TSTP Solution File: SEU357+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU357+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:11:03 EDT 2022
% Result : Theorem 0.38s 0.62s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 30
% Syntax : Number of formulae : 492 ( 95 unt; 20 typ; 0 def)
% Number of atoms : 6970 (2056 equ; 0 cnn)
% Maximal formula atoms : 13 ( 14 avg)
% Number of connectives : 16400 (2625 ~;2620 |; 79 &;11019 @)
% ( 7 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 1314 ( 0 ^1297 !; 17 ?;1314 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric_relstr,type,
antisymmetric_relstr: $i > $o ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_ex_inf_of_relstr_set,type,
ex_inf_of_relstr_set: $i > $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_sK10_E,type,
sK10_E: $i > $i > $i > $i ).
thf(tp_sK11_D,type,
sK11_D: $i > $i > $i > $i ).
thf(tp_sK12_D,type,
sK12_D: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY18,type,
sK2_SY18: $i ).
thf(tp_sK3_SY22,type,
sK3_SY22: $i > $i ).
thf(tp_sK4_SY18,type,
sK4_SY18: $i ).
thf(tp_sK5_SY23,type,
sK5_SY23: $i ).
thf(tp_sK6_B,type,
sK6_B: $i > $i ).
thf(tp_sK7_A,type,
sK7_A: $i ).
thf(tp_sK8_A,type,
sK8_A: $i ).
thf(tp_sK9_C,type,
sK9_C: $i > $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(1,axiom,
! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ B ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_orders_2) ).
thf(2,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(3,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(4,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(5,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(6,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(7,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(8,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(9,axiom,
! [A: $i] :
( ( 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 ) ) )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( relstr_element_smaller @ A @ B @ D )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ E )
=> ( related @ A @ E @ D ) ) ) )
=> ( D = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_yellow_0) ).
thf(10,conjecture,
! [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/sandbox/benchmark/theBenchmark.p',t16_yellow_0) ).
thf(11,negated_conjecture,
( ( ! [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 ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,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 ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [A: $i] :
( ( ( antisymmetric_relstr @ A )
& ( rel_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( ( related @ A @ B @ C )
& ( related @ A @ C @ B ) )
=> ( B = C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
$true = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
$true = $true,
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
$true = $true,
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ! [A: $i] :
( ( 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 ) ) )
& ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ( ( ( relstr_element_smaller @ A @ B @ D )
& ! [E: $i] :
( ( element @ E @ ( the_carrier @ A ) )
=> ( ( relstr_element_smaller @ A @ B @ E )
=> ( related @ A @ E @ D ) ) ) )
=> ( D = C ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(22,plain,
( ( ( ( antisymmetric_relstr @ sK1_A )
& ( rel_str @ sK1_A ) )
=> ! [SY18: $i] :
( ( ex_inf_of_relstr_set @ sK1_A @ SY18 )
<=> ? [SY19: $i] :
( ( element @ SY19 @ ( the_carrier @ sK1_A ) )
& ( relstr_element_smaller @ sK1_A @ SY18 @ SY19 )
& ! [SY20: $i] :
( ( element @ SY20 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_element_smaller @ sK1_A @ SY18 @ SY20 )
=> ( related @ sK1_A @ SY20 @ SY19 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(23,plain,
( ( antisymmetric_relstr @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[22]) ).
thf(24,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [SY18: $i] :
( ( ex_inf_of_relstr_set @ sK1_A @ SY18 )
<=> ? [SY19: $i] :
( ( element @ SY19 @ ( the_carrier @ sK1_A ) )
& ( relstr_element_smaller @ sK1_A @ SY18 @ SY19 )
& ! [SY20: $i] :
( ( element @ SY20 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_element_smaller @ sK1_A @ SY18 @ SY20 )
=> ( related @ sK1_A @ SY20 @ SY19 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [SY18: $i] :
( ( ex_inf_of_relstr_set @ sK1_A @ SY18 )
=> ? [SY19: $i] :
( ( element @ SY19 @ ( the_carrier @ sK1_A ) )
& ( relstr_element_smaller @ sK1_A @ SY18 @ SY19 )
& ! [SY20: $i] :
( ( element @ SY20 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_element_smaller @ sK1_A @ SY18 @ SY20 )
=> ( related @ sK1_A @ SY20 @ SY19 ) ) ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[25]) ).
thf(27,plain,
( ( ! [SY18: $i] :
( ? [SY19: $i] :
( ( element @ SY19 @ ( the_carrier @ sK1_A ) )
& ( relstr_element_smaller @ sK1_A @ SY18 @ SY19 )
& ! [SY20: $i] :
( ( element @ SY20 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_element_smaller @ sK1_A @ SY18 @ SY20 )
=> ( related @ sK1_A @ SY20 @ SY19 ) ) ) )
=> ( ex_inf_of_relstr_set @ sK1_A @ SY18 ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[25]) ).
thf(28,plain,
( ( ~ ! [SY18: $i] :
( ( ex_inf_of_relstr_set @ sK1_A @ SY18 )
=> ? [SY19: $i] :
( ( element @ SY19 @ ( the_carrier @ sK1_A ) )
& ( relstr_element_smaller @ sK1_A @ SY18 @ SY19 )
& ! [SY20: $i] :
( ( element @ SY20 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_element_smaller @ sK1_A @ SY18 @ SY20 )
=> ( related @ sK1_A @ SY20 @ SY19 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ! [SY18: $i] :
( ? [SY19: $i] :
( ( element @ SY19 @ ( the_carrier @ sK1_A ) )
& ( relstr_element_smaller @ sK1_A @ SY18 @ SY19 )
& ! [SY20: $i] :
( ( element @ SY20 @ ( the_carrier @ sK1_A ) )
=> ( ( relstr_element_smaller @ sK1_A @ SY18 @ SY20 )
=> ( related @ sK1_A @ SY20 @ SY19 ) ) ) )
=> ( ex_inf_of_relstr_set @ sK1_A @ SY18 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(30,plain,
( ( ( ex_inf_of_relstr_set @ sK1_A @ sK2_SY18 )
& ! [SY21: $i] :
( ( ( element @ ( sK3_SY22 @ SY21 ) @ ( the_carrier @ sK1_A ) )
& ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SY21 ) )
& ~ ( related @ sK1_A @ ( sK3_SY22 @ SY21 ) @ SY21 ) )
| ~ ( element @ SY21 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SY21 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(31,plain,
( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SY25 )
| ( related @ sK1_A @ SY25 @ sK5_SY23 ) )
& ( element @ sK5_SY23 @ ( the_carrier @ sK1_A ) )
& ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ sK5_SY23 )
& ~ ( ex_inf_of_relstr_set @ sK1_A @ sK4_SY18 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(32,plain,
( ( ! [A: $i] :
( ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( related @ A @ B @ C )
| ~ ( related @ A @ C @ B )
| ( B = C ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(33,plain,
( ( ! [A: $i] : ( element @ ( sK6_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(34,plain,
( ( one_sorted_str @ sK7_A )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(35,plain,
( ( rel_str @ sK8_A )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(36,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(37,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i] :
( ! [C: $i] :
( ( ( element @ ( sK12_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ! [SY29: $i] :
( ~ ( element @ SY29 @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ SY29 )
| ( related @ A @ SY29 @ ( sK12_D @ C @ B @ A ) ) )
& ( relstr_element_smaller @ A @ B @ ( sK12_D @ C @ B @ A ) )
& ( ( sK12_D @ C @ B @ A )
!= C ) )
| ( ( element @ ( sK11_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK11_D @ C @ B @ A ) )
& ~ ( related @ A @ ( sK11_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 )
| ( ! [SY26: $i] :
( ~ ( element @ SY26 @ ( the_carrier @ A ) )
| ( ( element @ ( sK10_E @ SY26 @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK10_E @ SY26 @ B @ A ) )
& ~ ( related @ A @ ( sK10_E @ SY26 @ B @ A ) @ SY26 ) )
| ~ ( relstr_element_smaller @ A @ B @ SY26 )
| ( SY26
= ( sK9_C @ B @ A ) ) )
& ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ SY28 )
| ( related @ A @ SY28 @ ( sK9_C @ B @ A ) ) )
& ( element @ ( sK9_C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK9_C @ B @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(38,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i] :
( ! [C: $i] :
( ( ( element @ ( sK12_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ! [SY29: $i] :
( ~ ( element @ SY29 @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ SY29 )
| ( related @ A @ SY29 @ ( sK12_D @ C @ B @ A ) ) )
& ( relstr_element_smaller @ A @ B @ ( sK12_D @ C @ B @ A ) )
& ( ( sK12_D @ C @ B @ A )
!= C ) )
| ( ( element @ ( sK11_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK11_D @ C @ B @ A ) )
& ~ ( related @ A @ ( sK11_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 )
| ( ! [SY26: $i] :
( ~ ( element @ SY26 @ ( the_carrier @ A ) )
| ( ( element @ ( sK10_E @ SY26 @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK10_E @ SY26 @ B @ A ) )
& ~ ( related @ A @ ( sK10_E @ SY26 @ B @ A ) @ SY26 ) )
| ~ ( relstr_element_smaller @ A @ B @ SY26 )
| ( SY26
= ( sK9_C @ B @ A ) ) )
& ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ SY28 )
| ( related @ A @ SY28 @ ( sK9_C @ B @ A ) ) )
& ( element @ ( sK9_C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK9_C @ B @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(39,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(40,plain,
$true = $true,
inference(copy,[status(thm)],[19]) ).
thf(41,plain,
$true = $true,
inference(copy,[status(thm)],[18]) ).
thf(42,plain,
$true = $true,
inference(copy,[status(thm)],[17]) ).
