: $i] :
( ( ( ~ ( relstr_set_smaller @ SV13 @ SV30 @ SV36 ) )
= $true )
| ( ( related @ SV13 @ ( sK4_C @ SV30 @ SV13 ) @ SV36 )
= $true )
| ( ( element @ SV36 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(336,plain,
! [SV34: $i,SV31: $i,SV14: $i] :
( ( ( relstr_element_smaller @ SV14 @ SV31 @ SV34 )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( element @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ ( the_carrier @ SV14 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(337,plain,
! [SV34: $i,SV31: $i,SV14: $i] :
( ( ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(338,plain,
! [SV31: $i,SV34: $i,SV14: $i] :
( ( ( ~ ( related @ SV14 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ SV34 ) )
= $true )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(339,plain,
! [SV37: $i,SV32: $i,SV14: $i] :
( ( ( ~ ( relstr_element_smaller @ SV14 @ SV32 @ SV37 ) )
= $true )
| ( ( related @ SV14 @ SV37 @ ( sK2_C @ SV32 @ SV14 ) )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(340,plain,
! [SV29: $i,SV13: $i,SV33: $i] :
( ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(341,plain,
! [SV29: $i,SV33: $i,SV13: $i] :
( ( ( related @ SV13 @ SV33 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
= $false )
| ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) )
| ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(342,plain,
! [SV36: $i,SV30: $i,SV13: $i] :
( ( ( relstr_set_smaller @ SV13 @ SV30 @ SV36 )
= $false )
| ( ( related @ SV13 @ ( sK4_C @ SV30 @ SV13 ) @ SV36 )
= $true )
| ( ( element @ SV36 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV30 )
= $false )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(343,plain,
! [SV31: $i,SV14: $i,SV34: $i] :
( ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(344,plain,
! [SV31: $i,SV34: $i,SV14: $i] :
( ( ( related @ SV14 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ SV34 )
= $false )
| ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) )
| ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(345,plain,
! [SV37: $i,SV32: $i,SV14: $i] :
( ( ( relstr_element_smaller @ SV14 @ SV32 @ SV37 )
= $false )
| ( ( related @ SV14 @ SV37 @ ( sK2_C @ SV32 @ SV14 ) )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV32 )
= $false )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(346,plain,
! [SV29: $i,SV13: $i,SV33: $i] :
( ( ( element @ SV33 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(347,plain,
! [SV29: $i,SV13: $i,SV33: $i] :
( ( ( ~ ( element @ SV33 @ ( the_carrier @ SV13 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( related @ SV13 @ SV33 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(348,plain,
! [SV31: $i,SV14: $i,SV34: $i] :
( ( ( element @ SV34 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(349,plain,
! [SV31: $i,SV14: $i,SV34: $i] :
( ( ( ~ ( element @ SV34 @ ( the_carrier @ SV14 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( related @ SV14 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ SV34 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(350,plain,
! [SV33: $i,SV29: $i,SV13: $i] :
( ( ( relstr_set_smaller @ SV13 @ SV29 @ SV33 )
= $false )
| ( ( element @ SV33 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( relstr_set_smaller @ SV13 @ SV29 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(351,plain,
! [SV29: $i,SV13: $i,SV33: $i] :
( ( ( element @ SV33 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV13 @ SV29 @ SV33 ) )
= $true )
| ( ( related @ SV13 @ SV33 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(352,plain,
! [SV34: $i,SV31: $i,SV14: $i] :
( ( ( relstr_element_smaller @ SV14 @ SV31 @ SV34 )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( relstr_element_smaller @ SV14 @ SV31 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(353,plain,
! [SV31: $i,SV14: $i,SV34: $i] :
( ( ( element @ SV34 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV14 @ SV31 @ SV34 ) )
= $true )
| ( ( related @ SV14 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ SV34 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(354,plain,
! [SV33: $i,SV29: $i,SV13: $i] :
( ( ( relstr_set_smaller @ SV13 @ SV29 @ SV33 )
= $false )
| ( ( element @ SV33 @ ( the_carrier @ SV13 ) )
= $false )
| ( ( related @ SV13 @ SV33 @ ( sK5_D @ SV33 @ SV29 @ SV13 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV13 @ SV29 )
= $true )
| ( ( antisymmetric_relstr @ SV13 )
= $false )
| ( ( rel_str @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(355,plain,
! [SV34: $i,SV31: $i,SV14: $i] :
( ( ( relstr_element_smaller @ SV14 @ SV31 @ SV34 )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV14 ) )
= $false )
| ( ( related @ SV14 @ ( sK3_D @ SV34 @ SV31 @ SV14 ) @ SV34 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV14 @ SV31 )
= $true )
| ( ( antisymmetric_relstr @ SV14 )
= $false )
| ( ( rel_str @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(356,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[91,355,354,352,350,345,342,336,332,331,330,329,324,323,318,316,282,264,263,262,240,239,210,200,199,198,197,196,192,185,181,177,170,166,165,137,136,130,128,115,114,113,102,100,97,96,95,94,93]) ).
thf(357,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(358,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(359,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ ( the_carrier @ A ) @ B ) )
| ( lower_bounded_relstr @ A ) )
& ! [A: $i] :
( ~ ( rel_str @ A )
| ~ ( lower_bounded_relstr @ A )
| ( ( element @ ( sK14_B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ ( the_carrier @ A ) @ ( sK14_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(360,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ( ( element @ ( sK13_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( in @ ( sK13_D @ C @ B @ A ) @ B )
& ~ ( related @ A @ C @ ( sK13_D @ C @ B @ A ) ) )
| ( relstr_element_smaller @ A @ B @ C ) )
& ! [B: $i,C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ C )
| ! [D: $i] :
( ~ ( element @ D @ ( the_carrier @ A ) )
| ~ ( in @ D @ B )
| ( related @ A @ C @ D ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(361,plain,
$true = $true,
inference(copy,[status(thm)],[51]) ).
thf(362,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(363,plain,
$true = $true,
inference(copy,[status(thm)],[49]) ).
thf(364,plain,
$true = $true,
inference(copy,[status(thm)],[48]) ).
thf(365,plain,
$true = $true,
inference(copy,[status(thm)],[47]) ).
thf(366,plain,
( ( rel_str @ sK12_A )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(367,plain,
( ( one_sorted_str @ sK11_A )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(368,plain,
( ( ! [A: $i] : ( element @ ( sK10_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(369,plain,
( ( ! [A: $i] :
( ( empty_carrier @ A )
| ~ ( one_sorted_str @ A )
| ~ ( empty @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(370,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(371,plain,
( ( ~ ( empty @ sK9_A )
& ( finite @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(372,plain,
( ( empty @ sK8_A )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(373,plain,
( ( ~ ( empty @ sK7_A ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(374,plain,
( ( ( one_sorted_str @ sK6_A )
& ~ ( empty_carrier @ sK6_A ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(375,plain,
( ( ! [A: $i] :
( ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( ! [B: $i] :
( ! [C: $i] :
( ( ( element @ ( sK5_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ ( sK5_D @ C @ B @ A ) )
& ~ ( related @ A @ C @ ( sK5_D @ C @ B @ A ) ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_set_smaller @ A @ B @ C ) )
| ( ex_sup_of_relstr_set @ A @ B ) )
& ! [B: $i] :
( ~ ( ex_sup_of_relstr_set @ A @ B )
| ( ! [SY40: $i] :
( ~ ( element @ SY40 @ ( the_carrier @ A ) )
| ~ ( relstr_set_smaller @ A @ B @ SY40 )
| ( related @ A @ ( sK4_C @ B @ A ) @ SY40 ) )
& ( element @ ( sK4_C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_set_smaller @ A @ B @ ( sK4_C @ B @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(376,plain,
( ( ! [A: $i] :
( ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ( ! [B: $i] :
( ! [C: $i] :
( ( ( element @ ( sK3_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK3_D @ C @ B @ A ) )
& ~ ( related @ A @ ( sK3_D @ C @ B @ A ) @ C ) )
| ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ C ) )
| ( ex_inf_of_relstr_set @ A @ B ) )
& ! [B: $i] :
( ~ ( ex_inf_of_relstr_set @ A @ B )
| ( ! [SY39: $i] :
( ~ ( element @ SY39 @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ SY39 )
| ( related @ A @ SY39 @ ( sK2_C @ B @ A ) ) )
& ( element @ ( sK2_C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK2_C @ B @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(377,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(378,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(379,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(380,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ( relstr_element_smaller @ A @ empty_set @ B ) )
& ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ( relstr_set_smaller @ A @ empty_set @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(381,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(382,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(383,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(384,plain,
( ( lower_bounded_relstr @ sK1_A )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(385,plain,
( ( antisymmetric_relstr @ sK1_A )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(386,plain,
( ( ~ ( empty_carrier @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(387,plain,
( ( ~ ( ex_inf_of_relstr_set @ sK1_A @ ( the_carrier @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(388,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( ~ ( element @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( related @ SX0 @ SX2 @ ( sK13_D @ SX2 @ SX1 @ SX0 ) ) ) )
| ( relstr_element_smaller @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( in @ SX3 @ SX1 )
| ( related @ SX0 @ SX2 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(389,plain,
( ( ! [SX0: $i] :
( ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SX0 @ SX1 @ ( sK3_D @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( related @ SX0 @ ( sK3_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX2 ) )
| ( ex_inf_of_relstr_set @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ex_inf_of_relstr_set @ SX0 @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX2 )
