TSTP Solution File: SEU362+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU362+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 : n004.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 12:11:06 EDT 2022
% Result : Theorem 35.79s 36.03s
% Output : CNFRefutation 35.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 77
% Syntax : Number of formulae : 451 ( 258 unt; 35 typ; 0 def)
% Number of atoms : 2406 ( 661 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 4427 ( 909 ~; 666 |; 74 &;2684 @)
% ( 8 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 14 con; 0-3 aty)
% Number of variables : 721 ( 0 ^ 699 !; 22 ?; 721 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_rel_str,type,
rel_str: $i > $o ).
thf(tp_related,type,
related: $i > $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_sK10_A,type,
sK10_A: $i ).
thf(tp_sK11_A,type,
sK11_A: $i ).
thf(tp_sK12_C,type,
sK12_C: $i > $i > $i ).
thf(tp_sK13_B,type,
sK13_B: $i > $i ).
thf(tp_sK14_B,type,
sK14_B: $i > $i ).
thf(tp_sK15_C,type,
sK15_C: $i > $i > $i ).
thf(tp_sK16_A,type,
sK16_A: $i ).
thf(tp_sK17_A,type,
sK17_A: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY69,type,
sK2_SY69: $i ).
thf(tp_sK3_SY74,type,
sK3_SY74: $i ).
thf(tp_sK4_SY78,type,
sK4_SY78: $i ).
thf(tp_sK5_SY81,type,
sK5_SY81: $i ).
thf(tp_sK6_SY83,type,
sK6_SY83: $i ).
thf(tp_sK7_B,type,
sK7_B: $i > $i ).
thf(tp_sK8_B,type,
sK8_B: $i > $i ).
thf(tp_sK9_A,type,
sK9_A: $i ).
thf(tp_subrelstr,type,
subrelstr: $i > $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_the_InternalRel,type,
the_InternalRel: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(2,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(9,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(11,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(12,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(13,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(14,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(15,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(16,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(18,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(19,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] : ( subrelstr @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_yellow_0) ).
thf(20,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(21,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(22,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(23,axiom,
? [A: $i] : ( rel_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(25,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(27,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( rel_str @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
thf(28,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(29,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(30,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(31,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(32,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(33,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(34,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(35,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(36,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( related @ A @ B @ C )
<=> ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
thf(37,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( subrelstr @ B @ A )
<=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_yellow_0) ).
thf(38,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(40,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(42,conjecture,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
=> ( ( ( E = C )
& ( F = D )
& ( related @ B @ E @ F ) )
=> ( related @ A @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_yellow_0) ).
thf(43,negated_conjecture,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
=> ( ( ( E = C )
& ( F = D )
& ( related @ B @ E @ F ) )
=> ( related @ A @ C @ D ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[42]) ).
thf(44,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ A ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ B ) )
=> ( ( ( E = C )
& ( F = D )
& ( related @ B @ E @ F ) )
=> ( related @ A @ C @ D ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[43]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(47,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(49,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(50,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(53,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(54,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(55,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(56,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(57,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(58,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(59,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(60,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(61,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ? [B: $i] : ( subrelstr @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(64,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(66,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(67,plain,
( ( ? [A: $i] : ( rel_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(68,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(70,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(71,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( subrelstr @ B @ A )
=> ( rel_str @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(72,plain,
$true = $true,
inference(unfold_def,[status(thm)],[28]) ).
thf(73,plain,
$true = $true,
inference(unfold_def,[status(thm)],[29]) ).
thf(74,plain,
$true = $true,
inference(unfold_def,[status(thm)],[30]) ).
thf(75,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(76,plain,
$true = $true,
inference(unfold_def,[status(thm)],[32]) ).
thf(77,plain,
$true = $true,
inference(unfold_def,[status(thm)],[33]) ).
thf(78,plain,
$true = $true,
inference(unfold_def,[status(thm)],[34]) ).
thf(79,plain,
$true = $true,
inference(unfold_def,[status(thm)],[35]) ).
thf(80,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ! [C: $i] :
( ( element @ C @ ( the_carrier @ A ) )
=> ( ( related @ A @ B @ C )
<=> ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(81,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( subrelstr @ B @ A )
<=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(82,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(83,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(84,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(86,plain,
( ( ( rel_str @ sK1_A )
=> ! [SY69: $i] :
( ( subrelstr @ SY69 @ sK1_A )
=> ! [SY70: $i] :
( ( element @ SY70 @ ( the_carrier @ sK1_A ) )
=> ! [SY71: $i] :
( ( element @ SY71 @ ( the_carrier @ sK1_A ) )
=> ! [SY72: $i] :
( ( element @ SY72 @ ( the_carrier @ SY69 ) )
=> ! [SY73: $i] :
( ( element @ SY73 @ ( the_carrier @ SY69 ) )
=> ( ( ( SY72 = SY70 )
& ( SY73 = SY71 )
& ( related @ SY69 @ SY72 @ SY73 ) )
=> ( related @ sK1_A @ SY70 @ SY71 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[44]) ).