thf(43,plain,
( ( rel_str @ sK8_A )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(44,plain,
( ( one_sorted_str @ sK7_A )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(45,plain,
( ( ! [A: $i] : ( element @ ( sK6_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(46,plain,
( ( ! [A: $i] :
( ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( related @ A @ B @ C )
| ~ ( related @ A @ C @ B )
| ( B = C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(47,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(48,plain,
( ( antisymmetric_relstr @ sK1_A )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(49,plain,
( ( ( ex_inf_of_relstr_set @ sK1_A @ sK2_SY18 )
& ! [SY21: $i] :
( ( ( element @ ( sK3_SY22 @ SY21 ) @ ( the_carrier @ sK1_A ) )
& ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SY21 ) )
& ~ ( related @ sK1_A @ ( sK3_SY22 @ SY21 ) @ SY21 ) )
| ~ ( element @ SY21 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SY21 ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(50,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX3 )
| ( related @ SX0 @ SX3 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( ( sK12_D @ SX2 @ SX1 @ SX0 )
!= SX2 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SX0 @ SX1 @ ( sK11_D @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( related @ SX0 @ ( sK11_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 ) )
| ~ ( ~ ( element @ ( sK10_E @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SX0 @ SX1 @ ( sK10_E @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( related @ SX0 @ ( sK10_E @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX2 )
| ( SX2
= ( sK9_C @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX2 )
| ( related @ SX0 @ SX2 @ ( sK9_C @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ ( sK9_C @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(51,plain,
( ( ~ ( ~ ( ex_inf_of_relstr_set @ sK1_A @ sK2_SY18 )
| ~ ! [SX0: $i] :
( ~ ( ~ ( element @ ( sK3_SY22 @ SX0 ) @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SX0 ) )
| ~ ~ ( related @ sK1_A @ ( sK3_SY22 @ SX0 ) @ SX0 ) ) )
| ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(52,plain,
! [SV1: $i] :
( ( ~ ( rel_str @ SV1 )
| ( one_sorted_str @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(53,plain,
! [SV2: $i] :
( ( element @ ( sK6_B @ SV2 ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV3: $i] :
( ( ~ ( antisymmetric_relstr @ SV3 )
| ~ ( rel_str @ SV3 )
| ! [SY30: $i] :
( ~ ( element @ SY30 @ ( the_carrier @ SV3 ) )
| ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV3 ) )
| ~ ( related @ SV3 @ SY30 @ SY31 )
| ~ ( related @ SV3 @ SY31 @ SY30 )
| ( SY30 = SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(55,plain,
! [SV4: $i] :
( ( ~ ( rel_str @ SV4 )
| ~ ( ~ ! [SY32: $i] :
( ! [SY33: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY33 @ SY32 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY34: $i] :
( ~ ( element @ SY34 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ SY34 )
| ( related @ SV4 @ SY34 @ ( sK12_D @ SY33 @ SY32 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ ( sK12_D @ SY33 @ SY32 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SY33 @ SY32 @ SV4 )
!= SY33 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY33 @ SY32 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SY32 @ ( sK11_D @ SY33 @ SY32 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SY33 @ SY32 @ SV4 ) @ SY33 ) ) )
| ~ ( element @ SY33 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ SY33 ) )
| ( ex_inf_of_relstr_set @ SV4 @ SY32 ) )
| ~ ! [SY35: $i] :
( ~ ( ex_inf_of_relstr_set @ SV4 @ SY35 )
| ~ ( ~ ! [SY36: $i] :
( ~ ( element @ SY36 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY36 @ SY35 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SY35 @ ( sK10_E @ SY36 @ SY35 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SY36 @ SY35 @ SV4 ) @ SY36 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ SY36 )
| ( SY36
= ( sK9_C @ SY35 @ SV4 ) ) )
| ~ ~ ( ~ ! [SY37: $i] :
( ~ ( element @ SY37 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ SY37 )
| ( related @ SV4 @ SY37 @ ( sK9_C @ SY35 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SY35 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ ( sK9_C @ SY35 @ SV4 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(56,plain,
( ( ~ ( ex_inf_of_relstr_set @ sK1_A @ sK2_SY18 )
| ~ ! [SX0: $i] :
( ~ ( ~ ( element @ ( sK3_SY22 @ SX0 ) @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SX0 ) )
| ~ ~ ( related @ sK1_A @ ( sK3_SY22 @ SX0 ) @ SX0 ) ) )
| ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV1: $i] :
( ( ( ~ ( rel_str @ SV1 ) )
= $true )
| ( ( one_sorted_str @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV3: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV3 )
| ~ ( rel_str @ SV3 ) )
= $true )
| ( ( ! [SY30: $i] :
( ~ ( element @ SY30 @ ( the_carrier @ SV3 ) )
| ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV3 ) )
| ~ ( related @ SV3 @ SY30 @ SY31 )
| ~ ( related @ SV3 @ SY31 @ SY30 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV4: $i] :
( ( ( ~ ( rel_str @ SV4 ) )
= $true )
| ( ( ~ ( ~ ! [SY32: $i] :
( ! [SY33: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY33 @ SY32 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY34: $i] :
( ~ ( element @ SY34 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ SY34 )
| ( related @ SV4 @ SY34 @ ( sK12_D @ SY33 @ SY32 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ ( sK12_D @ SY33 @ SY32 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SY33 @ SY32 @ SV4 )
!= SY33 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY33 @ SY32 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SY32 @ ( sK11_D @ SY33 @ SY32 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SY33 @ SY32 @ SV4 ) @ SY33 ) ) )
| ~ ( element @ SY33 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ SY33 ) )
| ( ex_inf_of_relstr_set @ SV4 @ SY32 ) )
| ~ ! [SY35: $i] :
( ~ ( ex_inf_of_relstr_set @ SV4 @ SY35 )
| ~ ( ~ ! [SY36: $i] :
( ~ ( element @ SY36 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY36 @ SY35 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SY35 @ ( sK10_E @ SY36 @ SY35 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SY36 @ SY35 @ SV4 ) @ SY36 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ SY36 )
| ( SY36
= ( sK9_C @ SY35 @ SV4 ) ) )
| ~ ~ ( ~ ! [SY37: $i] :
( ~ ( element @ SY37 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ SY37 )
| ( related @ SV4 @ SY37 @ ( sK9_C @ SY35 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SY35 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ ( sK9_C @ SY35 @ SV4 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(60,plain,
( ( ~ ( ex_inf_of_relstr_set @ sK1_A @ sK2_SY18 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(61,plain,
( ( ~ ! [SX0: $i] :
( ~ ( ~ ( element @ ( sK3_SY22 @ SX0 ) @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SX0 ) )
| ~ ~ ( related @ sK1_A @ ( sK3_SY22 @ SX0 ) @ SX0 ) ) )
| ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(62,plain,
! [SV1: $i] :
( ( ( rel_str @ SV1 )
= $false )
| ( ( one_sorted_str @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV3: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV3 ) )
= $true )
| ( ( ~ ( rel_str @ SV3 ) )
= $true )
| ( ( ! [SY30: $i] :
( ~ ( element @ SY30 @ ( the_carrier @ SV3 ) )
| ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV3 ) )
| ~ ( related @ SV3 @ SY30 @ SY31 )
| ~ ( related @ SV3 @ SY31 @ SY30 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV4: $i] :
( ( ( rel_str @ SV4 )
= $false )
| ( ( ~ ( ~ ! [SY32: $i] :
( ! [SY33: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY33 @ SY32 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY34: $i] :
( ~ ( element @ SY34 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ SY34 )
| ( related @ SV4 @ SY34 @ ( sK12_D @ SY33 @ SY32 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ ( sK12_D @ SY33 @ SY32 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SY33 @ SY32 @ SV4 )
!= SY33 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY33 @ SY32 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SY32 @ ( sK11_D @ SY33 @ SY32 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SY33 @ SY32 @ SV4 ) @ SY33 ) ) )
| ~ ( element @ SY33 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ SY33 ) )
| ( ex_inf_of_relstr_set @ SV4 @ SY32 ) )
| ~ ! [SY35: $i] :
( ~ ( ex_inf_of_relstr_set @ SV4 @ SY35 )
| ~ ( ~ ! [SY36: $i] :
( ~ ( element @ SY36 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY36 @ SY35 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SY35 @ ( sK10_E @ SY36 @ SY35 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SY36 @ SY35 @ SV4 ) @ SY36 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ SY36 )
| ( SY36
= ( sK9_C @ SY35 @ SV4 ) ) )
| ~ ~ ( ~ ! [SY37: $i] :
( ~ ( element @ SY37 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ SY37 )
| ( related @ SV4 @ SY37 @ ( sK9_C @ SY35 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SY35 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ ( sK9_C @ SY35 @ SV4 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(65,plain,
( ( ex_inf_of_relstr_set @ sK1_A @ sK2_SY18 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(66,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ( element @ ( sK3_SY22 @ SX0 ) @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SX0 ) )
| ~ ~ ( related @ sK1_A @ ( sK3_SY22 @ SX0 ) @ SX0 ) ) )
| ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(67,plain,
! [SV3: $i] :
( ( ( antisymmetric_relstr @ SV3 )
= $false )
| ( ( ~ ( rel_str @ SV3 ) )
= $true )
| ( ( ! [SY30: $i] :
( ~ ( element @ SY30 @ ( the_carrier @ SV3 ) )
| ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV3 ) )
| ~ ( related @ SV3 @ SY30 @ SY31 )
| ~ ( related @ SV3 @ SY31 @ SY30 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV4: $i] :
( ( ( ~ ! [SY32: $i] :
( ! [SY33: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY33 @ SY32 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY34: $i] :
( ~ ( element @ SY34 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ SY34 )
| ( related @ SV4 @ SY34 @ ( sK12_D @ SY33 @ SY32 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ ( sK12_D @ SY33 @ SY32 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SY33 @ SY32 @ SV4 )
!= SY33 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY33 @ SY32 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SY32 @ ( sK11_D @ SY33 @ SY32 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SY33 @ SY32 @ SV4 ) @ SY33 ) ) )
| ~ ( element @ SY33 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ SY33 ) )
| ( ex_inf_of_relstr_set @ SV4 @ SY32 ) )
| ~ ! [SY35: $i] :
( ~ ( ex_inf_of_relstr_set @ SV4 @ SY35 )
| ~ ( ~ ! [SY36: $i] :
( ~ ( element @ SY36 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY36 @ SY35 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SY35 @ ( sK10_E @ SY36 @ SY35 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SY36 @ SY35 @ SV4 ) @ SY36 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ SY36 )
| ( SY36
= ( sK9_C @ SY35 @ SV4 ) ) )
| ~ ~ ( ~ ! [SY37: $i] :
( ~ ( element @ SY37 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ SY37 )
| ( related @ SV4 @ SY37 @ ( sK9_C @ SY35 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SY35 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ ( sK9_C @ SY35 @ SV4 ) ) ) ) ) ) )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV5: $i] :
( ( ~ ( ~ ( element @ ( sK3_SY22 @ SV5 ) @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SV5 ) )
| ~ ~ ( related @ sK1_A @ ( sK3_SY22 @ SV5 ) @ SV5 ) ) )
| ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV3: $i] :
( ( ( rel_str @ SV3 )
= $false )
| ( ( antisymmetric_relstr @ SV3 )
= $false )
| ( ( ! [SY30: $i] :
( ~ ( element @ SY30 @ ( the_carrier @ SV3 ) )
| ! [SY31: $i] :
( ~ ( element @ SY31 @ ( the_carrier @ SV3 ) )
| ~ ( related @ SV3 @ SY30 @ SY31 )
| ~ ( related @ SV3 @ SY31 @ SY30 )
| ( SY30 = SY31 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV4: $i] :
( ( ( ~ ! [SY32: $i] :
( ! [SY33: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY33 @ SY32 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY34: $i] :
( ~ ( element @ SY34 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ SY34 )