| ( related @ SX0 @ SX2 @ ( sK2_C @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ ( sK2_C @ SX1 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(390,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ( relstr_element_smaller @ SX0 @ empty_set @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ( relstr_set_smaller @ SX0 @ empty_set @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(391,plain,
( ( ~ ( ~ ( one_sorted_str @ sK6_A )
| ~ ~ ( empty_carrier @ sK6_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(392,plain,
( ( ! [SX0: $i] :
( ~ ( antisymmetric_relstr @ SX0 )
| ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SX0 @ SX1 @ ( sK5_D @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( related @ SX0 @ SX2 @ ( sK5_D @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 ) )
| ( ex_sup_of_relstr_set @ SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( ex_sup_of_relstr_set @ SX0 @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ SX2 )
| ( related @ SX0 @ ( sK4_C @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_set_smaller @ SX0 @ SX1 @ ( sK4_C @ SX1 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(393,plain,
( ( ~ ( ~ ~ ( empty @ sK9_A )
| ~ ( finite @ sK9_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(394,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ SX1 ) )
| ( lower_bounded_relstr @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( ~ ( element @ ( sK14_B @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ ( sK14_B @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(395,plain,
! [SV38: $i] :
( ( ! [SY70: $i] :
( ~ ( in @ SV38 @ SY70 )
| ~ ( in @ SY70 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(396,plain,
! [SV39: $i] :
( ( ~ ( empty @ SV39 )
| ( finite @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(397,plain,
! [SV40: $i] :
( ( ~ ( rel_str @ SV40 )
| ( one_sorted_str @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(398,plain,
! [SV41: $i] :
( ( element @ ( sK10_B @ SV41 ) @ SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(399,plain,
! [SV42: $i] :
( ( ( empty_carrier @ SV42 )
| ~ ( one_sorted_str @ SV42 )
| ~ ( empty @ ( the_carrier @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(400,plain,
( ( empty @ sK7_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(401,plain,
! [SV43: $i] :
( ( ! [SY71: $i] :
( ~ ( in @ SV43 @ SY71 )
| ( element @ SV43 @ SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(402,plain,
! [SV44: $i] :
( ( ! [SY72: $i] :
( ~ ( element @ SV44 @ SY72 )
| ( empty @ SY72 )
| ( in @ SV44 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(403,plain,
! [SV45: $i] :
( ( ~ ( empty @ SV45 )
| ( SV45 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(404,plain,
! [SV46: $i] :
( ( ! [SY73: $i] :
( ~ ( empty @ SY73 )
| ~ ( in @ SV46 @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(405,plain,
! [SV47: $i] :
( ( ! [SY74: $i] :
( ( SV47 = SY74 )
| ~ ( empty @ SV47 )
| ~ ( empty @ SY74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(406,plain,
( ( empty_carrier @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(407,plain,
( ( ex_inf_of_relstr_set @ sK1_A @ ( the_carrier @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(408,plain,
! [SV48: $i] :
( ( ~ ( rel_str @ SV48 )
| ~ ( ~ ! [SY75: $i,SY76: $i] :
( ~ ( element @ SY76 @ ( the_carrier @ SV48 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY76 @ SY75 @ SV48 ) @ ( the_carrier @ SV48 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY76 @ SY75 @ SV48 ) @ SY75 )
| ~ ~ ( related @ SV48 @ SY76 @ ( sK13_D @ SY76 @ SY75 @ SV48 ) ) ) )
| ( relstr_element_smaller @ SV48 @ SY75 @ SY76 ) )
| ~ ! [SY77: $i,SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ SV48 ) )
| ~ ( relstr_element_smaller @ SV48 @ SY77 @ SY78 )
| ! [SY79: $i] :
( ~ ( element @ SY79 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SY79 @ SY77 )
| ( related @ SV48 @ SY78 @ SY79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(409,plain,
! [SV49: $i] :
( ( ~ ( antisymmetric_relstr @ SV49 )
| ~ ( rel_str @ SV49 )
| ~ ( ~ ! [SY80: $i] :
( ! [SY81: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SY80 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ SY81 ) ) )
| ~ ( element @ SY81 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY80 @ SY81 ) )
| ( ex_inf_of_relstr_set @ SV49 @ SY80 ) )
| ~ ! [SY82: $i] :
( ~ ( ex_inf_of_relstr_set @ SV49 @ SY82 )
| ~ ( ~ ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ SY83 )
| ( related @ SV49 @ SY83 @ ( sK2_C @ SY82 @ SV49 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY82 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ ( sK2_C @ SY82 @ SV49 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(410,plain,
! [SV50: $i] :
( ( ~ ( rel_str @ SV50 )
| ~ ( ~ ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV50 ) )
| ( relstr_element_smaller @ SV50 @ empty_set @ SY84 ) )
| ~ ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV50 ) )
| ( relstr_set_smaller @ SV50 @ empty_set @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(411,plain,
( ( ~ ( one_sorted_str @ sK6_A )
| ~ ~ ( empty_carrier @ sK6_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(412,plain,
! [SV51: $i] :
( ( ~ ( antisymmetric_relstr @ SV51 )
| ~ ( rel_str @ SV51 )
| ~ ( ~ ! [SY86: $i] :
( ! [SY87: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY87 @ SY86 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SY86 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SY87 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) ) ) )
| ~ ( element @ SY87 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY86 @ SY87 ) )
| ( ex_sup_of_relstr_set @ SV51 @ SY86 ) )
| ~ ! [SY88: $i] :
( ~ ( ex_sup_of_relstr_set @ SV51 @ SY88 )
| ~ ( ~ ! [SY89: $i] :
( ~ ( element @ SY89 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ SY89 )
| ( related @ SV51 @ ( sK4_C @ SY88 @ SV51 ) @ SY89 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY88 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ ( sK4_C @ SY88 @ SV51 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(413,plain,
( ( ~ ~ ( empty @ sK9_A )
| ~ ( finite @ sK9_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(414,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ SX1 ) )
| ( lower_bounded_relstr @ SX0 ) )
| ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( ~ ( element @ ( sK14_B @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ ( sK14_B @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(415,plain,
! [SV52: $i,SV38: $i] :
( ( ~ ( in @ SV38 @ SV52 )
| ~ ( in @ SV52 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(416,plain,
! [SV39: $i] :
( ( ( ~ ( empty @ SV39 ) )
= $true )
| ( ( finite @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(417,plain,
! [SV40: $i] :
( ( ( ~ ( rel_str @ SV40 ) )
= $true )
| ( ( one_sorted_str @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(418,plain,
! [SV42: $i] :
( ( ( ( empty_carrier @ SV42 )
| ~ ( one_sorted_str @ SV42 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(419,plain,
! [SV53: $i,SV43: $i] :
( ( ~ ( in @ SV43 @ SV53 )
| ( element @ SV43 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(420,plain,
! [SV54: $i,SV44: $i] :
( ( ~ ( element @ SV44 @ SV54 )
| ( empty @ SV54 )
| ( in @ SV44 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(421,plain,
! [SV45: $i] :
( ( ( ~ ( empty @ SV45 ) )
= $true )
| ( ( SV45 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(422,plain,
! [SV46: $i,SV55: $i] :
( ( ~ ( empty @ SV55 )
| ~ ( in @ SV46 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(423,plain,
! [SV56: $i,SV47: $i] :
( ( ( SV47 = SV56 )
| ~ ( empty @ SV47 )
| ~ ( empty @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(424,plain,
! [SV48: $i] :
( ( ( ~ ( rel_str @ SV48 ) )
= $true )
| ( ( ~ ( ~ ! [SY75: $i,SY76: $i] :
( ~ ( element @ SY76 @ ( the_carrier @ SV48 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY76 @ SY75 @ SV48 ) @ ( the_carrier @ SV48 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY76 @ SY75 @ SV48 ) @ SY75 )
| ~ ~ ( related @ SV48 @ SY76 @ ( sK13_D @ SY76 @ SY75 @ SV48 ) ) ) )
| ( relstr_element_smaller @ SV48 @ SY75 @ SY76 ) )
| ~ ! [SY77: $i,SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ SV48 ) )
| ~ ( relstr_element_smaller @ SV48 @ SY77 @ SY78 )
| ! [SY79: $i] :
( ~ ( element @ SY79 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SY79 @ SY77 )
| ( related @ SV48 @ SY78 @ SY79 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(425,plain,
! [SV49: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV49 )
| ~ ( rel_str @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY80: $i] :
( ! [SY81: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SY80 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ SY81 ) ) )
| ~ ( element @ SY81 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY80 @ SY81 ) )
| ( ex_inf_of_relstr_set @ SV49 @ SY80 ) )
| ~ ! [SY82: $i] :
( ~ ( ex_inf_of_relstr_set @ SV49 @ SY82 )
| ~ ( ~ ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ SY83 )
| ( related @ SV49 @ SY83 @ ( sK2_C @ SY82 @ SV49 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY82 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ ( sK2_C @ SY82 @ SV49 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(426,plain,
! [SV50: $i] :
( ( ( ~ ( rel_str @ SV50 ) )
= $true )
| ( ( ~ ( ~ ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV50 ) )
| ( relstr_element_smaller @ SV50 @ empty_set @ SY84 ) )
| ~ ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV50 ) )
| ( relstr_set_smaller @ SV50 @ empty_set @ SY85 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(427,plain,
( ( ~ ( one_sorted_str @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(428,plain,
( ( ~ ~ ( empty_carrier @ sK6_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(429,plain,
! [SV51: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV51 )
| ~ ( rel_str @ SV51 ) )
= $true )
| ( ( ~ ( ~ ! [SY86: $i] :
( ! [SY87: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY87 @ SY86 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SY86 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SY87 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) ) ) )
| ~ ( element @ SY87 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY86 @ SY87 ) )
| ( ex_sup_of_relstr_set @ SV51 @ SY86 ) )
| ~ ! [SY88: $i] :
( ~ ( ex_sup_of_relstr_set @ SV51 @ SY88 )
| ~ ( ~ ! [SY89: $i] :
( ~ ( element @ SY89 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ SY89 )