thf(87,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(88,plain,
( ( ! [SY69: $i] :
( ( subrelstr @ SY69 @ sK1_A )
=> ! [SY70: $i] :
( ( element @ SY70 @ ( the_carrier @ sK1_A ) )
=> ! [SY71: $i] :
( ( element @ SY71 @ ( the_carrier @ sK1_A ) )
=> ! [SY72: $i] :
( ( element @ SY72 @ ( the_carrier @ SY69 ) )
=> ! [SY73: $i] :
( ( element @ SY73 @ ( the_carrier @ SY69 ) )
=> ( ( ( SY72 = SY70 )
& ( SY73 = SY71 )
& ( related @ SY69 @ SY72 @ SY73 ) )
=> ( related @ sK1_A @ SY70 @ SY71 ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(89,plain,
( ( ~ ! [SY69: $i] :
( ( subrelstr @ SY69 @ sK1_A )
=> ! [SY70: $i] :
( ( element @ SY70 @ ( the_carrier @ sK1_A ) )
=> ! [SY71: $i] :
( ( element @ SY71 @ ( the_carrier @ sK1_A ) )
=> ! [SY72: $i] :
( ( element @ SY72 @ ( the_carrier @ SY69 ) )
=> ! [SY73: $i] :
( ( element @ SY73 @ ( the_carrier @ SY69 ) )
=> ( ( ( SY72 = SY70 )
& ( SY73 = SY71 )
& ( related @ SY69 @ SY72 @ SY73 ) )
=> ( related @ sK1_A @ SY70 @ SY71 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[88]) ).
thf(90,plain,
( ( ( subrelstr @ sK2_SY69 @ sK1_A )
& ( element @ sK3_SY74 @ ( the_carrier @ sK1_A ) )
& ( element @ sK4_SY78 @ ( the_carrier @ sK1_A ) )
& ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
& ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
& ( sK5_SY81 = sK3_SY74 )
& ( sK6_SY83 = sK4_SY78 )
& ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 )
& ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(93,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(94,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(95,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(99,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(100,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(101,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK7_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK7_B @ A ) )
& ( finite @ ( sK7_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(102,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) )
& ( finite @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(103,plain,
( ( ~ ( empty @ sK9_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(104,plain,
( ( empty @ sK10_A )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(105,plain,
( ( ~ ( empty @ sK11_A )
& ( finite @ sK11_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(106,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK12_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(108,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( subrelstr @ ( sK13_B @ A ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(109,plain,
( ( ! [A: $i] : ( element @ ( sK14_B @ A ) @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK15_C @ B @ A ) @ A @ B ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(111,plain,
( ( one_sorted_str @ sK16_A )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(112,plain,
( ( rel_str @ sK17_A )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(113,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(114,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(115,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( subrelstr @ B @ A )
| ( rel_str @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(116,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(117,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) )
| ( related @ A @ B @ C ) )
& ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( related @ A @ B @ C )
| ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(118,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i] :
( ~ ( rel_str @ B )
| ~ ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
| ~ ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) )
| ( subrelstr @ B @ A ) )
& ! [B: $i] :
( ~ ( rel_str @ B )
| ~ ( subrelstr @ B @ A )
| ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) )
& ! [B: $i] :
( ~ ( rel_str @ B )
| ~ ( subrelstr @ B @ A )
| ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(119,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(120,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[83]) ).
thf(121,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(122,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(123,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(124,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(125,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
| ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(126,plain,
( ( ! [A: $i] :
( ~ ( finite @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( powerset @ A ) )
| ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(127,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( ! [B: $i] :
( ~ ( rel_str @ B )
| ~ ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
| ~ ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) )
| ( subrelstr @ B @ A ) )
& ! [B: $i] :
( ~ ( rel_str @ B )
| ~ ( subrelstr @ B @ A )
| ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) ) )
& ! [B: $i] :
( ~ ( rel_str @ B )
| ~ ( subrelstr @ B @ A )
| ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(128,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( element @ B @ ( the_carrier @ A ) )
| ( ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) )
| ( related @ A @ B @ C ) )
& ! [C: $i] :
( ~ ( element @ C @ ( the_carrier @ A ) )
| ~ ( related @ A @ B @ C )
| ( in @ ( ordered_pair @ B @ C ) @ ( the_InternalRel @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(129,plain,
$true = $true,
inference(copy,[status(thm)],[79]) ).
thf(130,plain,
$true = $true,
inference(copy,[status(thm)],[78]) ).
thf(131,plain,
$true = $true,
inference(copy,[status(thm)],[77]) ).