| ( related @ SV4 @ SY34 @ ( sK12_D @ SY33 @ SY32 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ ( sK12_D @ SY33 @ SY32 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SY33 @ SY32 @ SV4 )
!= SY33 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY33 @ SY32 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SY32 @ ( sK11_D @ SY33 @ SY32 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SY33 @ SY32 @ SV4 ) @ SY33 ) ) )
| ~ ( element @ SY33 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ SY33 ) )
| ( ex_inf_of_relstr_set @ SV4 @ SY32 ) ) )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(72,plain,
! [SV4: $i] :
( ( ( ~ ! [SY35: $i] :
( ~ ( ex_inf_of_relstr_set @ SV4 @ SY35 )
| ~ ( ~ ! [SY36: $i] :
( ~ ( element @ SY36 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY36 @ SY35 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SY35 @ ( sK10_E @ SY36 @ SY35 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SY36 @ SY35 @ SV4 ) @ SY36 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ SY36 )
| ( SY36
= ( sK9_C @ SY35 @ SV4 ) ) )
| ~ ~ ( ~ ! [SY37: $i] :
( ~ ( element @ SY37 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ SY37 )
| ( related @ SV4 @ SY37 @ ( sK9_C @ SY35 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SY35 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ ( sK9_C @ SY35 @ SV4 ) ) ) ) ) ) )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(73,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( element @ ( sK3_SY22 @ SV5 ) @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SV5 ) )
| ~ ~ ( related @ sK1_A @ ( sK3_SY22 @ SV5 ) @ SV5 ) ) ) )
= $true )
| ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(74,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( element @ SV6 @ ( the_carrier @ SV3 ) )
| ! [SY38: $i] :
( ~ ( element @ SY38 @ ( the_carrier @ SV3 ) )
| ~ ( related @ SV3 @ SV6 @ SY38 )
| ~ ( related @ SV3 @ SY38 @ SV6 )
| ( SV6 = SY38 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV3 )
= $false )
| ( ( rel_str @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV4: $i] :
( ( ( ! [SY32: $i] :
( ! [SY33: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY33 @ SY32 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY34: $i] :
( ~ ( element @ SY34 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ SY34 )
| ( related @ SV4 @ SY34 @ ( sK12_D @ SY33 @ SY32 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ ( sK12_D @ SY33 @ SY32 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SY33 @ SY32 @ SV4 )
!= SY33 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY33 @ SY32 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SY32 @ ( sK11_D @ SY33 @ SY32 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SY33 @ SY32 @ SV4 ) @ SY33 ) ) )
| ~ ( element @ SY33 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY32 @ SY33 ) )
| ( ex_inf_of_relstr_set @ SV4 @ SY32 ) ) )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(76,plain,
! [SV4: $i] :
( ( ( ! [SY35: $i] :
( ~ ( ex_inf_of_relstr_set @ SV4 @ SY35 )
| ~ ( ~ ! [SY36: $i] :
( ~ ( element @ SY36 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY36 @ SY35 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SY35 @ ( sK10_E @ SY36 @ SY35 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SY36 @ SY35 @ SV4 ) @ SY36 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ SY36 )
| ( SY36
= ( sK9_C @ SY35 @ SV4 ) ) )
| ~ ~ ( ~ ! [SY37: $i] :
( ~ ( element @ SY37 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ SY37 )
| ( related @ SV4 @ SY37 @ ( sK9_C @ SY35 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SY35 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SY35 @ ( sK9_C @ SY35 @ SV4 ) ) ) ) ) ) )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(77,plain,
! [SV5: $i] :
( ( ( ~ ( element @ ( sK3_SY22 @ SV5 ) @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SV5 ) )
| ~ ~ ( related @ sK1_A @ ( sK3_SY22 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( element @ SV6 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ! [SY38: $i] :
( ~ ( element @ SY38 @ ( the_carrier @ SV3 ) )
| ~ ( related @ SV3 @ SV6 @ SY38 )
| ~ ( related @ SV3 @ SY38 @ SV6 )
| ( SV6 = SY38 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV3 )
= $false )
| ( ( rel_str @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV4: $i,SV7: $i] :
( ( ( ! [SY39: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY39 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY40: $i] :
( ~ ( element @ SY40 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY40 )
| ( related @ SV4 @ SY40 @ ( sK12_D @ SY39 @ SV7 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SY39 @ SV7 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SY39 @ SV7 @ SV4 )
!= SY39 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY39 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SY39 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SY39 @ SV7 @ SV4 ) @ SY39 ) ) )
| ~ ( element @ SY39 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY39 ) )
| ( ex_inf_of_relstr_set @ SV4 @ SV7 ) )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( ex_inf_of_relstr_set @ SV4 @ SV8 )
| ~ ( ~ ! [SY41: $i] :
( ~ ( element @ SY41 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY41 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SY41 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SY41 @ SV8 @ SV4 ) @ SY41 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY41 )
| ( SY41
= ( sK9_C @ SV8 @ SV4 ) ) )
| ~ ~ ( ~ ! [SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY42 )
| ( related @ SV4 @ SY42 @ ( sK9_C @ SV8 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK9_C @ SV8 @ SV4 ) ) ) ) ) )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV5: $i] :
( ( ( ~ ( element @ ( sK3_SY22 @ SV5 ) @ ( the_carrier @ sK1_A ) ) )
= $false )
| ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(82,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SV5 ) )
| ~ ~ ( related @ sK1_A @ ( sK3_SY22 @ SV5 ) @ SV5 ) ) )
= $false )
| ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(83,plain,
! [SV3: $i,SV6: $i] :
( ( ( element @ SV6 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( ! [SY38: $i] :
( ~ ( element @ SY38 @ ( the_carrier @ SV3 ) )
| ~ ( related @ SV3 @ SV6 @ SY38 )
| ~ ( related @ SV3 @ SY38 @ SV6 )
| ( SV6 = SY38 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV3 )
= $false )
| ( ( rel_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV4: $i,SV7: $i] :
( ( ( ! [SY39: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY39 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY40: $i] :
( ~ ( element @ SY40 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY40 )
| ( related @ SV4 @ SY40 @ ( sK12_D @ SY39 @ SV7 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SY39 @ SV7 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SY39 @ SV7 @ SV4 )
!= SY39 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY39 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SY39 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SY39 @ SV7 @ SV4 ) @ SY39 ) ) )
| ~ ( element @ SY39 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY39 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(85,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( ex_inf_of_relstr_set @ SV4 @ SV8 ) )
= $true )
| ( ( ~ ( ~ ! [SY41: $i] :
( ~ ( element @ SY41 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY41 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SY41 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SY41 @ SV8 @ SV4 ) @ SY41 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY41 )
| ( SY41
= ( sK9_C @ SV8 @ SV4 ) ) )
| ~ ~ ( ~ ! [SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY42 )
| ( related @ SV4 @ SY42 @ ( sK9_C @ SV8 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK9_C @ SV8 @ SV4 ) ) ) ) ) )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV5: $i] :
( ( ( element @ ( sK3_SY22 @ SV5 ) @ ( the_carrier @ sK1_A ) )
= $true )
| ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(87,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SV5 ) )
| ~ ~ ( related @ sK1_A @ ( sK3_SY22 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(88,plain,
! [SV6: $i,SV3: $i,SV9: $i] :
( ( ( ~ ( element @ SV9 @ ( the_carrier @ SV3 ) )
| ~ ( related @ SV3 @ SV6 @ SV9 )
| ~ ( related @ SV3 @ SV9 @ SV6 )
| ( SV6 = SV9 ) )
= $true )
| ( ( element @ SV6 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( antisymmetric_relstr @ SV3 )
= $false )
| ( ( rel_str @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(89,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( ~ ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY43: $i] :
( ~ ( element @ SY43 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY43 )
| ( related @ SV4 @ SY43 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
!= SV10 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV8: $i,SV4: $i] :
( ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( ~ ( ~ ! [SY41: $i] :
( ~ ( element @ SY41 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY41 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SY41 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SY41 @ SV8 @ SV4 ) @ SY41 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY41 )
| ( SY41
= ( sK9_C @ SV8 @ SV4 ) ) )
| ~ ~ ( ~ ! [SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY42 )
| ( related @ SV4 @ SY42 @ ( sK9_C @ SV8 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK9_C @ SV8 @ SV4 ) ) ) ) ) )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV5: $i] :
( ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true )
| ( ( element @ ( sK3_SY22 @ SV5 ) @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV5: $i] :
( ( ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SV5 ) )
| ~ ~ ( related @ sK1_A @ ( sK3_SY22 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV6: $i,SV3: $i,SV9: $i] :
( ( ( ~ ( element @ SV9 @ ( the_carrier @ SV3 ) ) )
= $true )
| ( ( ~ ( related @ SV3 @ SV6 @ SV9 )
| ~ ( related @ SV3 @ SV9 @ SV6 )
| ( SV6 = SV9 ) )
= $true )
| ( ( element @ SV6 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( antisymmetric_relstr @ SV3 )
= $false )
| ( ( rel_str @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( ~ ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY43: $i] :
( ~ ( element @ SY43 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY43 )
| ( related @ SV4 @ SY43 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
!= SV10 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ! [SY41: $i] :
( ~ ( element @ SY41 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY41 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SY41 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SY41 @ SV8 @ SV4 ) @ SY41 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY41 )
| ( SY41
= ( sK9_C @ SV8 @ SV4 ) ) )
| ~ ~ ( ~ ! [SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY42 )
| ( related @ SV4 @ SY42 @ ( sK9_C @ SV8 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK9_C @ SV8 @ SV4 ) ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV5: $i] :
( ( ( element @ SV5 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true )
| ( ( element @ ( sK3_SY22 @ SV5 ) @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV5: $i] :
( ( ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SV5 ) ) )
= $false )
| ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(98,plain,
! [SV5: $i] :
( ( ( ~ ~ ( related @ sK1_A @ ( sK3_SY22 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(99,plain,
! [SV6: $i,SV3: $i,SV9: $i] :
( ( ( element @ SV9 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( ~ ( related @ SV3 @ SV6 @ SV9 )
| ~ ( related @ SV3 @ SV9 @ SV6 )
| ( SV6 = SV9 ) )
= $true )
| ( ( element @ SV6 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( antisymmetric_relstr @ SV3 )
= $false )
| ( ( rel_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(100,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY43: $i] :
( ~ ( element @ SY43 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY43 )
| ( related @ SV4 @ SY43 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
!= SV10 ) ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ! [SY41: $i] :