| ( related @ SV51 @ ( sK4_C @ SY88 @ SV51 ) @ SY89 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY88 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ ( sK4_C @ SY88 @ SV51 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(430,plain,
( ( ~ ~ ( empty @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(431,plain,
( ( ~ ( finite @ sK9_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(432,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ SX1 ) )
| ( lower_bounded_relstr @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(433,plain,
( ( ~ ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( ~ ( element @ ( sK14_B @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ ( sK14_B @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(434,plain,
! [SV52: $i,SV38: $i] :
( ( ( ~ ( in @ SV38 @ SV52 ) )
= $true )
| ( ( ~ ( in @ SV52 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(435,plain,
! [SV39: $i] :
( ( ( empty @ SV39 )
= $false )
| ( ( finite @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(436,plain,
! [SV40: $i] :
( ( ( rel_str @ SV40 )
= $false )
| ( ( one_sorted_str @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(437,plain,
! [SV42: $i] :
( ( ( empty_carrier @ SV42 )
= $true )
| ( ( ~ ( one_sorted_str @ SV42 ) )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(438,plain,
! [SV53: $i,SV43: $i] :
( ( ( ~ ( in @ SV43 @ SV53 ) )
= $true )
| ( ( element @ SV43 @ SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(439,plain,
! [SV54: $i,SV44: $i] :
( ( ( ~ ( element @ SV44 @ SV54 ) )
= $true )
| ( ( ( empty @ SV54 )
| ( in @ SV44 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(440,plain,
! [SV45: $i] :
( ( ( empty @ SV45 )
= $false )
| ( ( SV45 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(441,plain,
! [SV46: $i,SV55: $i] :
( ( ( ~ ( empty @ SV55 ) )
= $true )
| ( ( ~ ( in @ SV46 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(442,plain,
! [SV56: $i,SV47: $i] :
( ( ( ( SV47 = SV56 )
| ~ ( empty @ SV47 ) )
= $true )
| ( ( ~ ( empty @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(443,plain,
! [SV48: $i] :
( ( ( rel_str @ SV48 )
= $false )
| ( ( ~ ( ~ ! [SY75: $i,SY76: $i] :
( ~ ( element @ SY76 @ ( the_carrier @ SV48 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY76 @ SY75 @ SV48 ) @ ( the_carrier @ SV48 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY76 @ SY75 @ SV48 ) @ SY75 )
| ~ ~ ( related @ SV48 @ SY76 @ ( sK13_D @ SY76 @ SY75 @ SV48 ) ) ) )
| ( relstr_element_smaller @ SV48 @ SY75 @ SY76 ) )
| ~ ! [SY77: $i,SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ SV48 ) )
| ~ ( relstr_element_smaller @ SV48 @ SY77 @ SY78 )
| ! [SY79: $i] :
( ~ ( element @ SY79 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SY79 @ SY77 )
| ( related @ SV48 @ SY78 @ SY79 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(444,plain,
! [SV49: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV49 ) )
= $true )
| ( ( ~ ( rel_str @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY80: $i] :
( ! [SY81: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SY80 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ SY81 ) ) )
| ~ ( element @ SY81 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY80 @ SY81 ) )
| ( ex_inf_of_relstr_set @ SV49 @ SY80 ) )
| ~ ! [SY82: $i] :
( ~ ( ex_inf_of_relstr_set @ SV49 @ SY82 )
| ~ ( ~ ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ SY83 )
| ( related @ SV49 @ SY83 @ ( sK2_C @ SY82 @ SV49 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY82 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ ( sK2_C @ SY82 @ SV49 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(445,plain,
! [SV50: $i] :
( ( ( rel_str @ SV50 )
= $false )
| ( ( ~ ( ~ ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV50 ) )
| ( relstr_element_smaller @ SV50 @ empty_set @ SY84 ) )
| ~ ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV50 ) )
| ( relstr_set_smaller @ SV50 @ empty_set @ SY85 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(446,plain,
( ( one_sorted_str @ sK6_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[427]) ).
thf(447,plain,
( ( ~ ( empty_carrier @ sK6_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(448,plain,
! [SV51: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV51 ) )
= $true )
| ( ( ~ ( rel_str @ SV51 ) )
= $true )
| ( ( ~ ( ~ ! [SY86: $i] :
( ! [SY87: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY87 @ SY86 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SY86 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SY87 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) ) ) )
| ~ ( element @ SY87 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY86 @ SY87 ) )
| ( ex_sup_of_relstr_set @ SV51 @ SY86 ) )
| ~ ! [SY88: $i] :
( ~ ( ex_sup_of_relstr_set @ SV51 @ SY88 )
| ~ ( ~ ! [SY89: $i] :
( ~ ( element @ SY89 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ SY89 )
| ( related @ SV51 @ ( sK4_C @ SY88 @ SV51 ) @ SY89 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY88 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ ( sK4_C @ SY88 @ SV51 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(449,plain,
( ( ~ ( empty @ sK9_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[430]) ).
thf(450,plain,
( ( finite @ sK9_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(451,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ SX1 ) )
| ( lower_bounded_relstr @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(452,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( lower_bounded_relstr @ SX0 )
| ~ ( ~ ( element @ ( sK14_B @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ ( the_carrier @ SX0 ) @ ( sK14_B @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(453,plain,
! [SV52: $i,SV38: $i] :
( ( ( in @ SV38 @ SV52 )
= $false )
| ( ( ~ ( in @ SV52 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(454,plain,
! [SV42: $i] :
( ( ( one_sorted_str @ SV42 )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( ~ ( empty @ ( the_carrier @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(455,plain,
! [SV53: $i,SV43: $i] :
( ( ( in @ SV43 @ SV53 )
= $false )
| ( ( element @ SV43 @ SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(456,plain,
! [SV54: $i,SV44: $i] :
( ( ( element @ SV44 @ SV54 )
= $false )
| ( ( ( empty @ SV54 )
| ( in @ SV44 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(457,plain,
! [SV46: $i,SV55: $i] :
( ( ( empty @ SV55 )
= $false )
| ( ( ~ ( in @ SV46 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(458,plain,
! [SV56: $i,SV47: $i] :
( ( ( SV47 = SV56 )
= $true )
| ( ( ~ ( empty @ SV47 ) )
= $true )
| ( ( ~ ( empty @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(459,plain,
! [SV48: $i] :
( ( ( ~ ! [SY75: $i,SY76: $i] :
( ~ ( element @ SY76 @ ( the_carrier @ SV48 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY76 @ SY75 @ SV48 ) @ ( the_carrier @ SV48 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY76 @ SY75 @ SV48 ) @ SY75 )
| ~ ~ ( related @ SV48 @ SY76 @ ( sK13_D @ SY76 @ SY75 @ SV48 ) ) ) )
| ( relstr_element_smaller @ SV48 @ SY75 @ SY76 ) )
| ~ ! [SY77: $i,SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ SV48 ) )
| ~ ( relstr_element_smaller @ SV48 @ SY77 @ SY78 )
| ! [SY79: $i] :
( ~ ( element @ SY79 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SY79 @ SY77 )
| ( related @ SV48 @ SY78 @ SY79 ) ) ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(460,plain,
! [SV49: $i] :
( ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( ~ ( rel_str @ SV49 ) )
= $true )
| ( ( ~ ( ~ ! [SY80: $i] :
( ! [SY81: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SY80 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ SY81 ) ) )
| ~ ( element @ SY81 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY80 @ SY81 ) )
| ( ex_inf_of_relstr_set @ SV49 @ SY80 ) )
| ~ ! [SY82: $i] :
( ~ ( ex_inf_of_relstr_set @ SV49 @ SY82 )
| ~ ( ~ ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ SY83 )
| ( related @ SV49 @ SY83 @ ( sK2_C @ SY82 @ SV49 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY82 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ ( sK2_C @ SY82 @ SV49 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(461,plain,
! [SV50: $i] :
( ( ( ~ ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV50 ) )
| ( relstr_element_smaller @ SV50 @ empty_set @ SY84 ) )
| ~ ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV50 ) )
| ( relstr_set_smaller @ SV50 @ empty_set @ SY85 ) ) )
= $false )
| ( ( rel_str @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(462,plain,
( ( empty_carrier @ sK6_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(463,plain,
! [SV51: $i] :
( ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( ~ ( rel_str @ SV51 ) )
= $true )
| ( ( ~ ( ~ ! [SY86: $i] :
( ! [SY87: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY87 @ SY86 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SY86 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SY87 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) ) ) )
| ~ ( element @ SY87 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY86 @ SY87 ) )
| ( ex_sup_of_relstr_set @ SV51 @ SY86 ) )
| ~ ! [SY88: $i] :
( ~ ( ex_sup_of_relstr_set @ SV51 @ SY88 )
| ~ ( ~ ! [SY89: $i] :
( ~ ( element @ SY89 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ SY89 )
| ( related @ SV51 @ ( sK4_C @ SY88 @ SV51 ) @ SY89 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY88 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ ( sK4_C @ SY88 @ SV51 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(464,plain,
( ( empty @ sK9_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(465,plain,
! [SV57: $i] :
( ( ~ ( rel_str @ SV57 )
| ! [SY90: $i] :
( ~ ( element @ SY90 @ ( the_carrier @ SV57 ) )
| ~ ( relstr_element_smaller @ SV57 @ ( the_carrier @ SV57 ) @ SY90 ) )
| ( lower_bounded_relstr @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(466,plain,
! [SV58: $i] :
( ( ~ ( rel_str @ SV58 )
| ~ ( lower_bounded_relstr @ SV58 )
| ~ ( ~ ( element @ ( sK14_B @ SV58 ) @ ( the_carrier @ SV58 ) )
| ~ ( relstr_element_smaller @ SV58 @ ( the_carrier @ SV58 ) @ ( sK14_B @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(467,plain,
! [SV38: $i,SV52: $i] :
( ( ( in @ SV52 @ SV38 )
= $false )
| ( ( in @ SV38 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(468,plain,
! [SV42: $i] :
( ( ( empty @ ( the_carrier @ SV42 ) )
= $false )
| ( ( empty_carrier @ SV42 )
= $true )
| ( ( one_sorted_str @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(469,plain,
! [SV44: $i,SV54: $i] :