thf(132,plain,
$true = $true,
inference(copy,[status(thm)],[76]) ).
thf(133,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(134,plain,
$true = $true,
inference(copy,[status(thm)],[74]) ).
thf(135,plain,
$true = $true,
inference(copy,[status(thm)],[73]) ).
thf(136,plain,
$true = $true,
inference(copy,[status(thm)],[72]) ).
thf(137,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ! [B: $i] :
( ~ ( subrelstr @ B @ A )
| ( rel_str @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(138,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(139,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(140,plain,
$true = $true,
inference(copy,[status(thm)],[68]) ).
thf(141,plain,
( ( rel_str @ sK17_A )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(142,plain,
( ( one_sorted_str @ sK16_A )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(143,plain,
( ( ! [A: $i,B: $i] : ( relation_of2 @ ( sK15_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(144,plain,
( ( ! [A: $i] : ( element @ ( sK14_B @ A ) @ A ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(145,plain,
( ( ! [A: $i] :
( ~ ( rel_str @ A )
| ( subrelstr @ ( sK13_B @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(146,plain,
( ( ! [A: $i,B: $i] : ( relation_of2_as_subset @ ( sK12_C @ B @ A ) @ A @ B ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(147,plain,
( ( ! [A: $i,B: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(148,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(149,plain,
( ( ~ ( empty @ sK11_A )
& ( finite @ sK11_A ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(150,plain,
( ( empty @ sK10_A )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(151,plain,
( ( ~ ( empty @ sK9_A ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(152,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK8_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK8_B @ A ) )
& ( finite @ ( sK8_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(153,plain,
( ( ! [A: $i] :
( ( empty @ A )
| ( ( element @ ( sK7_B @ A ) @ ( powerset @ A ) )
& ~ ( empty @ ( sK7_B @ A ) )
& ( finite @ ( sK7_B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(154,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ~ ( relation_of2 @ C @ A @ B )
| ( relation_of2_as_subset @ C @ A @ B ) )
& ! [B: $i,C: $i] :
( ~ ( relation_of2_as_subset @ C @ A @ B )
| ( relation_of2 @ C @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(155,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(156,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(157,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(158,plain,
( ( ! [A: $i,B: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(159,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(160,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( element @ B @ ( powerset @ C ) )
| ~ ( in @ A @ B )
| ~ ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(161,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(162,plain,
( ( ! [A: $i,B: $i] :
( ~ ( empty @ B )
| ~ ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(163,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(164,plain,
( ( rel_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(165,plain,
( ( ( subrelstr @ sK2_SY69 @ sK1_A )
& ( element @ sK3_SY74 @ ( the_carrier @ sK1_A ) )
& ( element @ sK4_SY78 @ ( the_carrier @ sK1_A ) )
& ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
& ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
& ( sK5_SY81 = sK3_SY74 )
& ( sK6_SY83 = sK4_SY78 )
& ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 )
& ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(166,plain,
( ( ~ ( ~ ~ ( empty @ sK11_A )
| ~ ( finite @ sK11_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(167,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(168,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( relation_of2 @ SX2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(169,plain,
( ( ~ ( ~ ( subrelstr @ sK2_SY69 @ sK1_A )
| ~ ~ ( ~ ( element @ sK3_SY74 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK4_SY78 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(170,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( the_carrier @ SX0 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( in @ ( ordered_pair @ SX1 @ SX2 ) @ ( the_InternalRel @ SX0 ) )
| ( related @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ~ ( related @ SX0 @ SX1 @ SX2 )