( ~ ( element @ SY41 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY41 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SY41 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SY41 @ SV8 @ SV4 ) @ SY41 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY41 )
| ( SY41
= ( sK9_C @ SV8 @ SV4 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(102,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ! [SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY42 )
| ( related @ SV4 @ SY42 @ ( sK9_C @ SV8 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK9_C @ SV8 @ SV4 ) ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(103,plain,
! [SV5: $i] :
( ( ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 )
= $false )
| ( ( element @ SV5 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( element @ ( sK3_SY22 @ SV5 ) @ ( the_carrier @ sK1_A ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(104,plain,
! [SV5: $i] :
( ( ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(105,plain,
! [SV5: $i] :
( ( ( ~ ( related @ sK1_A @ ( sK3_SY22 @ SV5 ) @ SV5 ) )
= $true )
| ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(106,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( related @ SV3 @ SV6 @ SV9 )
| ~ ( related @ SV3 @ SV9 @ SV6 ) )
= $true )
| ( ( SV6 = SV9 )
= $true )
| ( ( element @ SV9 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV6 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( antisymmetric_relstr @ SV3 )
= $false )
| ( ( rel_str @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(108,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY43: $i] :
( ~ ( element @ SY43 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY43 )
| ( related @ SV4 @ SY43 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
!= SV10 ) ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(109,plain,
! [SV8: $i,SV4: $i] :
( ( ( ! [SY41: $i] :
( ~ ( element @ SY41 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY41 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SY41 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SY41 @ SV8 @ SV4 ) @ SY41 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY41 )
| ( SY41
= ( sK9_C @ SV8 @ SV4 ) ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(110,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( ~ ! [SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY42 )
| ( related @ SV4 @ SY42 @ ( sK9_C @ SV8 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK9_C @ SV8 @ SV4 ) ) ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(111,plain,
! [SV5: $i] :
( ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true )
| ( ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(112,plain,
! [SV5: $i] :
( ( ( related @ sK1_A @ ( sK3_SY22 @ SV5 ) @ SV5 )
= $false )
| ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(113,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( related @ SV3 @ SV6 @ SV9 ) )
= $true )
| ( ( ~ ( related @ SV3 @ SV9 @ SV6 ) )
= $true )
| ( ( SV6 = SV9 )
= $true )
| ( ( element @ SV9 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV6 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( antisymmetric_relstr @ SV3 )
= $false )
| ( ( rel_str @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(114,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(115,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY43: $i] :
( ~ ( element @ SY43 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY43 )
| ( related @ SV4 @ SY43 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
!= SV10 ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(116,plain,
! [SV8: $i,SV4: $i,SV11: $i] :
( ( ( ~ ( element @ SV11 @ ( the_carrier @ SV4 ) )
| ~ ( ~ ( element @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 )
| ( SV11
= ( sK9_C @ SV8 @ SV4 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(117,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ! [SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY42 )
| ( related @ SV4 @ SY42 @ ( sK9_C @ SV8 @ SV4 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK9_C @ SV8 @ SV4 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV5: $i] :
( ( ( element @ SV5 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true )
| ( ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(119,plain,
! [SV5: $i] :
( ( ( ~ ( element @ SV5 @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true )
| ( ( related @ sK1_A @ ( sK3_SY22 @ SV5 ) @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(120,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ( related @ SV3 @ SV6 @ SV9 )
= $false )
| ( ( ~ ( related @ SV3 @ SV9 @ SV6 ) )
= $true )
| ( ( SV6 = SV9 )
= $true )
| ( ( element @ SV9 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV6 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( antisymmetric_relstr @ SV3 )
= $false )
| ( ( rel_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(121,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(122,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ! [SY43: $i] :
( ~ ( element @ SY43 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY43 )
| ( related @ SV4 @ SY43 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
!= SV10 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(123,plain,
! [SV8: $i,SV4: $i,SV11: $i] :
( ( ( ~ ( element @ SV11 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 )
| ( SV11
= ( sK9_C @ SV8 @ SV4 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(124,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ! [SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY42 )
| ( related @ SV4 @ SY42 @ ( sK9_C @ SV8 @ SV4 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(125,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_C @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK9_C @ SV8 @ SV4 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(126,plain,
! [SV5: $i] :
( ( ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 )
= $false )
| ( ( element @ SV5 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ ( sK3_SY22 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(127,plain,
! [SV5: $i] :
( ( ( element @ SV5 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 ) )
= $true )
| ( ( related @ sK1_A @ ( sK3_SY22 @ SV5 ) @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(128,plain,
! [SV6: $i,SV9: $i,SV3: $i] :
( ( ( related @ SV3 @ SV9 @ SV6 )
= $false )
| ( ( related @ SV3 @ SV6 @ SV9 )
= $false )
| ( ( SV6 = SV9 )
= $true )
| ( ( element @ SV9 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( element @ SV6 @ ( the_carrier @ SV3 ) )
= $false )
| ( ( antisymmetric_relstr @ SV3 )
= $false )
| ( ( rel_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(129,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(130,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ! [SY43: $i] :
( ~ ( element @ SY43 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY43 )
| ( related @ SV4 @ SY43 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(131,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
!= SV10 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(132,plain,
! [SV8: $i,SV4: $i,SV11: $i] :
( ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 )
| ( SV11
= ( sK9_C @ SV8 @ SV4 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(133,plain,
! [SV8: $i,SV4: $i] :
( ( ( ! [SY42: $i] :
( ~ ( element @ SY42 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SY42 )
| ( related @ SV4 @ SY42 @ ( sK9_C @ SV8 @ SV4 ) ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(134,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_C @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK9_C @ SV8 @ SV4 ) ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(135,plain,
! [SV5: $i] :
( ( ( relstr_element_smaller @ sK1_A @ sK2_SY18 @ SV5 )
= $false )
| ( ( element @ SV5 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( related @ sK1_A @ ( sK3_SY22 @ SV5 ) @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(136,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(137,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(138,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( ~ ! [SY43: $i] :
( ~ ( element @ SY43 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY43 )
| ( related @ SV4 @ SY43 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(139,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
!= SV10 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(140,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( ~ ( element @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(141,plain,
! [SV8: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV12 )
| ( related @ SV4 @ SV12 @ ( sK9_C @ SV8 @ SV4 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( element @ ( sK9_C @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK9_C @ SV8 @ SV4 ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(143,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(144,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(145,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ! [SY43: $i] :
( ~ ( element @ SY43 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY43 )
| ( related @ SV4 @ SY43 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(146,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(147,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( ~ ( element @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(148,plain,
! [SV8: $i,SV4: $i,SV12: $i] :
( ( ( ~ ( element @ SV12 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV12 )
| ( related @ SV4 @ SV12 @ ( sK9_C @ SV8 @ SV4 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(149,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( element @ ( sK9_C @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(150,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK9_C @ SV8 @ SV4 ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(151,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(152,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(153,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ! [SY43: $i] :
( ~ ( element @ SY43 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY43 )
| ( related @ SV4 @ SY43 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(154,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(155,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(156,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( element @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(157,plain,
! [SV8: $i,SV4: $i,SV12: $i] :
( ( ( element @ SV12 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV12 )
| ( related @ SV4 @ SV12 @ ( sK9_C @ SV8 @ SV4 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(158,plain,
! [SV4: $i,SV8: $i] :
( ( ( element @ ( sK9_C @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(159,plain,
! [SV8: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV8 @ ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(160,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(161,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(162,plain,
! [SV7: $i,SV10: $i,SV4: $i] :
( ( ( ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(163,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ! [SY43: $i] :
( ~ ( element @ SY43 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SY43 )
| ( related @ SV4 @ SY43 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(164,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(165,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( ~ ( element @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(167,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(168,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV12 ) )
= $true )
| ( ( related @ SV4 @ SV12 @ ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV12 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(169,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV10 )
= $false )
| ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(170,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(171,plain,
! [SV7: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(172,plain,
! [SV10: $i,SV7: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
| ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(173,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(174,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(175,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[165]) ).