( ( ( empty @ SV54 )
= $true )
| ( ( in @ SV44 @ SV54 )
= $true )
| ( ( element @ SV44 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(470,plain,
! [SV55: $i,SV46: $i] :
( ( ( in @ SV46 @ SV55 )
= $false )
| ( ( empty @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(471,plain,
! [SV56: $i,SV47: $i] :
( ( ( empty @ SV47 )
= $false )
| ( ( SV47 = SV56 )
= $true )
| ( ( ~ ( empty @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(472,plain,
! [SV48: $i] :
( ( ( ~ ! [SY75: $i,SY76: $i] :
( ~ ( element @ SY76 @ ( the_carrier @ SV48 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY76 @ SY75 @ SV48 ) @ ( the_carrier @ SV48 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY76 @ SY75 @ SV48 ) @ SY75 )
| ~ ~ ( related @ SV48 @ SY76 @ ( sK13_D @ SY76 @ SY75 @ SV48 ) ) ) )
| ( relstr_element_smaller @ SV48 @ SY75 @ SY76 ) ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(473,plain,
! [SV48: $i] :
( ( ( ~ ! [SY77: $i,SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ SV48 ) )
| ~ ( relstr_element_smaller @ SV48 @ SY77 @ SY78 )
| ! [SY79: $i] :
( ~ ( element @ SY79 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SY79 @ SY77 )
| ( related @ SV48 @ SY78 @ SY79 ) ) ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(474,plain,
! [SV49: $i] :
( ( ( rel_str @ SV49 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( ~ ( ~ ! [SY80: $i] :
( ! [SY81: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SY80 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ SY81 ) ) )
| ~ ( element @ SY81 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY80 @ SY81 ) )
| ( ex_inf_of_relstr_set @ SV49 @ SY80 ) )
| ~ ! [SY82: $i] :
( ~ ( ex_inf_of_relstr_set @ SV49 @ SY82 )
| ~ ( ~ ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ SY83 )
| ( related @ SV49 @ SY83 @ ( sK2_C @ SY82 @ SV49 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY82 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ ( sK2_C @ SY82 @ SV49 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(475,plain,
! [SV50: $i] :
( ( ( ~ ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV50 ) )
| ( relstr_element_smaller @ SV50 @ empty_set @ SY84 ) ) )
= $false )
| ( ( rel_str @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(476,plain,
! [SV50: $i] :
( ( ( ~ ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV50 ) )
| ( relstr_set_smaller @ SV50 @ empty_set @ SY85 ) ) )
= $false )
| ( ( rel_str @ SV50 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[461]) ).
thf(477,plain,
! [SV51: $i] :
( ( ( rel_str @ SV51 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( ~ ( ~ ! [SY86: $i] :
( ! [SY87: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY87 @ SY86 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SY86 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SY87 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) ) ) )
| ~ ( element @ SY87 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY86 @ SY87 ) )
| ( ex_sup_of_relstr_set @ SV51 @ SY86 ) )
| ~ ! [SY88: $i] :
( ~ ( ex_sup_of_relstr_set @ SV51 @ SY88 )
| ~ ( ~ ! [SY89: $i] :
( ~ ( element @ SY89 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ SY89 )
| ( related @ SV51 @ ( sK4_C @ SY88 @ SV51 ) @ SY89 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY88 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ ( sK4_C @ SY88 @ SV51 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(478,plain,
! [SV57: $i] :
( ( ( ~ ( rel_str @ SV57 ) )
= $true )
| ( ( ! [SY90: $i] :
( ~ ( element @ SY90 @ ( the_carrier @ SV57 ) )
| ~ ( relstr_element_smaller @ SV57 @ ( the_carrier @ SV57 ) @ SY90 ) )
| ( lower_bounded_relstr @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(479,plain,
! [SV58: $i] :
( ( ( ~ ( rel_str @ SV58 ) )
= $true )
| ( ( ~ ( lower_bounded_relstr @ SV58 )
| ~ ( ~ ( element @ ( sK14_B @ SV58 ) @ ( the_carrier @ SV58 ) )
| ~ ( relstr_element_smaller @ SV58 @ ( the_carrier @ SV58 ) @ ( sK14_B @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[466]) ).
thf(480,plain,
! [SV47: $i,SV56: $i] :
( ( ( empty @ SV56 )
= $false )
| ( ( SV47 = SV56 )
= $true )
| ( ( empty @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(481,plain,
! [SV48: $i] :
( ( ( ! [SY75: $i,SY76: $i] :
( ~ ( element @ SY76 @ ( the_carrier @ SV48 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY76 @ SY75 @ SV48 ) @ ( the_carrier @ SV48 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY76 @ SY75 @ SV48 ) @ SY75 )
| ~ ~ ( related @ SV48 @ SY76 @ ( sK13_D @ SY76 @ SY75 @ SV48 ) ) ) )
| ( relstr_element_smaller @ SV48 @ SY75 @ SY76 ) ) )
= $true )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(482,plain,
! [SV48: $i] :
( ( ( ! [SY77: $i,SY78: $i] :
( ~ ( element @ SY78 @ ( the_carrier @ SV48 ) )
| ~ ( relstr_element_smaller @ SV48 @ SY77 @ SY78 )
| ! [SY79: $i] :
( ~ ( element @ SY79 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SY79 @ SY77 )
| ( related @ SV48 @ SY78 @ SY79 ) ) ) )
= $true )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(483,plain,
! [SV49: $i] :
( ( ( ~ ! [SY80: $i] :
( ! [SY81: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SY80 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ SY81 ) ) )
| ~ ( element @ SY81 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY80 @ SY81 ) )
| ( ex_inf_of_relstr_set @ SV49 @ SY80 ) )
| ~ ! [SY82: $i] :
( ~ ( ex_inf_of_relstr_set @ SV49 @ SY82 )
| ~ ( ~ ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ SY83 )
| ( related @ SV49 @ SY83 @ ( sK2_C @ SY82 @ SV49 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY82 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ ( sK2_C @ SY82 @ SV49 ) ) ) ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(484,plain,
! [SV50: $i] :
( ( ( ! [SY84: $i] :
( ~ ( element @ SY84 @ ( the_carrier @ SV50 ) )
| ( relstr_element_smaller @ SV50 @ empty_set @ SY84 ) ) )
= $true )
| ( ( rel_str @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(485,plain,
! [SV50: $i] :
( ( ( ! [SY85: $i] :
( ~ ( element @ SY85 @ ( the_carrier @ SV50 ) )
| ( relstr_set_smaller @ SV50 @ empty_set @ SY85 ) ) )
= $true )
| ( ( rel_str @ SV50 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(486,plain,
! [SV51: $i] :
( ( ( ~ ! [SY86: $i] :
( ! [SY87: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY87 @ SY86 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SY86 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SY87 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) ) ) )
| ~ ( element @ SY87 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY86 @ SY87 ) )
| ( ex_sup_of_relstr_set @ SV51 @ SY86 ) )
| ~ ! [SY88: $i] :
( ~ ( ex_sup_of_relstr_set @ SV51 @ SY88 )
| ~ ( ~ ! [SY89: $i] :
( ~ ( element @ SY89 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ SY89 )
| ( related @ SV51 @ ( sK4_C @ SY88 @ SV51 ) @ SY89 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY88 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ ( sK4_C @ SY88 @ SV51 ) ) ) ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(487,plain,
! [SV57: $i] :
( ( ( rel_str @ SV57 )
= $false )
| ( ( ! [SY90: $i] :
( ~ ( element @ SY90 @ ( the_carrier @ SV57 ) )
| ~ ( relstr_element_smaller @ SV57 @ ( the_carrier @ SV57 ) @ SY90 ) )
| ( lower_bounded_relstr @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(488,plain,
! [SV58: $i] :
( ( ( rel_str @ SV58 )
= $false )
| ( ( ~ ( lower_bounded_relstr @ SV58 )
| ~ ( ~ ( element @ ( sK14_B @ SV58 ) @ ( the_carrier @ SV58 ) )
| ~ ( relstr_element_smaller @ SV58 @ ( the_carrier @ SV58 ) @ ( sK14_B @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(489,plain,
! [SV59: $i,SV48: $i] :
( ( ( ! [SY91: $i] :
( ~ ( element @ SY91 @ ( the_carrier @ SV48 ) )
| ~ ( ~ ( element @ ( sK13_D @ SY91 @ SV59 @ SV48 ) @ ( the_carrier @ SV48 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SY91 @ SV59 @ SV48 ) @ SV59 )
| ~ ~ ( related @ SV48 @ SY91 @ ( sK13_D @ SY91 @ SV59 @ SV48 ) ) ) )
| ( relstr_element_smaller @ SV48 @ SV59 @ SY91 ) ) )
= $true )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(490,plain,
! [SV60: $i,SV48: $i] :
( ( ( ! [SY92: $i] :
( ~ ( element @ SY92 @ ( the_carrier @ SV48 ) )
| ~ ( relstr_element_smaller @ SV48 @ SV60 @ SY92 )
| ! [SY93: $i] :
( ~ ( element @ SY93 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SY93 @ SV60 )
| ( related @ SV48 @ SY92 @ SY93 ) ) ) )
= $true )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(491,plain,
! [SV49: $i] :
( ( ( ~ ! [SY80: $i] :
( ! [SY81: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SY80 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ SY81 ) ) )
| ~ ( element @ SY81 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY80 @ SY81 ) )
| ( ex_inf_of_relstr_set @ SV49 @ SY80 ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(492,plain,
! [SV49: $i] :
( ( ( ~ ! [SY82: $i] :
( ~ ( ex_inf_of_relstr_set @ SV49 @ SY82 )
| ~ ( ~ ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ SY83 )
| ( related @ SV49 @ SY83 @ ( sK2_C @ SY82 @ SV49 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY82 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ ( sK2_C @ SY82 @ SV49 ) ) ) ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(493,plain,
! [SV50: $i,SV61: $i] :
( ( ( ~ ( element @ SV61 @ ( the_carrier @ SV50 ) )
| ( relstr_element_smaller @ SV50 @ empty_set @ SV61 ) )
= $true )
| ( ( rel_str @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(494,plain,
! [SV50: $i,SV62: $i] :
( ( ( ~ ( element @ SV62 @ ( the_carrier @ SV50 ) )
| ( relstr_set_smaller @ SV50 @ empty_set @ SV62 ) )
= $true )
| ( ( rel_str @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(495,plain,
! [SV51: $i] :
( ( ( ~ ! [SY86: $i] :
( ! [SY87: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY87 @ SY86 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SY86 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SY87 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) ) ) )
| ~ ( element @ SY87 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY86 @ SY87 ) )
| ( ex_sup_of_relstr_set @ SV51 @ SY86 ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(496,plain,
! [SV51: $i] :
( ( ( ~ ! [SY88: $i] :
( ~ ( ex_sup_of_relstr_set @ SV51 @ SY88 )
| ~ ( ~ ! [SY89: $i] :
( ~ ( element @ SY89 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ SY89 )
| ( related @ SV51 @ ( sK4_C @ SY88 @ SV51 ) @ SY89 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY88 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ ( sK4_C @ SY88 @ SV51 ) ) ) ) ) )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[486]) ).