| ( in @ ( ordered_pair @ SX1 @ SX2 ) @ ( the_InternalRel @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(171,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK7_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK7_B @ SX0 ) ) )
| ~ ( finite @ ( sK7_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(172,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ~ ( ~ ! [SX1: $i] :
( ~ ( rel_str @ SX1 )
| ~ ( subset @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) )
| ~ ( subset @ ( the_InternalRel @ SX1 ) @ ( the_InternalRel @ SX0 ) )
| ( subrelstr @ SX1 @ SX0 ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( rel_str @ SX1 )
| ~ ( subrelstr @ SX1 @ SX0 )
| ( subset @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) ) )
| ~ ! [SX1: $i] :
( ~ ( rel_str @ SX1 )
| ~ ( subrelstr @ SX1 @ SX0 )
| ( subset @ ( the_InternalRel @ SX1 ) @ ( the_InternalRel @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(173,plain,
( ( ! [SX0: $i] :
( ( empty @ SX0 )
| ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SX0 ) @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ ( sK8_B @ SX0 ) ) )
| ~ ( finite @ ( sK8_B @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(174,plain,
! [SV1: $i] :
( ( ! [SY84: $i] :
( ~ ( in @ SV1 @ SY84 )
| ~ ( in @ SY84 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(175,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( finite @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(176,plain,
! [SV3: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ~ ( element @ SY86 @ ( powerset @ ( cartesian_product2 @ SV3 @ SY85 ) ) )
| ( relation @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(177,plain,
! [SV4: $i] :
( ( ~ ( finite @ SV4 )
| ! [SY87: $i] :
( ~ ( element @ SY87 @ ( powerset @ SV4 ) )
| ( finite @ SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(178,plain,
! [SV5: $i] :
( ( ~ ( rel_str @ SV5 )
| ( one_sorted_str @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(179,plain,
! [SV6: $i] :
( ( ~ ( rel_str @ SV6 )
| ! [SY88: $i] :
( ~ ( subrelstr @ SY88 @ SV6 )
| ( rel_str @ SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(180,plain,
! [SV7: $i] :
( ( ! [SY89: $i,SY90: $i] :
( ~ ( relation_of2_as_subset @ SY90 @ SV7 @ SY89 )
| ( element @ SY90 @ ( powerset @ ( cartesian_product2 @ SV7 @ SY89 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(181,plain,
! [SV8: $i] :
( ( ~ ( rel_str @ SV8 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(182,plain,
! [SV9: $i] :
( ( ! [SY91: $i] : ( relation_of2 @ ( sK15_C @ SY91 @ SV9 ) @ SV9 @ SY91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(183,plain,
! [SV10: $i] :
( ( element @ ( sK14_B @ SV10 ) @ SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(184,plain,
! [SV11: $i] :
( ( ~ ( rel_str @ SV11 )
| ( subrelstr @ ( sK13_B @ SV11 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(185,plain,
! [SV12: $i] :
( ( ! [SY92: $i] : ( relation_of2_as_subset @ ( sK12_C @ SY92 @ SV12 ) @ SV12 @ SY92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(186,plain,
! [SV13: $i] :
( ( ! [SY93: $i] :
( ~ ( finite @ SV13 )
| ~ ( finite @ SY93 )
| ( finite @ ( cartesian_product2 @ SV13 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(187,plain,
( ( empty @ sK9_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(188,plain,
! [SV14: $i] :
( ( subset @ SV14 @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(189,plain,
! [SV15: $i] :
( ( ! [SY94: $i] :
( ~ ( in @ SV15 @ SY94 )
| ( element @ SV15 @ SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(190,plain,
! [SV16: $i] :
( ( ! [SY95: $i] :
( ~ ( element @ SV16 @ SY95 )
| ( empty @ SY95 )
| ( in @ SV16 @ SY95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(191,plain,
! [SV17: $i] :
( ( ! [SY96: $i,SY97: $i] :
( ~ ( element @ SY96 @ ( powerset @ SY97 ) )
| ~ ( in @ SV17 @ SY96 )
| ( element @ SV17 @ SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(192,plain,
! [SV18: $i] :
( ( ! [SY98: $i,SY99: $i] :
( ~ ( element @ SY98 @ ( powerset @ SY99 ) )
| ~ ( in @ SV18 @ SY98 )
| ~ ( empty @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(193,plain,
! [SV19: $i] :
( ( ~ ( empty @ SV19 )
| ( SV19 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(194,plain,
! [SV20: $i] :
( ( ! [SY100: $i] :
( ~ ( empty @ SY100 )
| ~ ( in @ SV20 @ SY100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(195,plain,
! [SV21: $i] :
( ( ! [SY101: $i] :
( ( SV21 = SY101 )
| ~ ( empty @ SV21 )