thf(176,plain,
! [SV4: $i,SV8: $i,SV11: $i] :
( ( ( element @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(177,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(178,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV8 @ SV12 )
= $false )
| ( ( related @ SV4 @ SV12 @ ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV12 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(180,plain,
! [SV7: $i,SV10: $i,SV4: $i] :
( ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(181,plain,
! [SV10: $i,SV7: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( element @ SV13 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
| ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(182,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(183,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(184,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(185,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV8 @ SV11 )
= $false )
| ( ( element @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(186,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(187,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(189,plain,
! [SV10: $i,SV7: $i,SV4: $i,SV13: $i] :
( ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
| ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(190,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(191,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(192,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(193,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(194,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(195,plain,
! [SV8: $i,SV11: $i,SV4: $i] :
( ( ( ~ ~ ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(196,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV10 )
= $false )
| ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(197,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(198,plain,
! [SV10: $i,SV13: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV13 ) )
= $true )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(199,plain,
! [SV4: $i,SV7: $i,SV10: $i] :
( ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(200,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(201,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(202,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(203,plain,
! [SV7: $i,SV10: $i,SV4: $i] :
( ( ( ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(204,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(205,plain,
! [SV8: $i,SV11: $i,SV4: $i] :
( ( ( ~ ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(206,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV10 )
= $false )
| ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( element @ ( sK12_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(207,plain,
! [SV10: $i,SV13: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
| ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(208,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(209,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(210,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV10 )
= $false )
| ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(211,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(212,plain,
! [SV7: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(213,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV8 @ SV11 )
= $false )
| ( ( relstr_element_smaller @ SV4 @ SV8 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(214,plain,
! [SV8: $i,SV11: $i,SV4: $i] :
( ( ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV8 @ SV11 ) )
= $true )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(215,plain,
! [SV13: $i,SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(216,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(217,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(218,plain,
! [SV7: $i,SV10: $i,SV4: $i] :
( ( ( ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(219,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(220,plain,
! [SV7: $i,SV10: $i,SV4: $i] :
( ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(221,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV8 @ SV11 )
= $false )
| ( ( related @ SV4 @ ( sK10_E @ SV11 @ SV8 @ SV4 ) @ SV11 )
= $false )
| ( ( SV11
= ( sK9_C @ SV8 @ SV4 ) )
= $true )
| ( ( element @ SV11 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV8 )
= $false )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(222,plain,
! [SV13: $i,SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(223,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV10 )
= $false )
| ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(224,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(225,plain,
! [SV7: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(226,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(227,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(228,plain,
! [SV13: $i,SV4: $i,SV7: $i,SV10: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(229,plain,
! [SV13: $i,SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(230,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(231,plain,
! [SV7: $i,SV10: $i,SV4: $i] :
( ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(232,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV10 )
= $false )
| ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(233,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(234,plain,
! [SV13: $i,SV4: $i,SV7: $i,SV10: $i] :
( ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(235,plain,
! [SV13: $i,SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(236,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(237,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(238,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV10 )
= $false )
| ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( ( sK12_D @ SV10 @ SV7 @ SV4 )
= SV10 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(239,plain,
! [SV13: $i,SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(240,plain,
! [SV13: $i,SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
| ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(241,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV10 )
= $false )
| ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(242,plain,
! [SV7: $i,SV4: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(243,plain,
! [SV13: $i,SV7: $i,SV4: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(244,plain,
! [SV13: $i,SV10: $i,SV7: $i,SV4: $i] :
( ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(245,plain,
! [SV13: $i,SV7: $i,SV10: $i,SV4: $i] :
( ( ( ~ ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(246,plain,
! [SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV10 )
= $false )
| ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(247,plain,
! [SV13: $i,SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV10 )
= $false )
| ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( element @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ ( the_carrier @ SV4 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(248,plain,
! [SV13: $i,SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(249,plain,
! [SV13: $i,SV7: $i,SV10: $i,SV4: $i] :
( ( ( ~ ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 ) )
= $true )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(250,plain,
! [SV13: $i,SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(251,plain,
! [SV13: $i,SV7: $i,SV10: $i,SV4: $i] :
( ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) )
| ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(252,plain,
! [SV13: $i,SV7: $i,SV4: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(253,plain,
! [SV13: $i,SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( element @ SV10 @ ( the_carrier @ SV4 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(254,plain,
! [SV13: $i,SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV10 )
= $false )
| ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(255,plain,
! [SV13: $i,SV7: $i,SV4: $i,SV10: $i] :
( ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV4 @ SV7 @ SV10 ) )
= $true )
| ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(256,plain,
! [SV13: $i,SV10: $i,SV7: $i,SV4: $i] :
( ( ( relstr_element_smaller @ SV4 @ SV7 @ SV10 )
= $false )
| ( ( element @ SV10 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ ( sK11_D @ SV10 @ SV7 @ SV4 ) @ SV10 )
= $false )
| ( ( element @ SV13 @ ( the_carrier @ SV4 ) )
= $false )
| ( ( related @ SV4 @ SV13 @ ( sK12_D @ SV10 @ SV7 @ SV4 ) )
= $true )
| ( ( relstr_element_smaller @ SV4 @ SV7 @ SV13 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV4 @ SV7 )
= $true )
| ( ( rel_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(257,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,256,254,247,246,241,238,232,223,221,213,210,206,196,185,178,169,159,158,135,128,126,103,65,62,53,48,47,44,43,42,41]) ).
thf(258,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i] :
( ! [C: $i] :
( ( ( element @ ( sK12_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ! [SY29: $i] :
( ~ ( element @ SY29 @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ SY29 )
| ( related @ A @ SY29 @ ( sK12_D @ C @ B @ A ) ) )
& ( relstr_element_smaller @ A @ B @ ( sK12_D @ C @ B @ A ) )
& ( ( sK12_D @ C @ B @ A )
!= C ) )
| ( ( element @ ( sK11_D @ C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK11_D @ C @ B @ A ) )
& ~ ( related @ A @ ( sK11_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 )
| ( ! [SY26: $i] :
( ~ ( element @ SY26 @ ( the_carrier @ A ) )
| ( ( element @ ( sK10_E @ SY26 @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK10_E @ SY26 @ B @ A ) )
& ~ ( related @ A @ ( sK10_E @ SY26 @ B @ A ) @ SY26 ) )
| ~ ( relstr_element_smaller @ A @ B @ SY26 )
| ( SY26
= ( sK9_C @ B @ A ) ) )
& ! [SY28: $i] :
( ~ ( element @ SY28 @ ( the_carrier @ A ) )
| ~ ( relstr_element_smaller @ A @ B @ SY28 )
| ( related @ A @ SY28 @ ( sK9_C @ B @ A ) ) )
& ( element @ ( sK9_C @ B @ A ) @ ( the_carrier @ A ) )
& ( relstr_element_smaller @ A @ B @ ( sK9_C @ B @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(259,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(260,plain,
$true = $true,
inference(copy,[status(thm)],[19]) ).
thf(261,plain,
$true = $true,
inference(copy,[status(thm)],[18]) ).
thf(262,plain,
$true = $true,
inference(copy,[status(thm)],[17]) ).
thf(263,plain,
( ( rel_str @ sK8_A )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(264,plain,
( ( one_sorted_str @ sK7_A )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(265,plain,
( ( ! [A: $i] : ( element @ ( sK6_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(266,plain,
( ( ! [A: $i] :
( ~ ( antisymmetric_relstr @ A )
| ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( related @ A @ B @ C )
| ~ ( related @ A @ C @ B )
| ( B = C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(267,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(268,plain,
( ( antisymmetric_relstr @ sK1_A )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(269,plain,
( ( ! [SY25: $i] :
( ~ ( element @ SY25 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SY25 )
| ( related @ sK1_A @ SY25 @ sK5_SY23 ) )
& ( element @ sK5_SY23 @ ( the_carrier @ sK1_A ) )
& ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ sK5_SY23 )
& ~ ( ex_inf_of_relstr_set @ sK1_A @ sK4_SY18 ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(270,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SX0 )
| ( related @ sK1_A @ SX0 @ sK5_SY23 ) )
| ~ ~ ( ~ ( element @ sK5_SY23 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ sK5_SY23 ) ) )
| ~ ~ ( ex_inf_of_relstr_set @ sK1_A @ sK4_SY18 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(271,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ! [SX2: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX3 )
| ( related @ SX0 @ SX3 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ ( sK12_D @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( ( sK12_D @ SX2 @ SX1 @ SX0 )
!= SX2 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SX0 @ SX1 @ ( sK11_D @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( related @ SX0 @ ( sK11_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 ) )
| ~ ( ~ ( element @ ( sK10_E @ SX2 @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SX0 @ SX1 @ ( sK10_E @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( related @ SX0 @ ( sK10_E @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX2 )
| ( SX2
= ( sK9_C @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ SX2 )
| ( related @ SX0 @ SX2 @ ( sK9_C @ SX1 @ SX0 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SX1 @ SX0 ) @ ( the_carrier @ SX0 ) )
| ~ ( relstr_element_smaller @ SX0 @ SX1 @ ( sK9_C @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(272,plain,
! [SV14: $i] :
( ( ~ ( rel_str @ SV14 )
| ( one_sorted_str @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(273,plain,
! [SV15: $i] :
( ( element @ ( sK6_B @ SV15 ) @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(274,plain,
! [SV16: $i] :
( ( ~ ( antisymmetric_relstr @ SV16 )
| ~ ( rel_str @ SV16 )
| ! [SY44: $i] :
( ~ ( element @ SY44 @ ( the_carrier @ SV16 ) )
| ! [SY45: $i] :
( ~ ( element @ SY45 @ ( the_carrier @ SV16 ) )
| ~ ( related @ SV16 @ SY44 @ SY45 )
| ~ ( related @ SV16 @ SY45 @ SY44 )
| ( SY44 = SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(275,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SX0 )
| ( related @ sK1_A @ SX0 @ sK5_SY23 ) )
| ~ ~ ( ~ ( element @ sK5_SY23 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ sK5_SY23 ) ) )
| ~ ~ ( ex_inf_of_relstr_set @ sK1_A @ sK4_SY18 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(276,plain,
! [SV17: $i] :
( ( ~ ( rel_str @ SV17 )
| ~ ( ~ ! [SY46: $i] :
( ! [SY47: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY47 @ SY46 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY48: $i] :
( ~ ( element @ SY48 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ SY48 )
| ( related @ SV17 @ SY48 @ ( sK12_D @ SY47 @ SY46 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ ( sK12_D @ SY47 @ SY46 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SY47 @ SY46 @ SV17 )
!= SY47 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY47 @ SY46 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SY46 @ ( sK11_D @ SY47 @ SY46 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SY47 @ SY46 @ SV17 ) @ SY47 ) ) )
| ~ ( element @ SY47 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ SY47 ) )
| ( ex_inf_of_relstr_set @ SV17 @ SY46 ) )
| ~ ! [SY49: $i] :
( ~ ( ex_inf_of_relstr_set @ SV17 @ SY49 )
| ~ ( ~ ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY50 @ SY49 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SY49 @ ( sK10_E @ SY50 @ SY49 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SY50 @ SY49 @ SV17 ) @ SY50 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ SY50 )
| ( SY50
= ( sK9_C @ SY49 @ SV17 ) ) )
| ~ ~ ( ~ ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ SY51 )
| ( related @ SV17 @ SY51 @ ( sK9_C @ SY49 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SY49 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ ( sK9_C @ SY49 @ SV17 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(277,plain,
! [SV14: $i] :
( ( ( ~ ( rel_str @ SV14 ) )
= $true )
| ( ( one_sorted_str @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(278,plain,
! [SV16: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV16 )
| ~ ( rel_str @ SV16 ) )
= $true )
| ( ( ! [SY44: $i] :
( ~ ( element @ SY44 @ ( the_carrier @ SV16 ) )
| ! [SY45: $i] :
( ~ ( element @ SY45 @ ( the_carrier @ SV16 ) )
| ~ ( related @ SV16 @ SY44 @ SY45 )
| ~ ( related @ SV16 @ SY45 @ SY44 )
| ( SY44 = SY45 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(279,plain,
( ( ~ ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SX0 )
| ( related @ sK1_A @ SX0 @ sK5_SY23 ) )
| ~ ~ ( ~ ( element @ sK5_SY23 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ sK5_SY23 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(280,plain,
( ( ~ ~ ( ex_inf_of_relstr_set @ sK1_A @ sK4_SY18 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[275]) ).