thf(497,plain,
! [SV57: $i] :
( ( ( ! [SY90: $i] :
( ~ ( element @ SY90 @ ( the_carrier @ SV57 ) )
| ~ ( relstr_element_smaller @ SV57 @ ( the_carrier @ SV57 ) @ SY90 ) ) )
= $true )
| ( ( lower_bounded_relstr @ SV57 )
= $true )
| ( ( rel_str @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(498,plain,
! [SV58: $i] :
( ( ( ~ ( lower_bounded_relstr @ SV58 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK14_B @ SV58 ) @ ( the_carrier @ SV58 ) )
| ~ ( relstr_element_smaller @ SV58 @ ( the_carrier @ SV58 ) @ ( sK14_B @ SV58 ) ) ) )
= $true )
| ( ( rel_str @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(499,plain,
! [SV59: $i,SV48: $i,SV63: $i] :
( ( ( ~ ( element @ SV63 @ ( the_carrier @ SV48 ) )
| ~ ( ~ ( element @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ ( the_carrier @ SV48 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ SV59 )
| ~ ~ ( related @ SV48 @ SV63 @ ( sK13_D @ SV63 @ SV59 @ SV48 ) ) ) )
| ( relstr_element_smaller @ SV48 @ SV59 @ SV63 ) )
= $true )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(500,plain,
! [SV60: $i,SV48: $i,SV64: $i] :
( ( ( ~ ( element @ SV64 @ ( the_carrier @ SV48 ) )
| ~ ( relstr_element_smaller @ SV48 @ SV60 @ SV64 )
| ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SY94 @ SV60 )
| ( related @ SV48 @ SV64 @ SY94 ) ) )
= $true )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(501,plain,
! [SV49: $i] :
( ( ( ! [SY80: $i] :
( ! [SY81: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SY80 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SY81 @ SY80 @ SV49 ) @ SY81 ) ) )
| ~ ( element @ SY81 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY80 @ SY81 ) )
| ( ex_inf_of_relstr_set @ SV49 @ SY80 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(502,plain,
! [SV49: $i] :
( ( ( ! [SY82: $i] :
( ~ ( ex_inf_of_relstr_set @ SV49 @ SY82 )
| ~ ( ~ ! [SY83: $i] :
( ~ ( element @ SY83 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ SY83 )
| ( related @ SV49 @ SY83 @ ( sK2_C @ SY82 @ SV49 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SY82 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SY82 @ ( sK2_C @ SY82 @ SV49 ) ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(503,plain,
! [SV50: $i,SV61: $i] :
( ( ( ~ ( element @ SV61 @ ( the_carrier @ SV50 ) ) )
= $true )
| ( ( relstr_element_smaller @ SV50 @ empty_set @ SV61 )
= $true )
| ( ( rel_str @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(504,plain,
! [SV50: $i,SV62: $i] :
( ( ( ~ ( element @ SV62 @ ( the_carrier @ SV50 ) ) )
= $true )
| ( ( relstr_set_smaller @ SV50 @ empty_set @ SV62 )
= $true )
| ( ( rel_str @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(505,plain,
! [SV51: $i] :
( ( ( ! [SY86: $i] :
( ! [SY87: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY87 @ SY86 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SY86 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SY87 @ ( sK5_D @ SY87 @ SY86 @ SV51 ) ) ) )
| ~ ( element @ SY87 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY86 @ SY87 ) )
| ( ex_sup_of_relstr_set @ SV51 @ SY86 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(506,plain,
! [SV51: $i] :
( ( ( ! [SY88: $i] :
( ~ ( ex_sup_of_relstr_set @ SV51 @ SY88 )
| ~ ( ~ ! [SY89: $i] :
( ~ ( element @ SY89 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ SY89 )
| ( related @ SV51 @ ( sK4_C @ SY88 @ SV51 ) @ SY89 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SY88 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SY88 @ ( sK4_C @ SY88 @ SV51 ) ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(507,plain,
! [SV57: $i,SV65: $i] :
( ( ( ~ ( element @ SV65 @ ( the_carrier @ SV57 ) )
| ~ ( relstr_element_smaller @ SV57 @ ( the_carrier @ SV57 ) @ SV65 ) )
= $true )
| ( ( lower_bounded_relstr @ SV57 )
= $true )
| ( ( rel_str @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(508,plain,
! [SV58: $i] :
( ( ( lower_bounded_relstr @ SV58 )
= $false )
| ( ( ~ ( ~ ( element @ ( sK14_B @ SV58 ) @ ( the_carrier @ SV58 ) )
| ~ ( relstr_element_smaller @ SV58 @ ( the_carrier @ SV58 ) @ ( sK14_B @ SV58 ) ) ) )
= $true )
| ( ( rel_str @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(509,plain,
! [SV59: $i,SV48: $i,SV63: $i] :
( ( ( ~ ( element @ SV63 @ ( the_carrier @ SV48 ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ ( the_carrier @ SV48 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ SV59 )
| ~ ~ ( related @ SV48 @ SV63 @ ( sK13_D @ SV63 @ SV59 @ SV48 ) ) ) )
| ( relstr_element_smaller @ SV48 @ SV59 @ SV63 ) )
= $true )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(510,plain,
! [SV60: $i,SV48: $i,SV64: $i] :
( ( ( ~ ( element @ SV64 @ ( the_carrier @ SV48 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV48 @ SV60 @ SV64 )
| ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SY94 @ SV60 )
| ( related @ SV48 @ SV64 @ SY94 ) ) )
= $true )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(511,plain,
! [SV49: $i,SV66: $i] :
( ( ( ! [SY95: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY95 @ SV66 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SY95 @ SV66 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SY95 @ SV66 @ SV49 ) @ SY95 ) ) )
| ~ ( element @ SY95 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SY95 ) )
| ( ex_inf_of_relstr_set @ SV49 @ SV66 ) )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(512,plain,
! [SV67: $i,SV49: $i] :
( ( ( ~ ( ex_inf_of_relstr_set @ SV49 @ SV67 )
| ~ ( ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ SY96 )
| ( related @ SV49 @ SY96 @ ( sK2_C @ SV67 @ SV49 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SV67 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ ( sK2_C @ SV67 @ SV49 ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(513,plain,
! [SV50: $i,SV61: $i] :
( ( ( element @ SV61 @ ( the_carrier @ SV50 ) )
= $false )
| ( ( relstr_element_smaller @ SV50 @ empty_set @ SV61 )
= $true )
| ( ( rel_str @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(514,plain,
! [SV50: $i,SV62: $i] :
( ( ( element @ SV62 @ ( the_carrier @ SV50 ) )
= $false )
| ( ( relstr_set_smaller @ SV50 @ empty_set @ SV62 )
= $true )
| ( ( rel_str @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(515,plain,
! [SV51: $i,SV68: $i] :
( ( ( ! [SY97: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY97 @ SV68 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SY97 @ SV68 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SY97 @ ( sK5_D @ SY97 @ SV68 @ SV51 ) ) ) )
| ~ ( element @ SY97 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SY97 ) )
| ( ex_sup_of_relstr_set @ SV51 @ SV68 ) )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(516,plain,
! [SV69: $i,SV51: $i] :
( ( ( ~ ( ex_sup_of_relstr_set @ SV51 @ SV69 )
| ~ ( ~ ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ SY98 )
| ( related @ SV51 @ ( sK4_C @ SV69 @ SV51 ) @ SY98 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SV69 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ ( sK4_C @ SV69 @ SV51 ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(517,plain,
! [SV57: $i,SV65: $i] :
( ( ( ~ ( element @ SV65 @ ( the_carrier @ SV57 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV57 @ ( the_carrier @ SV57 ) @ SV65 ) )
= $true )
| ( ( lower_bounded_relstr @ SV57 )
= $true )
| ( ( rel_str @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(518,plain,
! [SV58: $i] :
( ( ( ~ ( element @ ( sK14_B @ SV58 ) @ ( the_carrier @ SV58 ) )
| ~ ( relstr_element_smaller @ SV58 @ ( the_carrier @ SV58 ) @ ( sK14_B @ SV58 ) ) )
= $false )
| ( ( lower_bounded_relstr @ SV58 )
= $false )
| ( ( rel_str @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(519,plain,
! [SV59: $i,SV48: $i,SV63: $i] :
( ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ ( the_carrier @ SV48 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ SV59 )
| ~ ~ ( related @ SV48 @ SV63 @ ( sK13_D @ SV63 @ SV59 @ SV48 ) ) ) )
| ( relstr_element_smaller @ SV48 @ SV59 @ SV63 ) )
= $true )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(520,plain,
! [SV60: $i,SV48: $i,SV64: $i] :
( ( ( element @ SV64 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV48 @ SV60 @ SV64 )
| ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SY94 @ SV60 )
| ( related @ SV48 @ SV64 @ SY94 ) ) )
= $true )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(521,plain,
! [SV49: $i,SV66: $i] :
( ( ( ! [SY95: $i] :