| ~ ( empty @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(196,plain,
( ( ~ ~ ( empty @ sK11_A )
| ~ ( finite @ sK11_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(197,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(198,plain,
! [SV22: $i] :
( ( ~ ( ~ ! [SY102: $i,SY103: $i] :
( ~ ( relation_of2 @ SY103 @ SV22 @ SY102 )
| ( relation_of2_as_subset @ SY103 @ SV22 @ SY102 ) )
| ~ ! [SY104: $i,SY105: $i] :
( ~ ( relation_of2_as_subset @ SY105 @ SV22 @ SY104 )
| ( relation_of2 @ SY105 @ SV22 @ SY104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(199,plain,
( ( ~ ( subrelstr @ sK2_SY69 @ sK1_A )
| ~ ~ ( ~ ( element @ sK3_SY74 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK4_SY78 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(200,plain,
! [SV23: $i] :
( ( ~ ( rel_str @ SV23 )
| ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ SV23 ) )
| ~ ( ~ ! [SY107: $i] :
( ~ ( element @ SY107 @ ( the_carrier @ SV23 ) )
| ~ ( in @ ( ordered_pair @ SY106 @ SY107 ) @ ( the_InternalRel @ SV23 ) )
| ( related @ SV23 @ SY106 @ SY107 ) )
| ~ ! [SY108: $i] :
( ~ ( element @ SY108 @ ( the_carrier @ SV23 ) )
| ~ ( related @ SV23 @ SY106 @ SY108 )
| ( in @ ( ordered_pair @ SY106 @ SY108 ) @ ( the_InternalRel @ SV23 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(201,plain,
! [SV24: $i] :
( ( ( empty @ SV24 )
| ~ ( ~ ~ ( ~ ( element @ ( sK7_B @ SV24 ) @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ ( sK7_B @ SV24 ) ) )
| ~ ( finite @ ( sK7_B @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(202,plain,
! [SV25: $i] :
( ( ~ ( rel_str @ SV25 )
| ~ ( ~ ! [SY109: $i] :
( ~ ( rel_str @ SY109 )
| ~ ( subset @ ( the_carrier @ SY109 ) @ ( the_carrier @ SV25 ) )
| ~ ( subset @ ( the_InternalRel @ SY109 ) @ ( the_InternalRel @ SV25 ) )
| ( subrelstr @ SY109 @ SV25 ) )
| ~ ~ ( ~ ! [SY110: $i] :
( ~ ( rel_str @ SY110 )
| ~ ( subrelstr @ SY110 @ SV25 )
| ( subset @ ( the_carrier @ SY110 ) @ ( the_carrier @ SV25 ) ) )
| ~ ! [SY111: $i] :
( ~ ( rel_str @ SY111 )
| ~ ( subrelstr @ SY111 @ SV25 )
| ( subset @ ( the_InternalRel @ SY111 ) @ ( the_InternalRel @ SV25 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(203,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
| ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK8_B @ SV26 ) ) )
| ~ ( finite @ ( sK8_B @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(204,plain,
! [SV27: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV27 )
| ~ ( in @ SV27 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(205,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( finite @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(206,plain,
! [SV28: $i,SV3: $i] :
( ( ! [SY112: $i] :
( ~ ( element @ SY112 @ ( powerset @ ( cartesian_product2 @ SV3 @ SV28 ) ) )
| ( relation @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(207,plain,
! [SV4: $i] :
( ( ( ~ ( finite @ SV4 ) )
= $true )
| ( ( ! [SY87: $i] :
( ~ ( element @ SY87 @ ( powerset @ SV4 ) )
| ( finite @ SY87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(208,plain,
! [SV5: $i] :
( ( ( ~ ( rel_str @ SV5 ) )
= $true )
| ( ( one_sorted_str @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(209,plain,
! [SV6: $i] :
( ( ( ~ ( rel_str @ SV6 ) )
= $true )
| ( ( ! [SY88: $i] :
( ~ ( subrelstr @ SY88 @ SV6 )
| ( rel_str @ SY88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(210,plain,
! [SV29: $i,SV7: $i] :
( ( ! [SY113: $i] :
( ~ ( relation_of2_as_subset @ SY113 @ SV7 @ SV29 )
| ( element @ SY113 @ ( powerset @ ( cartesian_product2 @ SV7 @ SV29 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(211,plain,
! [SV8: $i] :
( ( ( ~ ( rel_str @ SV8 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(212,plain,
! [SV9: $i,SV30: $i] :
( ( relation_of2 @ ( sK15_C @ SV30 @ SV9 ) @ SV9 @ SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(213,plain,
! [SV11: $i] :
( ( ( ~ ( rel_str @ SV11 ) )
= $true )
| ( ( subrelstr @ ( sK13_B @ SV11 ) @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(214,plain,
! [SV12: $i,SV31: $i] :
( ( relation_of2_as_subset @ ( sK12_C @ SV31 @ SV12 ) @ SV12 @ SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(215,plain,
! [SV32: $i,SV13: $i] :
( ( ~ ( finite @ SV13 )
| ~ ( finite @ SV32 )
| ( finite @ ( cartesian_product2 @ SV13 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(216,plain,
! [SV33: $i,SV15: $i] :
( ( ~ ( in @ SV15 @ SV33 )
| ( element @ SV15 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(217,plain,