thf(281,plain,
! [SV17: $i] :
( ( ( ~ ( rel_str @ SV17 ) )
= $true )
| ( ( ~ ( ~ ! [SY46: $i] :
( ! [SY47: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY47 @ SY46 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY48: $i] :
( ~ ( element @ SY48 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ SY48 )
| ( related @ SV17 @ SY48 @ ( sK12_D @ SY47 @ SY46 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ ( sK12_D @ SY47 @ SY46 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SY47 @ SY46 @ SV17 )
!= SY47 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY47 @ SY46 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SY46 @ ( sK11_D @ SY47 @ SY46 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SY47 @ SY46 @ SV17 ) @ SY47 ) ) )
| ~ ( element @ SY47 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ SY47 ) )
| ( ex_inf_of_relstr_set @ SV17 @ SY46 ) )
| ~ ! [SY49: $i] :
( ~ ( ex_inf_of_relstr_set @ SV17 @ SY49 )
| ~ ( ~ ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY50 @ SY49 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SY49 @ ( sK10_E @ SY50 @ SY49 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SY50 @ SY49 @ SV17 ) @ SY50 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ SY50 )
| ( SY50
= ( sK9_C @ SY49 @ SV17 ) ) )
| ~ ~ ( ~ ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ SY51 )
| ( related @ SV17 @ SY51 @ ( sK9_C @ SY49 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SY49 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ ( sK9_C @ SY49 @ SV17 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(282,plain,
! [SV14: $i] :
( ( ( rel_str @ SV14 )
= $false )
| ( ( one_sorted_str @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(283,plain,
! [SV16: $i] :
( ( ( ~ ( antisymmetric_relstr @ SV16 ) )
= $true )
| ( ( ~ ( rel_str @ SV16 ) )
= $true )
| ( ( ! [SY44: $i] :
( ~ ( element @ SY44 @ ( the_carrier @ SV16 ) )
| ! [SY45: $i] :
( ~ ( element @ SY45 @ ( the_carrier @ SV16 ) )
| ~ ( related @ SV16 @ SY44 @ SY45 )
| ~ ( related @ SV16 @ SY45 @ SY44 )
| ( SY44 = SY45 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(284,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SX0 )
| ( related @ sK1_A @ SX0 @ sK5_SY23 ) )
| ~ ~ ( ~ ( element @ sK5_SY23 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ sK5_SY23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(285,plain,
( ( ~ ( ex_inf_of_relstr_set @ sK1_A @ sK4_SY18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(286,plain,
! [SV17: $i] :
( ( ( rel_str @ SV17 )
= $false )
| ( ( ~ ( ~ ! [SY46: $i] :
( ! [SY47: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY47 @ SY46 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY48: $i] :
( ~ ( element @ SY48 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ SY48 )
| ( related @ SV17 @ SY48 @ ( sK12_D @ SY47 @ SY46 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ ( sK12_D @ SY47 @ SY46 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SY47 @ SY46 @ SV17 )
!= SY47 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY47 @ SY46 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SY46 @ ( sK11_D @ SY47 @ SY46 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SY47 @ SY46 @ SV17 ) @ SY47 ) ) )
| ~ ( element @ SY47 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ SY47 ) )
| ( ex_inf_of_relstr_set @ SV17 @ SY46 ) )
| ~ ! [SY49: $i] :
( ~ ( ex_inf_of_relstr_set @ SV17 @ SY49 )
| ~ ( ~ ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY50 @ SY49 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SY49 @ ( sK10_E @ SY50 @ SY49 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SY50 @ SY49 @ SV17 ) @ SY50 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ SY50 )
| ( SY50
= ( sK9_C @ SY49 @ SV17 ) ) )
| ~ ~ ( ~ ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ SY51 )
| ( related @ SV17 @ SY51 @ ( sK9_C @ SY49 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SY49 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ ( sK9_C @ SY49 @ SV17 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[281]) ).
thf(287,plain,
! [SV16: $i] :
( ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( ~ ( rel_str @ SV16 ) )
= $true )
| ( ( ! [SY44: $i] :
( ~ ( element @ SY44 @ ( the_carrier @ SV16 ) )
| ! [SY45: $i] :
( ~ ( element @ SY45 @ ( the_carrier @ SV16 ) )
| ~ ( related @ SV16 @ SY44 @ SY45 )
| ~ ( related @ SV16 @ SY45 @ SY44 )
| ( SY44 = SY45 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(288,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SX0 )
| ( related @ sK1_A @ SX0 @ sK5_SY23 ) )
| ~ ~ ( ~ ( element @ sK5_SY23 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ sK5_SY23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(289,plain,
( ( ex_inf_of_relstr_set @ sK1_A @ sK4_SY18 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(290,plain,
! [SV17: $i] :
( ( ( ~ ! [SY46: $i] :
( ! [SY47: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY47 @ SY46 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY48: $i] :
( ~ ( element @ SY48 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ SY48 )
| ( related @ SV17 @ SY48 @ ( sK12_D @ SY47 @ SY46 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ ( sK12_D @ SY47 @ SY46 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SY47 @ SY46 @ SV17 )
!= SY47 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY47 @ SY46 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SY46 @ ( sK11_D @ SY47 @ SY46 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SY47 @ SY46 @ SV17 ) @ SY47 ) ) )
| ~ ( element @ SY47 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ SY47 ) )
| ( ex_inf_of_relstr_set @ SV17 @ SY46 ) )
| ~ ! [SY49: $i] :
( ~ ( ex_inf_of_relstr_set @ SV17 @ SY49 )
| ~ ( ~ ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY50 @ SY49 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SY49 @ ( sK10_E @ SY50 @ SY49 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SY50 @ SY49 @ SV17 ) @ SY50 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ SY50 )
| ( SY50
= ( sK9_C @ SY49 @ SV17 ) ) )
| ~ ~ ( ~ ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ SY51 )
| ( related @ SV17 @ SY51 @ ( sK9_C @ SY49 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SY49 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ ( sK9_C @ SY49 @ SV17 ) ) ) ) ) ) )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(291,plain,
! [SV16: $i] :
( ( ( rel_str @ SV16 )
= $false )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( ! [SY44: $i] :
( ~ ( element @ SY44 @ ( the_carrier @ SV16 ) )
| ! [SY45: $i] :
( ~ ( element @ SY45 @ ( the_carrier @ SV16 ) )
| ~ ( related @ SV16 @ SY44 @ SY45 )
| ~ ( related @ SV16 @ SY45 @ SY44 )
| ( SY44 = SY45 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(292,plain,
( ( ~ ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SX0 )
| ( related @ sK1_A @ SX0 @ sK5_SY23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(293,plain,
( ( ~ ~ ( ~ ( element @ sK5_SY23 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ sK5_SY23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(294,plain,
! [SV17: $i] :
( ( ( ~ ! [SY46: $i] :
( ! [SY47: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY47 @ SY46 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY48: $i] :
( ~ ( element @ SY48 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ SY48 )
| ( related @ SV17 @ SY48 @ ( sK12_D @ SY47 @ SY46 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ ( sK12_D @ SY47 @ SY46 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SY47 @ SY46 @ SV17 )
!= SY47 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY47 @ SY46 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SY46 @ ( sK11_D @ SY47 @ SY46 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SY47 @ SY46 @ SV17 ) @ SY47 ) ) )
| ~ ( element @ SY47 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ SY47 ) )
| ( ex_inf_of_relstr_set @ SV17 @ SY46 ) ) )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(295,plain,
! [SV17: $i] :
( ( ( ~ ! [SY49: $i] :
( ~ ( ex_inf_of_relstr_set @ SV17 @ SY49 )
| ~ ( ~ ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY50 @ SY49 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SY49 @ ( sK10_E @ SY50 @ SY49 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SY50 @ SY49 @ SV17 ) @ SY50 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ SY50 )
| ( SY50
= ( sK9_C @ SY49 @ SV17 ) ) )
| ~ ~ ( ~ ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ SY51 )
| ( related @ SV17 @ SY51 @ ( sK9_C @ SY49 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SY49 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ ( sK9_C @ SY49 @ SV17 ) ) ) ) ) ) )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[290]) ).
thf(296,plain,
! [SV16: $i,SV18: $i] :
( ( ( ~ ( element @ SV18 @ ( the_carrier @ SV16 ) )
| ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV16 ) )
| ~ ( related @ SV16 @ SV18 @ SY52 )
| ~ ( related @ SV16 @ SY52 @ SV18 )
| ( SV18 = SY52 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(297,plain,
( ( ! [SX0: $i] :
( ~ ( element @ SX0 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SX0 )
| ( related @ sK1_A @ SX0 @ sK5_SY23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(298,plain,
( ( ~ ( ~ ( element @ sK5_SY23 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ sK5_SY23 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(299,plain,
! [SV17: $i] :
( ( ( ! [SY46: $i] :
( ! [SY47: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY47 @ SY46 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY48: $i] :
( ~ ( element @ SY48 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ SY48 )
| ( related @ SV17 @ SY48 @ ( sK12_D @ SY47 @ SY46 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ ( sK12_D @ SY47 @ SY46 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SY47 @ SY46 @ SV17 )
!= SY47 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY47 @ SY46 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SY46 @ ( sK11_D @ SY47 @ SY46 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SY47 @ SY46 @ SV17 ) @ SY47 ) ) )
| ~ ( element @ SY47 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY46 @ SY47 ) )
| ( ex_inf_of_relstr_set @ SV17 @ SY46 ) ) )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(300,plain,
! [SV17: $i] :
( ( ( ! [SY49: $i] :
( ~ ( ex_inf_of_relstr_set @ SV17 @ SY49 )
| ~ ( ~ ! [SY50: $i] :
( ~ ( element @ SY50 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY50 @ SY49 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SY49 @ ( sK10_E @ SY50 @ SY49 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SY50 @ SY49 @ SV17 ) @ SY50 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ SY50 )
| ( SY50
= ( sK9_C @ SY49 @ SV17 ) ) )
| ~ ~ ( ~ ! [SY51: $i] :
( ~ ( element @ SY51 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ SY51 )
| ( related @ SV17 @ SY51 @ ( sK9_C @ SY49 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SY49 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SY49 @ ( sK9_C @ SY49 @ SV17 ) ) ) ) ) ) )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(301,plain,
! [SV16: $i,SV18: $i] :
( ( ( ~ ( element @ SV18 @ ( the_carrier @ SV16 ) ) )
= $true )
| ( ( ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV16 ) )
| ~ ( related @ SV16 @ SV18 @ SY52 )
| ~ ( related @ SV16 @ SY52 @ SV18 )
| ( SV18 = SY52 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(302,plain,
! [SV19: $i] :
( ( ~ ( element @ SV19 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SV19 )
| ( related @ sK1_A @ SV19 @ sK5_SY23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(303,plain,
( ( ~ ( element @ sK5_SY23 @ ( the_carrier @ sK1_A ) )
| ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ sK5_SY23 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(304,plain,
! [SV17: $i,SV20: $i] :
( ( ( ! [SY53: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY53 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY54: $i] :
( ~ ( element @ SY54 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY54 )
| ( related @ SV17 @ SY54 @ ( sK12_D @ SY53 @ SV20 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SY53 @ SV20 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SY53 @ SV20 @ SV17 )
!= SY53 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY53 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SY53 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SY53 @ SV20 @ SV17 ) @ SY53 ) ) )
| ~ ( element @ SY53 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY53 ) )
| ( ex_inf_of_relstr_set @ SV17 @ SV20 ) )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(305,plain,
! [SV21: $i,SV17: $i] :
( ( ( ~ ( ex_inf_of_relstr_set @ SV17 @ SV21 )
| ~ ( ~ ! [SY55: $i] :
( ~ ( element @ SY55 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY55 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SY55 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SY55 @ SV21 @ SV17 ) @ SY55 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY55 )
| ( SY55
= ( sK9_C @ SV21 @ SV17 ) ) )
| ~ ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY56 )
| ( related @ SV17 @ SY56 @ ( sK9_C @ SV21 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK9_C @ SV21 @ SV17 ) ) ) ) ) )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(306,plain,
! [SV16: $i,SV18: $i] :
( ( ( element @ SV18 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( ! [SY52: $i] :
( ~ ( element @ SY52 @ ( the_carrier @ SV16 ) )
| ~ ( related @ SV16 @ SV18 @ SY52 )
| ~ ( related @ SV16 @ SY52 @ SV18 )
| ( SV18 = SY52 ) ) )
= $true )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(307,plain,
! [SV19: $i] :
( ( ( ~ ( element @ SV19 @ ( the_carrier @ sK1_A ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SV19 )
| ( related @ sK1_A @ SV19 @ sK5_SY23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(308,plain,
( ( ~ ( element @ sK5_SY23 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(309,plain,
( ( ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ sK5_SY23 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[303]) ).