( ~ ( ~ ( element @ ( sK3_D @ SY95 @ SV66 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SY95 @ SV66 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SY95 @ SV66 @ SV49 ) @ SY95 ) ) )
| ~ ( element @ SY95 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SY95 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(522,plain,
! [SV67: $i,SV49: $i] :
( ( ( ~ ( ex_inf_of_relstr_set @ SV49 @ SV67 ) )
= $true )
| ( ( ~ ( ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ SY96 )
| ( related @ SV49 @ SY96 @ ( sK2_C @ SV67 @ SV49 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SV67 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ ( sK2_C @ SV67 @ SV49 ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(523,plain,
! [SV51: $i,SV68: $i] :
( ( ( ! [SY97: $i] :
( ~ ( ~ ( element @ ( sK5_D @ SY97 @ SV68 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SY97 @ SV68 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SY97 @ ( sK5_D @ SY97 @ SV68 @ SV51 ) ) ) )
| ~ ( element @ SY97 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SY97 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(524,plain,
! [SV69: $i,SV51: $i] :
( ( ( ~ ( ex_sup_of_relstr_set @ SV51 @ SV69 ) )
= $true )
| ( ( ~ ( ~ ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ SY98 )
| ( related @ SV51 @ ( sK4_C @ SV69 @ SV51 ) @ SY98 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SV69 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ ( sK4_C @ SV69 @ SV51 ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(525,plain,
! [SV57: $i,SV65: $i] :
( ( ( element @ SV65 @ ( the_carrier @ SV57 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV57 @ ( the_carrier @ SV57 ) @ SV65 ) )
= $true )
| ( ( lower_bounded_relstr @ SV57 )
= $true )
| ( ( rel_str @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(526,plain,
! [SV58: $i] :
( ( ( ~ ( element @ ( sK14_B @ SV58 ) @ ( the_carrier @ SV58 ) ) )
= $false )
| ( ( lower_bounded_relstr @ SV58 )
= $false )
| ( ( rel_str @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(527,plain,
! [SV58: $i] :
( ( ( ~ ( relstr_element_smaller @ SV58 @ ( the_carrier @ SV58 ) @ ( sK14_B @ SV58 ) ) )
= $false )
| ( ( lower_bounded_relstr @ SV58 )
= $false )
| ( ( rel_str @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[518]) ).
thf(528,plain,
! [SV48: $i,SV59: $i,SV63: $i] :
( ( ( ~ ( ~ ( element @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ ( the_carrier @ SV48 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ SV59 )
| ~ ~ ( related @ SV48 @ SV63 @ ( sK13_D @ SV63 @ SV59 @ SV48 ) ) ) ) )
= $true )
| ( ( relstr_element_smaller @ SV48 @ SV59 @ SV63 )
= $true )
| ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(529,plain,
! [SV64: $i,SV60: $i,SV48: $i] :
( ( ( ~ ( relstr_element_smaller @ SV48 @ SV60 @ SV64 ) )
= $true )
| ( ( ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SY94 @ SV60 )
| ( related @ SV48 @ SV64 @ SY94 ) ) )
= $true )
| ( ( element @ SV64 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(530,plain,
! [SV49: $i,SV66: $i,SV70: $i] :
( ( ( ~ ( ~ ( element @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ SV70 ) ) )
| ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(531,plain,
! [SV67: $i,SV49: $i] :
( ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( ~ ( ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ SY96 )
| ( related @ SV49 @ SY96 @ ( sK2_C @ SV67 @ SV49 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SV67 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ ( sK2_C @ SV67 @ SV49 ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(532,plain,
! [SV51: $i,SV68: $i,SV71: $i] :
( ( ( ~ ( ~ ( element @ ( sK5_D @ SV71 @ SV68 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SV71 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) ) ) )
| ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(533,plain,
! [SV69: $i,SV51: $i] :
( ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( ~ ( ~ ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ SY98 )
| ( related @ SV51 @ ( sK4_C @ SV69 @ SV51 ) @ SY98 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SV69 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ ( sK4_C @ SV69 @ SV51 ) ) ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(534,plain,
! [SV65: $i,SV57: $i] :
( ( ( relstr_element_smaller @ SV57 @ ( the_carrier @ SV57 ) @ SV65 )
= $false )
| ( ( element @ SV65 @ ( the_carrier @ SV57 ) )
= $false )
| ( ( lower_bounded_relstr @ SV57 )
= $true )
| ( ( rel_str @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(535,plain,
! [SV58: $i] :
( ( ( element @ ( sK14_B @ SV58 ) @ ( the_carrier @ SV58 ) )
= $true )
| ( ( lower_bounded_relstr @ SV58 )
= $false )
| ( ( rel_str @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(536,plain,
! [SV58: $i] :
( ( ( relstr_element_smaller @ SV58 @ ( the_carrier @ SV58 ) @ ( sK14_B @ SV58 ) )
= $true )
| ( ( lower_bounded_relstr @ SV58 )
= $false )
| ( ( rel_str @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(537,plain,
! [SV48: $i,SV59: $i,SV63: $i] :
( ( ( ~ ( element @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ ( the_carrier @ SV48 ) )
| ~ ~ ( ~ ( in @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ SV59 )
| ~ ~ ( related @ SV48 @ SV63 @ ( sK13_D @ SV63 @ SV59 @ SV48 ) ) ) )
= $false )
| ( ( relstr_element_smaller @ SV48 @ SV59 @ SV63 )
= $true )
| ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(538,plain,
! [SV64: $i,SV60: $i,SV48: $i] :
( ( ( relstr_element_smaller @ SV48 @ SV60 @ SV64 )
= $false )
| ( ( ! [SY94: $i] :
( ~ ( element @ SY94 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SY94 @ SV60 )
| ( related @ SV48 @ SV64 @ SY94 ) ) )
= $true )
| ( ( element @ SV64 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(539,plain,
! [SV49: $i,SV66: $i,SV70: $i] :
( ( ( ~ ( ~ ( element @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ SV70 ) ) ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(540,plain,
! [SV67: $i,SV49: $i] :
( ( ( ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ SY96 )
| ( related @ SV49 @ SY96 @ ( sK2_C @ SV67 @ SV49 ) ) )
| ~ ~ ( ~ ( element @ ( sK2_C @ SV67 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ ( sK2_C @ SV67 @ SV49 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(541,plain,
! [SV51: $i,SV68: $i,SV71: $i] :
( ( ( ~ ( ~ ( element @ ( sK5_D @ SV71 @ SV68 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SV71 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) ) ) ) )
= $true )
| ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(542,plain,
! [SV69: $i,SV51: $i] :
( ( ( ~ ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ SY98 )
| ( related @ SV51 @ ( sK4_C @ SV69 @ SV51 ) @ SY98 ) )
| ~ ~ ( ~ ( element @ ( sK4_C @ SV69 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ ( sK4_C @ SV69 @ SV51 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(543,plain,
! [SV48: $i,SV59: $i,SV63: $i] :
( ( ( ~ ( element @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ ( the_carrier @ SV48 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV48 @ SV59 @ SV63 )
= $true )
| ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(544,plain,
! [SV48: $i,SV59: $i,SV63: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ SV59 )
| ~ ~ ( related @ SV48 @ SV63 @ ( sK13_D @ SV63 @ SV59 @ SV48 ) ) ) )
= $false )
| ( ( relstr_element_smaller @ SV48 @ SV59 @ SV63 )
= $true )
| ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[537]) ).
thf(545,plain,
! [SV64: $i,SV60: $i,SV48: $i,SV72: $i] :
( ( ( ~ ( element @ SV72 @ ( the_carrier @ SV48 ) )
| ~ ( in @ SV72 @ SV60 )
| ( related @ SV48 @ SV64 @ SV72 ) )
= $true )
| ( ( relstr_element_smaller @ SV48 @ SV60 @ SV64 )
= $false )
| ( ( element @ SV64 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(546,plain,
! [SV49: $i,SV66: $i,SV70: $i] :
( ( ( ~ ( element @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ SV70 ) ) )
= $false )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(547,plain,
! [SV67: $i,SV49: $i] :
( ( ( ~ ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ SY96 )
| ( related @ SV49 @ SY96 @ ( sK2_C @ SV67 @ SV49 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[540]) ).
thf(548,plain,
! [SV49: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK2_C @ SV67 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ ( sK2_C @ SV67 @ SV49 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[540]) ).