! [SV34: $i,SV16: $i] :
( ( ~ ( element @ SV16 @ SV34 )
| ( empty @ SV34 )
| ( in @ SV16 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(218,plain,
! [SV17: $i,SV35: $i] :
( ( ! [SY114: $i] :
( ~ ( element @ SV35 @ ( powerset @ SY114 ) )
| ~ ( in @ SV17 @ SV35 )
| ( element @ SV17 @ SY114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(219,plain,
! [SV18: $i,SV36: $i] :
( ( ! [SY115: $i] :
( ~ ( element @ SV36 @ ( powerset @ SY115 ) )
| ~ ( in @ SV18 @ SV36 )
| ~ ( empty @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(220,plain,
! [SV19: $i] :
( ( ( ~ ( empty @ SV19 ) )
= $true )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(221,plain,
! [SV20: $i,SV37: $i] :
( ( ~ ( empty @ SV37 )
| ~ ( in @ SV20 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(222,plain,
! [SV38: $i,SV21: $i] :
( ( ( SV21 = SV38 )
| ~ ( empty @ SV21 )
| ~ ( empty @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(223,plain,
( ( ~ ~ ( empty @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(224,plain,
( ( ~ ( finite @ sK11_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(225,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(226,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(227,plain,
! [SV22: $i] :
( ( ~ ! [SY102: $i,SY103: $i] :
( ~ ( relation_of2 @ SY103 @ SV22 @ SY102 )
| ( relation_of2_as_subset @ SY103 @ SV22 @ SY102 ) )
| ~ ! [SY104: $i,SY105: $i] :
( ~ ( relation_of2_as_subset @ SY105 @ SV22 @ SY104 )
| ( relation_of2 @ SY105 @ SV22 @ SY104 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(228,plain,
( ( ~ ( subrelstr @ sK2_SY69 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(229,plain,
( ( ~ ~ ( ~ ( element @ sK3_SY74 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK4_SY78 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(230,plain,
! [SV23: $i] :
( ( ( ~ ( rel_str @ SV23 ) )
= $true )
| ( ( ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ SV23 ) )
| ~ ( ~ ! [SY107: $i] :
( ~ ( element @ SY107 @ ( the_carrier @ SV23 ) )
| ~ ( in @ ( ordered_pair @ SY106 @ SY107 ) @ ( the_InternalRel @ SV23 ) )
| ( related @ SV23 @ SY106 @ SY107 ) )
| ~ ! [SY108: $i] :
( ~ ( element @ SY108 @ ( the_carrier @ SV23 ) )
| ~ ( related @ SV23 @ SY106 @ SY108 )
| ( in @ ( ordered_pair @ SY106 @ SY108 ) @ ( the_InternalRel @ SV23 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(231,plain,
! [SV24: $i] :
( ( ( empty @ SV24 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK7_B @ SV24 ) @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ ( sK7_B @ SV24 ) ) )
| ~ ( finite @ ( sK7_B @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(232,plain,
! [SV25: $i] :
( ( ( ~ ( rel_str @ SV25 ) )
= $true )
| ( ( ~ ( ~ ! [SY109: $i] :
( ~ ( rel_str @ SY109 )
| ~ ( subset @ ( the_carrier @ SY109 ) @ ( the_carrier @ SV25 ) )
| ~ ( subset @ ( the_InternalRel @ SY109 ) @ ( the_InternalRel @ SV25 ) )
| ( subrelstr @ SY109 @ SV25 ) )
| ~ ~ ( ~ ! [SY110: $i] :
( ~ ( rel_str @ SY110 )
| ~ ( subrelstr @ SY110 @ SV25 )
| ( subset @ ( the_carrier @ SY110 ) @ ( the_carrier @ SV25 ) ) )
| ~ ! [SY111: $i] :
( ~ ( rel_str @ SY111 )
| ~ ( subrelstr @ SY111 @ SV25 )
| ( subset @ ( the_InternalRel @ SY111 ) @ ( the_InternalRel @ SV25 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(233,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( element @ ( sK8_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK8_B @ SV26 ) ) )
| ~ ( finite @ ( sK8_B @ SV26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(234,plain,
! [SV27: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV27 ) )
= $true )
| ( ( ~ ( in @ SV27 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(235,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( finite @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(236,plain,
! [SV28: $i,SV3: $i,SV39: $i] :
( ( ~ ( element @ SV39 @ ( powerset @ ( cartesian_product2 @ SV3 @ SV28 ) ) )
| ( relation @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(237,plain,
! [SV4: $i] :
( ( ( finite @ SV4 )
= $false )
| ( ( ! [SY87: $i] :
( ~ ( element @ SY87 @ ( powerset @ SV4 ) )
| ( finite @ SY87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(238,plain,
! [SV5: $i] :
( ( ( rel_str @ SV5 )
= $false )
| ( ( one_sorted_str @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(239,plain,
! [SV6: $i] :
( ( ( rel_str @ SV6 )
= $false )
| ( ( ! [SY88: $i] :
( ~ ( subrelstr @ SY88 @ SV6 )
| ( rel_str @ SY88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(240,plain,