thf(310,plain,
! [SV17: $i,SV20: $i] :
( ( ( ! [SY53: $i] :
( ~ ( ~ ( element @ ( sK12_D @ SY53 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY54: $i] :
( ~ ( element @ SY54 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY54 )
| ( related @ SV17 @ SY54 @ ( sK12_D @ SY53 @ SV20 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SY53 @ SV20 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SY53 @ SV20 @ SV17 )
!= SY53 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SY53 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SY53 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SY53 @ SV20 @ SV17 ) @ SY53 ) ) )
| ~ ( element @ SY53 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY53 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(311,plain,
! [SV21: $i,SV17: $i] :
( ( ( ~ ( ex_inf_of_relstr_set @ SV17 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ! [SY55: $i] :
( ~ ( element @ SY55 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY55 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SY55 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SY55 @ SV21 @ SV17 ) @ SY55 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY55 )
| ( SY55
= ( sK9_C @ SV21 @ SV17 ) ) )
| ~ ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY56 )
| ( related @ SV17 @ SY56 @ ( sK9_C @ SV21 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK9_C @ SV21 @ SV17 ) ) ) ) ) )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(312,plain,
! [SV18: $i,SV16: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( the_carrier @ SV16 ) )
| ~ ( related @ SV16 @ SV18 @ SV22 )
| ~ ( related @ SV16 @ SV22 @ SV18 )
| ( SV18 = SV22 ) )
= $true )
| ( ( element @ SV18 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(313,plain,
! [SV19: $i] :
( ( ( element @ SV19 @ ( the_carrier @ sK1_A ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SV19 )
| ( related @ sK1_A @ SV19 @ sK5_SY23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(314,plain,
( ( element @ sK5_SY23 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(315,plain,
( ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ sK5_SY23 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(316,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( ~ ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY57: $i] :
( ~ ( element @ SY57 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY57 )
| ( related @ SV17 @ SY57 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
!= SV23 ) ) ) )
| ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(317,plain,
! [SV21: $i,SV17: $i] :
( ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( ~ ( ~ ! [SY55: $i] :
( ~ ( element @ SY55 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY55 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SY55 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SY55 @ SV21 @ SV17 ) @ SY55 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY55 )
| ( SY55
= ( sK9_C @ SV21 @ SV17 ) ) )
| ~ ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY56 )
| ( related @ SV17 @ SY56 @ ( sK9_C @ SV21 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK9_C @ SV21 @ SV17 ) ) ) ) ) )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(318,plain,
! [SV18: $i,SV16: $i,SV22: $i] :
( ( ( ~ ( element @ SV22 @ ( the_carrier @ SV16 ) ) )
= $true )
| ( ( ~ ( related @ SV16 @ SV18 @ SV22 )
| ~ ( related @ SV16 @ SV22 @ SV18 )
| ( SV18 = SV22 ) )
= $true )
| ( ( element @ SV18 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(319,plain,
! [SV19: $i] :
( ( ( ~ ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SV19 ) )
= $true )
| ( ( related @ sK1_A @ SV19 @ sK5_SY23 )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ sK1_A ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(320,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( ~ ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY57: $i] :
( ~ ( element @ SY57 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY57 )
| ( related @ SV17 @ SY57 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
!= SV23 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(321,plain,
! [SV21: $i,SV17: $i] :
( ( ( ~ ! [SY55: $i] :
( ~ ( element @ SY55 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY55 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SY55 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SY55 @ SV21 @ SV17 ) @ SY55 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY55 )
| ( SY55
= ( sK9_C @ SV21 @ SV17 ) ) )
| ~ ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY56 )
| ( related @ SV17 @ SY56 @ ( sK9_C @ SV21 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK9_C @ SV21 @ SV17 ) ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(322,plain,
! [SV18: $i,SV16: $i,SV22: $i] :
( ( ( element @ SV22 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( ~ ( related @ SV16 @ SV18 @ SV22 )
| ~ ( related @ SV16 @ SV22 @ SV18 )
| ( SV18 = SV22 ) )
= $true )
| ( ( element @ SV18 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(323,plain,
! [SV19: $i] :
( ( ( relstr_element_smaller @ sK1_A @ sK4_SY18 @ SV19 )
= $false )
| ( ( related @ sK1_A @ SV19 @ sK5_SY23 )
= $true )
| ( ( element @ SV19 @ ( the_carrier @ sK1_A ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(324,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ~ ( ~ ! [SY57: $i] :
( ~ ( element @ SY57 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY57 )
| ( related @ SV17 @ SY57 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
!= SV23 ) ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(325,plain,
! [SV21: $i,SV17: $i] :
( ( ( ~ ! [SY55: $i] :
( ~ ( element @ SY55 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY55 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SY55 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SY55 @ SV21 @ SV17 ) @ SY55 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY55 )
| ( SY55
= ( sK9_C @ SV21 @ SV17 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(326,plain,
! [SV21: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY56 )
| ( related @ SV17 @ SY56 @ ( sK9_C @ SV21 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK9_C @ SV21 @ SV17 ) ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(327,plain,
! [SV22: $i,SV18: $i,SV16: $i] :
( ( ( ~ ( related @ SV16 @ SV18 @ SV22 )
| ~ ( related @ SV16 @ SV22 @ SV18 ) )
= $true )
| ( ( SV18 = SV22 )
= $true )
| ( ( element @ SV22 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(328,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(329,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ! [SY57: $i] :
( ~ ( element @ SY57 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY57 )
| ( related @ SV17 @ SY57 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
!= SV23 ) ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(330,plain,
! [SV21: $i,SV17: $i] :
( ( ( ! [SY55: $i] :
( ~ ( element @ SY55 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SY55 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SY55 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SY55 @ SV21 @ SV17 ) @ SY55 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY55 )
| ( SY55
= ( sK9_C @ SV21 @ SV17 ) ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(331,plain,
! [SV21: $i,SV17: $i] :
( ( ( ~ ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY56 )
| ( related @ SV17 @ SY56 @ ( sK9_C @ SV21 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK9_C @ SV21 @ SV17 ) ) ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(332,plain,
! [SV22: $i,SV18: $i,SV16: $i] :
( ( ( ~ ( related @ SV16 @ SV18 @ SV22 ) )
= $true )
| ( ( ~ ( related @ SV16 @ SV22 @ SV18 ) )
= $true )
| ( ( SV18 = SV22 )
= $true )
| ( ( element @ SV22 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(333,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(334,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ! [SY57: $i] :
( ~ ( element @ SY57 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY57 )
| ( related @ SV17 @ SY57 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
!= SV23 ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(335,plain,
! [SV21: $i,SV17: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( the_carrier @ SV17 ) )
| ~ ( ~ ( element @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 )
| ( SV24
= ( sK9_C @ SV21 @ SV17 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(336,plain,
! [SV21: $i,SV17: $i] :
( ( ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY56 )
| ( related @ SV17 @ SY56 @ ( sK9_C @ SV21 @ SV17 ) ) )
| ~ ~ ( ~ ( element @ ( sK9_C @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK9_C @ SV21 @ SV17 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(337,plain,
! [SV22: $i,SV18: $i,SV16: $i] :
( ( ( related @ SV16 @ SV18 @ SV22 )
= $false )
| ( ( ~ ( related @ SV16 @ SV22 @ SV18 ) )
= $true )
| ( ( SV18 = SV22 )
= $true )
| ( ( element @ SV22 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(338,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(339,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ! [SY57: $i] :
( ~ ( element @ SY57 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY57 )
| ( related @ SV17 @ SY57 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
!= SV23 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(340,plain,
! [SV21: $i,SV17: $i,SV24: $i] :
( ( ( ~ ( element @ SV24 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 )
| ( SV24
= ( sK9_C @ SV21 @ SV17 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(341,plain,
! [SV21: $i,SV17: $i] :
( ( ( ~ ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY56 )
| ( related @ SV17 @ SY56 @ ( sK9_C @ SV21 @ SV17 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(342,plain,
! [SV17: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_C @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK9_C @ SV21 @ SV17 ) ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(343,plain,
! [SV18: $i,SV22: $i,SV16: $i] :
( ( ( related @ SV16 @ SV22 @ SV18 )
= $false )
| ( ( related @ SV16 @ SV18 @ SV22 )
= $false )
| ( ( SV18 = SV22 )
= $true )
| ( ( element @ SV22 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( element @ SV18 @ ( the_carrier @ SV16 ) )
= $false )
| ( ( antisymmetric_relstr @ SV16 )
= $false )
| ( ( rel_str @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(344,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(345,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ! [SY57: $i] :
( ~ ( element @ SY57 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY57 )
| ( related @ SV17 @ SY57 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(346,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
!= SV23 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(347,plain,
! [SV21: $i,SV17: $i,SV24: $i] :
( ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 )
| ( SV24
= ( sK9_C @ SV21 @ SV17 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(348,plain,
! [SV21: $i,SV17: $i] :
( ( ( ! [SY56: $i] :
( ~ ( element @ SY56 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SY56 )
| ( related @ SV17 @ SY56 @ ( sK9_C @ SV21 @ SV17 ) ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(349,plain,
! [SV17: $i,SV21: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_C @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK9_C @ SV21 @ SV17 ) ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(350,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(351,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(352,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( ~ ! [SY57: $i] :
( ~ ( element @ SY57 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY57 )
| ( related @ SV17 @ SY57 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(353,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
!= SV23 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(354,plain,
! [SV17: $i,SV21: $i,SV24: $i] :
( ( ( ~ ( ~ ( element @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(355,plain,
! [SV21: $i,SV17: $i,SV25: $i] :
( ( ( ~ ( element @ SV25 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV25 )
| ( related @ SV17 @ SV25 @ ( sK9_C @ SV21 @ SV17 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(356,plain,
! [SV17: $i,SV21: $i] :
( ( ( ~ ( element @ ( sK9_C @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK9_C @ SV21 @ SV17 ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(357,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[350]) ).