thf(549,plain,
! [SV51: $i,SV68: $i,SV71: $i] :
( ( ( ~ ( element @ ( sK5_D @ SV71 @ SV68 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SV71 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) ) ) )
= $false )
| ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(550,plain,
! [SV69: $i,SV51: $i] :
( ( ( ~ ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ SY98 )
| ( related @ SV51 @ ( sK4_C @ SV69 @ SV51 ) @ SY98 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(551,plain,
! [SV51: $i,SV69: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK4_C @ SV69 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ ( sK4_C @ SV69 @ SV51 ) ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(552,plain,
! [SV48: $i,SV59: $i,SV63: $i] :
( ( ( element @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ ( the_carrier @ SV48 ) )
= $true )
| ( ( relstr_element_smaller @ SV48 @ SV59 @ SV63 )
= $true )
| ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[543]) ).
thf(553,plain,
! [SV48: $i,SV59: $i,SV63: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ SV59 )
| ~ ~ ( related @ SV48 @ SV63 @ ( sK13_D @ SV63 @ SV59 @ SV48 ) ) ) )
= $true )
| ( ( relstr_element_smaller @ SV48 @ SV59 @ SV63 )
= $true )
| ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[544]) ).
thf(554,plain,
! [SV64: $i,SV60: $i,SV48: $i,SV72: $i] :
( ( ( ~ ( element @ SV72 @ ( the_carrier @ SV48 ) ) )
= $true )
| ( ( ~ ( in @ SV72 @ SV60 )
| ( related @ SV48 @ SV64 @ SV72 ) )
= $true )
| ( ( relstr_element_smaller @ SV48 @ SV60 @ SV64 )
= $false )
| ( ( element @ SV64 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(555,plain,
! [SV49: $i,SV66: $i,SV70: $i] :
( ( ( ~ ( element @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ ( the_carrier @ SV49 ) ) )
= $false )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(556,plain,
! [SV70: $i,SV66: $i,SV49: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ SV70 ) ) )
= $false )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[546]) ).
thf(557,plain,
! [SV67: $i,SV49: $i] :
( ( ( ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ SY96 )
| ( related @ SV49 @ SY96 @ ( sK2_C @ SV67 @ SV49 ) ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(558,plain,
! [SV49: $i,SV67: $i] :
( ( ( ~ ( ~ ( element @ ( sK2_C @ SV67 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ ( sK2_C @ SV67 @ SV49 ) ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(559,plain,
! [SV51: $i,SV68: $i,SV71: $i] :
( ( ( ~ ( element @ ( sK5_D @ SV71 @ SV68 @ SV51 ) @ ( the_carrier @ SV51 ) ) )
= $false )
| ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[549]) ).
thf(560,plain,
! [SV71: $i,SV68: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SV71 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) ) ) )
= $false )
| ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[549]) ).
thf(561,plain,
! [SV69: $i,SV51: $i] :
( ( ( ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ SY98 )
| ( related @ SV51 @ ( sK4_C @ SV69 @ SV51 ) @ SY98 ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(562,plain,
! [SV51: $i,SV69: $i] :
( ( ( ~ ( ~ ( element @ ( sK4_C @ SV69 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ ( sK4_C @ SV69 @ SV51 ) ) ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(563,plain,
! [SV48: $i,SV59: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ SV59 )
| ~ ~ ( related @ SV48 @ SV63 @ ( sK13_D @ SV63 @ SV59 @ SV48 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV48 @ SV59 @ SV63 )
= $true )
| ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(564,plain,
! [SV64: $i,SV60: $i,SV48: $i,SV72: $i] :
( ( ( element @ SV72 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( ~ ( in @ SV72 @ SV60 )
| ( related @ SV48 @ SV64 @ SV72 ) )
= $true )
| ( ( relstr_element_smaller @ SV48 @ SV60 @ SV64 )
= $false )
| ( ( element @ SV64 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(565,plain,
! [SV49: $i,SV66: $i,SV70: $i] :
( ( ( element @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ ( the_carrier @ SV49 ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(566,plain,
! [SV70: $i,SV66: $i,SV49: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ SV70 ) ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(567,plain,
! [SV67: $i,SV49: $i,SV73: $i] :
( ( ( ~ ( element @ SV73 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ SV73 )
| ( related @ SV49 @ SV73 @ ( sK2_C @ SV67 @ SV49 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(568,plain,
! [SV49: $i,SV67: $i] :
( ( ( ~ ( element @ ( sK2_C @ SV67 @ SV49 ) @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV67 @ ( sK2_C @ SV67 @ SV49 ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(569,plain,
! [SV51: $i,SV68: $i,SV71: $i] :
( ( ( element @ ( sK5_D @ SV71 @ SV68 @ SV51 ) @ ( the_carrier @ SV51 ) )
= $true )
| ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(570,plain,
! [SV71: $i,SV68: $i,SV51: $i] :
( ( ( ~ ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SV71 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) ) ) )
= $true )
| ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(571,plain,
! [SV69: $i,SV51: $i,SV74: $i] :
( ( ( ~ ( element @ SV74 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ SV74 )
| ( related @ SV51 @ ( sK4_C @ SV69 @ SV51 ) @ SV74 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(572,plain,
! [SV51: $i,SV69: $i] :
( ( ( ~ ( element @ ( sK4_C @ SV69 @ SV51 ) @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV69 @ ( sK4_C @ SV69 @ SV51 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(573,plain,
! [SV48: $i,SV59: $i,SV63: $i] :
( ( ( ~ ( in @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ SV59 ) )
= $false )
| ( ( relstr_element_smaller @ SV48 @ SV59 @ SV63 )
= $true )
| ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(574,plain,
! [SV59: $i,SV63: $i,SV48: $i] :
( ( ( ~ ~ ( related @ SV48 @ SV63 @ ( sK13_D @ SV63 @ SV59 @ SV48 ) ) )
= $false )
| ( ( relstr_element_smaller @ SV48 @ SV59 @ SV63 )
= $true )
| ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[563]) ).
thf(575,plain,
! [SV64: $i,SV48: $i,SV60: $i,SV72: $i] :
( ( ( ~ ( in @ SV72 @ SV60 ) )
= $true )
| ( ( related @ SV48 @ SV64 @ SV72 )
= $true )
| ( ( element @ SV72 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( relstr_element_smaller @ SV48 @ SV60 @ SV64 )
= $false )
| ( ( element @ SV64 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(576,plain,
! [SV66: $i,SV49: $i,SV70: $i] :
( ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( element @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ ( the_carrier @ SV49 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(577,plain,
! [SV70: $i,SV66: $i,SV49: $i] :
( ( ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) )
| ~ ~ ( related @ SV49 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ SV70 ) )
= $false )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(578,plain,
! [SV67: $i,SV49: $i,SV73: $i] :
( ( ( ~ ( element @ SV73 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV49 @ SV67 @ SV73 )
| ( related @ SV49 @ SV73 @ ( sK2_C @ SV67 @ SV49 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(579,plain,
! [SV49: $i,SV67: $i] :
( ( ( ~ ( element @ ( sK2_C @ SV67 @ SV49 ) @ ( the_carrier @ SV49 ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(580,plain,
! [SV67: $i,SV49: $i] :
( ( ( ~ ( relstr_element_smaller @ SV49 @ SV67 @ ( sK2_C @ SV67 @ SV49 ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[568]) ).
thf(581,plain,
! [SV68: $i,SV51: $i,SV71: $i] :
( ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( element @ ( sK5_D @ SV71 @ SV68 @ SV51 ) @ ( the_carrier @ SV51 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(582,plain,
! [SV71: $i,SV68: $i,SV51: $i] :
( ( ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
| ~ ~ ( related @ SV51 @ SV71 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) ) )
= $false )
| ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(583,plain,
! [SV69: $i,SV51: $i,SV74: $i] :
( ( ( ~ ( element @ SV74 @ ( the_carrier @ SV51 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV51 @ SV69 @ SV74 )
| ( related @ SV51 @ ( sK4_C @ SV69 @ SV51 ) @ SV74 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(584,plain,
! [SV51: $i,SV69: $i] :
( ( ( ~ ( element @ ( sK4_C @ SV69 @ SV51 ) @ ( the_carrier @ SV51 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(585,plain,
! [SV69: $i,SV51: $i] :
( ( ( ~ ( relstr_set_smaller @ SV51 @ SV69 @ ( sK4_C @ SV69 @ SV51 ) ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[572]) ).
thf(586,plain,
! [SV48: $i,SV59: $i,SV63: $i] :
( ( ( in @ ( sK13_D @ SV63 @ SV59 @ SV48 ) @ SV59 )
= $true )
| ( ( relstr_element_smaller @ SV48 @ SV59 @ SV63 )
= $true )
| ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(587,plain,
! [SV59: $i,SV63: $i,SV48: $i] :
( ( ( ~ ( related @ SV48 @ SV63 @ ( sK13_D @ SV63 @ SV59 @ SV48 ) ) )
= $true )
| ( ( relstr_element_smaller @ SV48 @ SV59 @ SV63 )
= $true )
| ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(588,plain,
! [SV64: $i,SV48: $i,SV60: $i,SV72: $i] :
( ( ( in @ SV72 @ SV60 )
= $false )
| ( ( related @ SV48 @ SV64 @ SV72 )
= $true )
| ( ( element @ SV72 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( relstr_element_smaller @ SV48 @ SV60 @ SV64 )
= $false )
| ( ( element @ SV64 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[575]) ).
thf(589,plain,
! [SV66: $i,SV49: $i,SV70: $i] :
( ( ( element @ SV70 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( element @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ ( the_carrier @ SV49 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[576]) ).