! [SV29: $i,SV7: $i,SV40: $i] :
( ( ~ ( relation_of2_as_subset @ SV40 @ SV7 @ SV29 )
| ( element @ SV40 @ ( powerset @ ( cartesian_product2 @ SV7 @ SV29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(241,plain,
! [SV8: $i] :
( ( ( rel_str @ SV8 )
= $false )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV8 ) @ ( the_carrier @ SV8 ) @ ( the_carrier @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(242,plain,
! [SV11: $i] :
( ( ( rel_str @ SV11 )
= $false )
| ( ( subrelstr @ ( sK13_B @ SV11 ) @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(243,plain,
! [SV32: $i,SV13: $i] :
( ( ( ~ ( finite @ SV13 )
| ~ ( finite @ SV32 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV13 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(244,plain,
! [SV33: $i,SV15: $i] :
( ( ( ~ ( in @ SV15 @ SV33 ) )
= $true )
| ( ( element @ SV15 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(245,plain,
! [SV34: $i,SV16: $i] :
( ( ( ~ ( element @ SV16 @ SV34 ) )
= $true )
| ( ( ( empty @ SV34 )
| ( in @ SV16 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(246,plain,
! [SV17: $i,SV41: $i,SV35: $i] :
( ( ~ ( element @ SV35 @ ( powerset @ SV41 ) )
| ~ ( in @ SV17 @ SV35 )
| ( element @ SV17 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(247,plain,
! [SV18: $i,SV42: $i,SV36: $i] :
( ( ~ ( element @ SV36 @ ( powerset @ SV42 ) )
| ~ ( in @ SV18 @ SV36 )
| ~ ( empty @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(248,plain,
! [SV19: $i] :
( ( ( empty @ SV19 )
= $false )
| ( ( SV19 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(249,plain,
! [SV20: $i,SV37: $i] :
( ( ( ~ ( empty @ SV37 ) )
= $true )
| ( ( ~ ( in @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(250,plain,
! [SV38: $i,SV21: $i] :
( ( ( ( SV21 = SV38 )
| ~ ( empty @ SV21 ) )
= $true )
| ( ( ~ ( empty @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(251,plain,
( ( ~ ( empty @ sK11_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(252,plain,
( ( finite @ sK11_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(253,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(254,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(255,plain,
! [SV22: $i] :
( ( ~ ! [SY102: $i,SY103: $i] :
( ~ ( relation_of2 @ SY103 @ SV22 @ SY102 )
| ( relation_of2_as_subset @ SY103 @ SV22 @ SY102 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(256,plain,
! [SV22: $i] :
( ( ~ ! [SY104: $i,SY105: $i] :
( ~ ( relation_of2_as_subset @ SY105 @ SV22 @ SY104 )
| ( relation_of2 @ SY105 @ SV22 @ SY104 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(257,plain,
( ( subrelstr @ sK2_SY69 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(258,plain,
( ( ~ ( ~ ( element @ sK3_SY74 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK4_SY78 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(259,plain,
! [SV23: $i] :
( ( ( rel_str @ SV23 )
= $false )
| ( ( ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ SV23 ) )
| ~ ( ~ ! [SY107: $i] :
( ~ ( element @ SY107 @ ( the_carrier @ SV23 ) )
| ~ ( in @ ( ordered_pair @ SY106 @ SY107 ) @ ( the_InternalRel @ SV23 ) )
| ( related @ SV23 @ SY106 @ SY107 ) )
| ~ ! [SY108: $i] :
( ~ ( element @ SY108 @ ( the_carrier @ SV23 ) )
| ~ ( related @ SV23 @ SY106 @ SY108 )
| ( in @ ( ordered_pair @ SY106 @ SY108 ) @ ( the_InternalRel @ SV23 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(260,plain,
! [SV24: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_B @ SV24 ) @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ ( sK7_B @ SV24 ) ) )
| ~ ( finite @ ( sK7_B @ SV24 ) ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(261,plain,
! [SV25: $i] :
( ( ( rel_str @ SV25 )
= $false )
| ( ( ~ ( ~ ! [SY109: $i] :
( ~ ( rel_str @ SY109 )
| ~ ( subset @ ( the_carrier @ SY109 ) @ ( the_carrier @ SV25 ) )
| ~ ( subset @ ( the_InternalRel @ SY109 ) @ ( the_InternalRel @ SV25 ) )
| ( subrelstr @ SY109 @ SV25 ) )
| ~ ~ ( ~ ! [SY110: $i] :
( ~ ( rel_str @ SY110 )
| ~ ( subrelstr @ SY110 @ SV25 )
| ( subset @ ( the_carrier @ SY110 ) @ ( the_carrier @ SV25 ) ) )
| ~ ! [SY111: $i] :
( ~ ( rel_str @ SY111 )
| ~ ( subrelstr @ SY111 @ SV25 )
| ( subset @ ( the_InternalRel @ SY111 ) @ ( the_InternalRel @ SV25 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(262,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK8_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK8_B @ SV26 ) ) )
| ~ ( finite @ ( sK8_B @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(263,plain,