thf(358,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[351]) ).
thf(359,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ! [SY57: $i] :
( ~ ( element @ SY57 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY57 )
| ( related @ SV17 @ SY57 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(360,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(361,plain,
! [SV17: $i,SV21: $i,SV24: $i] :
( ( ( ~ ( ~ ( element @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 ) ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(362,plain,
! [SV21: $i,SV17: $i,SV25: $i] :
( ( ( ~ ( element @ SV25 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV25 )
| ( related @ SV17 @ SV25 @ ( sK9_C @ SV21 @ SV17 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(363,plain,
! [SV17: $i,SV21: $i] :
( ( ( ~ ( element @ ( sK9_C @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(364,plain,
! [SV21: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK9_C @ SV21 @ SV17 ) ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(365,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(366,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(367,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ! [SY57: $i] :
( ~ ( element @ SY57 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY57 )
| ( related @ SV17 @ SY57 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(368,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(369,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(370,plain,
! [SV17: $i,SV21: $i,SV24: $i] :
( ( ( ~ ( element @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 ) ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(371,plain,
! [SV21: $i,SV17: $i,SV25: $i] :
( ( ( element @ SV25 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV25 )
| ( related @ SV17 @ SV25 @ ( sK9_C @ SV21 @ SV17 ) ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(372,plain,
! [SV17: $i,SV21: $i] :
( ( ( element @ ( sK9_C @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(373,plain,
! [SV21: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV21 @ ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(374,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(375,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(376,plain,
! [SV20: $i,SV23: $i,SV17: $i] :
( ( ( ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[366]) ).
thf(377,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ! [SY57: $i] :
( ~ ( element @ SY57 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SY57 )
| ( related @ SV17 @ SY57 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(378,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(379,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(380,plain,
! [SV17: $i,SV21: $i,SV24: $i] :
( ( ( ~ ( element @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(381,plain,
! [SV24: $i,SV21: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 ) ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(382,plain,
! [SV25: $i,SV21: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV25 ) )
= $true )
| ( ( related @ SV17 @ SV25 @ ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV25 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(383,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(384,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(385,plain,
! [SV20: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(386,plain,
! [SV23: $i,SV20: $i,SV17: $i,SV26: $i] :
( ( ( ~ ( element @ SV26 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
| ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(387,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(388,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(389,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(390,plain,
! [SV17: $i,SV21: $i,SV24: $i] :
( ( ( element @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(391,plain,
! [SV24: $i,SV21: $i,SV17: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(392,plain,
! [SV25: $i,SV21: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV21 @ SV25 )
= $false )
| ( ( related @ SV17 @ SV25 @ ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV25 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(393,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(394,plain,
! [SV20: $i,SV23: $i,SV17: $i] :
( ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(395,plain,
! [SV23: $i,SV20: $i,SV17: $i,SV26: $i] :
( ( ( ~ ( element @ SV26 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
| ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(396,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(397,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[388]) ).
thf(398,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(399,plain,
! [SV24: $i,SV21: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV21 @ SV24 )
= $false )
| ( ( element @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(400,plain,
! [SV24: $i,SV21: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(401,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(402,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(403,plain,
! [SV23: $i,SV20: $i,SV17: $i,SV26: $i] :
( ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
| ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) ) )
= $true )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(404,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[396]) ).
thf(405,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[396]) ).
thf(406,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(407,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(408,plain,
! [SV24: $i,SV21: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(409,plain,
! [SV21: $i,SV24: $i,SV17: $i] :
( ( ( ~ ~ ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(410,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(411,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(412,plain,
! [SV23: $i,SV26: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV26 ) )
= $true )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(413,plain,
! [SV17: $i,SV20: $i,SV23: $i] :
( ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(414,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(415,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(416,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(417,plain,
! [SV20: $i,SV23: $i,SV17: $i] :
( ( ( ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(418,plain,
! [SV24: $i,SV21: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(419,plain,
! [SV21: $i,SV24: $i,SV17: $i] :
( ( ( ~ ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(420,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( element @ ( sK12_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(421,plain,
! [SV23: $i,SV26: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
| ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(422,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(423,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(424,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(425,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(426,plain,
! [SV20: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(427,plain,
! [SV24: $i,SV21: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV21 @ SV24 )
= $false )
| ( ( relstr_element_smaller @ SV17 @ SV21 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(428,plain,
! [SV21: $i,SV24: $i,SV17: $i] :
( ( ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV21 @ SV24 ) )
= $true )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(429,plain,
! [SV26: $i,SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(430,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(431,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(432,plain,
! [SV20: $i,SV23: $i,SV17: $i] :
( ( ( ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(433,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(434,plain,
! [SV20: $i,SV23: $i,SV17: $i] :
( ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(435,plain,
! [SV24: $i,SV21: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV21 @ SV24 )
= $false )
| ( ( related @ SV17 @ ( sK10_E @ SV24 @ SV21 @ SV17 ) @ SV24 )
= $false )
| ( ( SV24
= ( sK9_C @ SV21 @ SV17 ) )
= $true )
| ( ( element @ SV24 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV21 )
= $false )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(436,plain,
! [SV26: $i,SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
| ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(437,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(438,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(439,plain,
! [SV20: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[432]) ).
thf(440,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(441,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(442,plain,
! [SV26: $i,SV17: $i,SV20: $i,SV23: $i] :
( ( ( ~ ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(443,plain,
! [SV26: $i,SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(444,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(445,plain,
! [SV20: $i,SV23: $i,SV17: $i] :
( ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(446,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(447,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(448,plain,
! [SV26: $i,SV17: $i,SV20: $i,SV23: $i] :
( ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(449,plain,
! [SV26: $i,SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[443]) ).
thf(450,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(451,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(452,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( ( sK12_D @ SV23 @ SV20 @ SV17 )
= SV23 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(453,plain,
! [SV26: $i,SV20: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(454,plain,
! [SV26: $i,SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
| ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(455,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(456,plain,
! [SV20: $i,SV17: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(457,plain,
! [SV26: $i,SV20: $i,SV17: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(458,plain,
! [SV26: $i,SV23: $i,SV20: $i,SV17: $i] :
( ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(459,plain,
! [SV26: $i,SV20: $i,SV23: $i,SV17: $i] :
( ( ( ~ ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(460,plain,
! [SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(461,plain,
! [SV26: $i,SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( element @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ ( the_carrier @ SV17 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(462,plain,
! [SV26: $i,SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(463,plain,
! [SV26: $i,SV20: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 ) )
= $true )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(464,plain,
! [SV26: $i,SV20: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(465,plain,
! [SV26: $i,SV20: $i,SV23: $i,SV17: $i] :
( ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) )
| ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(466,plain,
! [SV26: $i,SV20: $i,SV17: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(467,plain,
! [SV26: $i,SV20: $i,SV17: $i,SV23: $i] :
( ( ( ~ ( element @ SV23 @ ( the_carrier @ SV17 ) ) )
= $true )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(468,plain,
! [SV26: $i,SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(469,plain,
! [SV26: $i,SV20: $i,SV17: $i,SV23: $i] :
( ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( ~ ( relstr_element_smaller @ SV17 @ SV20 @ SV23 ) )
= $true )
| ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(470,plain,
! [SV26: $i,SV23: $i,SV20: $i,SV17: $i] :
( ( ( relstr_element_smaller @ SV17 @ SV20 @ SV23 )
= $false )
| ( ( element @ SV23 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ ( sK11_D @ SV23 @ SV20 @ SV17 ) @ SV23 )
= $false )
| ( ( element @ SV26 @ ( the_carrier @ SV17 ) )
= $false )
| ( ( related @ SV17 @ SV26 @ ( sK12_D @ SV23 @ SV20 @ SV17 ) )
= $true )
| ( ( relstr_element_smaller @ SV17 @ SV20 @ SV26 )
= $false )
| ( ( ex_inf_of_relstr_set @ SV17 @ SV20 )
= $true )
| ( ( rel_str @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(471,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[260,470,468,461,460,455,452,446,437,435,427,424,420,410,399,392,383,373,372,343,323,315,314,289,282,273,268,267,264,263,262,261]) ).
thf(472,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[471,257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SEU357+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.11 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Mon Jun 20 11:31:34 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.15/0.32
% 0.15/0.32 No.of.Axioms: 9
% 0.15/0.32
% 0.15/0.32 Length.of.Defs: 0
% 0.15/0.32
% 0.15/0.32 Contains.Choice.Funs: false
% 0.15/0.33 (rf:0,axioms:9,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:11,loop_count:0,foatp_calls:0,translation:fof_full)......................
% 0.38/0.62
% 0.38/0.62 ********************************
% 0.38/0.62 * All subproblems solved! *
% 0.38/0.62 ********************************
% 0.38/0.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,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:471,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.56/0.75
% 0.56/0.75 %**** Beginning of derivation protocol ****
% 0.56/0.75 % SZS output start CNFRefutation
% See solution above
% 0.56/0.76
% 0.56/0.76 %**** End of derivation protocol ****
% 0.56/0.76 %**** no. of clauses in derivation: 472 ****
% 0.56/0.76 %**** clause counter: 471 ****
% 0.56/0.76
% 0.56/0.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:11,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:471,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------