thf(590,plain,
! [SV70: $i,SV66: $i,SV49: $i] :
( ( ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) ) )
= $false )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(591,plain,
! [SV66: $i,SV70: $i,SV49: $i] :
( ( ( ~ ~ ( related @ SV49 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ SV70 ) )
= $false )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(592,plain,
! [SV67: $i,SV49: $i,SV73: $i] :
( ( ( element @ SV73 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV49 @ SV67 @ SV73 )
| ( related @ SV49 @ SV73 @ ( sK2_C @ SV67 @ SV49 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(593,plain,
! [SV49: $i,SV67: $i] :
( ( ( element @ ( sK2_C @ SV67 @ SV49 ) @ ( the_carrier @ SV49 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[579]) ).
thf(594,plain,
! [SV67: $i,SV49: $i] :
( ( ( relstr_element_smaller @ SV49 @ SV67 @ ( sK2_C @ SV67 @ SV49 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[580]) ).
thf(595,plain,
! [SV68: $i,SV51: $i,SV71: $i] :
( ( ( element @ SV71 @ ( the_carrier @ SV51 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( element @ ( sK5_D @ SV71 @ SV68 @ SV51 ) @ ( the_carrier @ SV51 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(596,plain,
! [SV71: $i,SV68: $i,SV51: $i] :
( ( ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) ) )
= $false )
| ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[582]) ).
thf(597,plain,
! [SV68: $i,SV71: $i,SV51: $i] :
( ( ( ~ ~ ( related @ SV51 @ SV71 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) ) )
= $false )
| ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[582]) ).
thf(598,plain,
! [SV69: $i,SV51: $i,SV74: $i] :
( ( ( element @ SV74 @ ( the_carrier @ SV51 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV51 @ SV69 @ SV74 )
| ( related @ SV51 @ ( sK4_C @ SV69 @ SV51 ) @ SV74 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(599,plain,
! [SV51: $i,SV69: $i] :
( ( ( element @ ( sK4_C @ SV69 @ SV51 ) @ ( the_carrier @ SV51 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(600,plain,
! [SV69: $i,SV51: $i] :
( ( ( relstr_set_smaller @ SV51 @ SV69 @ ( sK4_C @ SV69 @ SV51 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(601,plain,
! [SV59: $i,SV63: $i,SV48: $i] :
( ( ( related @ SV48 @ SV63 @ ( sK13_D @ SV63 @ SV59 @ SV48 ) )
= $false )
| ( ( relstr_element_smaller @ SV48 @ SV59 @ SV63 )
= $true )
| ( ( element @ SV63 @ ( the_carrier @ SV48 ) )
= $false )
| ( ( rel_str @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(602,plain,
! [SV70: $i,SV66: $i,SV49: $i] :
( ( ( relstr_element_smaller @ SV49 @ SV66 @ SV70 )
= $false )
| ( ( element @ SV70 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( element @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ ( the_carrier @ SV49 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(603,plain,
! [SV70: $i,SV66: $i,SV49: $i] :
( ( ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(604,plain,
! [SV66: $i,SV70: $i,SV49: $i] :
( ( ( ~ ( related @ SV49 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ SV70 ) )
= $true )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(605,plain,
! [SV73: $i,SV67: $i,SV49: $i] :
( ( ( ~ ( relstr_element_smaller @ SV49 @ SV67 @ SV73 ) )
= $true )
| ( ( related @ SV49 @ SV73 @ ( sK2_C @ SV67 @ SV49 ) )
= $true )
| ( ( element @ SV73 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(606,plain,
! [SV71: $i,SV68: $i,SV51: $i] :
( ( ( relstr_set_smaller @ SV51 @ SV68 @ SV71 )
= $false )
| ( ( element @ SV71 @ ( the_carrier @ SV51 ) )
= $false )
| ( ( element @ ( sK5_D @ SV71 @ SV68 @ SV51 ) @ ( the_carrier @ SV51 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(607,plain,
! [SV71: $i,SV68: $i,SV51: $i] :
( ( ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
= $true )
| ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(608,plain,
! [SV68: $i,SV71: $i,SV51: $i] :
( ( ( ~ ( related @ SV51 @ SV71 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) ) )
= $true )
| ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(609,plain,
! [SV74: $i,SV69: $i,SV51: $i] :
( ( ( ~ ( relstr_set_smaller @ SV51 @ SV69 @ SV74 ) )
= $true )
| ( ( related @ SV51 @ ( sK4_C @ SV69 @ SV51 ) @ SV74 )
= $true )
| ( ( element @ SV74 @ ( the_carrier @ SV51 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(610,plain,
! [SV66: $i,SV49: $i,SV70: $i] :
( ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(611,plain,
! [SV66: $i,SV70: $i,SV49: $i] :
( ( ( related @ SV49 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ SV70 )
= $false )
| ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) )
| ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(612,plain,
! [SV73: $i,SV67: $i,SV49: $i] :
( ( ( relstr_element_smaller @ SV49 @ SV67 @ SV73 )
= $false )
| ( ( related @ SV49 @ SV73 @ ( sK2_C @ SV67 @ SV49 ) )
= $true )
| ( ( element @ SV73 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV67 )
= $false )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(613,plain,
! [SV68: $i,SV51: $i,SV71: $i] :
( ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(614,plain,
! [SV68: $i,SV71: $i,SV51: $i] :
( ( ( related @ SV51 @ SV71 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
= $false )
| ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) )
| ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(615,plain,
! [SV74: $i,SV69: $i,SV51: $i] :
( ( ( relstr_set_smaller @ SV51 @ SV69 @ SV74 )
= $false )
| ( ( related @ SV51 @ ( sK4_C @ SV69 @ SV51 ) @ SV74 )
= $true )
| ( ( element @ SV74 @ ( the_carrier @ SV51 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV69 )
= $false )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(616,plain,
! [SV66: $i,SV49: $i,SV70: $i] :
( ( ( element @ SV70 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(617,plain,
! [SV66: $i,SV49: $i,SV70: $i] :
( ( ( ~ ( element @ SV70 @ ( the_carrier @ SV49 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( related @ SV49 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ SV70 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(618,plain,
! [SV68: $i,SV51: $i,SV71: $i] :
( ( ( element @ SV71 @ ( the_carrier @ SV51 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(619,plain,
! [SV68: $i,SV51: $i,SV71: $i] :
( ( ( ~ ( element @ SV71 @ ( the_carrier @ SV51 ) ) )
= $true )
| ( ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( related @ SV51 @ SV71 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(620,plain,
! [SV70: $i,SV66: $i,SV49: $i] :
( ( ( relstr_element_smaller @ SV49 @ SV66 @ SV70 )
= $false )
| ( ( element @ SV70 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( relstr_element_smaller @ SV49 @ SV66 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(621,plain,
! [SV66: $i,SV49: $i,SV70: $i] :
( ( ( element @ SV70 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV49 @ SV66 @ SV70 ) )
= $true )
| ( ( related @ SV49 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ SV70 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(622,plain,
! [SV71: $i,SV68: $i,SV51: $i] :
( ( ( relstr_set_smaller @ SV51 @ SV68 @ SV71 )
= $false )
| ( ( element @ SV71 @ ( the_carrier @ SV51 ) )
= $false )
| ( ( relstr_set_smaller @ SV51 @ SV68 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
= $true )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(623,plain,
! [SV68: $i,SV51: $i,SV71: $i] :
( ( ( element @ SV71 @ ( the_carrier @ SV51 ) )
= $false )
| ( ( ~ ( relstr_set_smaller @ SV51 @ SV68 @ SV71 ) )
= $true )
| ( ( related @ SV51 @ SV71 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(624,plain,
! [SV70: $i,SV66: $i,SV49: $i] :
( ( ( relstr_element_smaller @ SV49 @ SV66 @ SV70 )
= $false )
| ( ( element @ SV70 @ ( the_carrier @ SV49 ) )
= $false )
| ( ( related @ SV49 @ ( sK3_D @ SV70 @ SV66 @ SV49 ) @ SV70 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV49 @ SV66 )
= $true )
| ( ( antisymmetric_relstr @ SV49 )
= $false )
| ( ( rel_str @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(625,plain,
! [SV71: $i,SV68: $i,SV51: $i] :
( ( ( relstr_set_smaller @ SV51 @ SV68 @ SV71 )
= $false )
| ( ( element @ SV71 @ ( the_carrier @ SV51 ) )
= $false )
| ( ( related @ SV51 @ SV71 @ ( sK5_D @ SV71 @ SV68 @ SV51 ) )
= $false )
| ( ( ex_sup_of_relstr_set @ SV51 @ SV68 )
= $true )
| ( ( antisymmetric_relstr @ SV51 )
= $false )
| ( ( rel_str @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(626,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[361,625,624,622,620,615,612,606,602,601,600,599,594,593,588,586,552,536,535,534,514,513,480,470,469,468,467,464,462,455,450,446,440,436,435,407,406,400,398,385,384,383,372,370,367,366,365,364,363]) ).
thf(627,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[626,356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU360+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % 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 : Mon Jun 20 13:34:18 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 26
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.19/0.36 .
% 0.19/0.37 (rf:0,axioms:26,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:28,loop_count:0,foatp_calls:0,translation:fof_full)................................
% 0.51/0.78
% 0.51/0.78 ********************************
% 0.51/0.78 * All subproblems solved! *
% 0.51/0.78 ********************************
% 0.51/0.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:30,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:626,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.81/0.98
% 0.81/0.98 %**** Beginning of derivation protocol ****
% 0.81/0.98 % SZS output start CNFRefutation
% See solution above
% 0.81/0.98
% 0.81/0.98 %**** End of derivation protocol ****
% 0.81/0.98 %**** no. of clauses in derivation: 627 ****
% 0.81/0.98 %**** clause counter: 626 ****
% 0.81/0.98
% 0.81/0.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:30,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:626,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------