! [SV27: $i,SV1: $i] :
( ( ( in @ SV1 @ SV27 )
= $false )
| ( ( ~ ( in @ SV27 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(264,plain,
! [SV28: $i,SV3: $i,SV39: $i] :
( ( ( ~ ( element @ SV39 @ ( powerset @ ( cartesian_product2 @ SV3 @ SV28 ) ) ) )
= $true )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(265,plain,
! [SV4: $i,SV43: $i] :
( ( ( ~ ( element @ SV43 @ ( powerset @ SV4 ) )
| ( finite @ SV43 ) )
= $true )
| ( ( finite @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(266,plain,
! [SV6: $i,SV44: $i] :
( ( ( ~ ( subrelstr @ SV44 @ SV6 )
| ( rel_str @ SV44 ) )
= $true )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(267,plain,
! [SV29: $i,SV7: $i,SV40: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV40 @ SV7 @ SV29 ) )
= $true )
| ( ( element @ SV40 @ ( powerset @ ( cartesian_product2 @ SV7 @ SV29 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(268,plain,
! [SV32: $i,SV13: $i] :
( ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( ~ ( finite @ SV32 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV13 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(269,plain,
! [SV33: $i,SV15: $i] :
( ( ( in @ SV15 @ SV33 )
= $false )
| ( ( element @ SV15 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(270,plain,
! [SV34: $i,SV16: $i] :
( ( ( element @ SV16 @ SV34 )
= $false )
| ( ( ( empty @ SV34 )
| ( in @ SV16 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(271,plain,
! [SV17: $i,SV41: $i,SV35: $i] :
( ( ( ~ ( element @ SV35 @ ( powerset @ SV41 ) )
| ~ ( in @ SV17 @ SV35 ) )
= $true )
| ( ( element @ SV17 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(272,plain,
! [SV18: $i,SV42: $i,SV36: $i] :
( ( ( ~ ( element @ SV36 @ ( powerset @ SV42 ) )
| ~ ( in @ SV18 @ SV36 ) )
= $true )
| ( ( ~ ( empty @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(273,plain,
! [SV20: $i,SV37: $i] :
( ( ( empty @ SV37 )
= $false )
| ( ( ~ ( in @ SV20 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(274,plain,
! [SV38: $i,SV21: $i] :
( ( ( SV21 = SV38 )
= $true )
| ( ( ~ ( empty @ SV21 ) )
= $true )
| ( ( ~ ( empty @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(275,plain,
( ( empty @ sK11_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(276,plain,
! [SV45: $i] :
( ( ! [SY116: $i] :
( ~ ( element @ SV45 @ ( powerset @ SY116 ) )
| ( subset @ SV45 @ SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(277,plain,
! [SV46: $i] :
( ( ! [SY117: $i] :
( ~ ( subset @ SV46 @ SY117 )
| ( element @ SV46 @ ( powerset @ SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(278,plain,
! [SV22: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ~ ( relation_of2 @ SY103 @ SV22 @ SY102 )
| ( relation_of2_as_subset @ SY103 @ SV22 @ SY102 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(279,plain,
! [SV22: $i] :
( ( ! [SY104: $i,SY105: $i] :
( ~ ( relation_of2_as_subset @ SY105 @ SV22 @ SY104 )
| ( relation_of2 @ SY105 @ SV22 @ SY104 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(280,plain,
( ( ~ ( element @ sK3_SY74 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK4_SY78 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(281,plain,
! [SV23: $i,SV47: $i] :
( ( ( ~ ( element @ SV47 @ ( the_carrier @ SV23 ) )
| ~ ( ~ ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV23 ) )
| ~ ( in @ ( ordered_pair @ SV47 @ SY118 ) @ ( the_InternalRel @ SV23 ) )
| ( related @ SV23 @ SV47 @ SY118 ) )
| ~ ! [SY119: $i] :
( ~ ( element @ SY119 @ ( the_carrier @ SV23 ) )
| ~ ( related @ SV23 @ SV47 @ SY119 )
| ( in @ ( ordered_pair @ SV47 @ SY119 ) @ ( the_InternalRel @ SV23 ) ) ) ) )
= $true )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(282,plain,
! [SV24: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK7_B @ SV24 ) @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ ( sK7_B @ SV24 ) ) ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(283,plain,
! [SV24: $i] :
( ( ( ~ ( finite @ ( sK7_B @ SV24 ) ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(284,plain,
! [SV25: $i] :
( ( ( ~ ! [SY109: $i] :
( ~ ( rel_str @ SY109 )
| ~ ( subset @ ( the_carrier @ SY109 ) @ ( the_carrier @ SV25 ) )
| ~ ( subset @ ( the_InternalRel @ SY109 ) @ ( the_InternalRel @ SV25 ) )
| ( subrelstr @ SY109 @ SV25 ) )
| ~ ~ ( ~ ! [SY110: $i] :
( ~ ( rel_str @ SY110 )
| ~ ( subrelstr @ SY110 @ SV25 )
| ( subset @ ( the_carrier @ SY110 ) @ ( the_carrier @ SV25 ) ) )
| ~ ! [SY111: $i] :
( ~ ( rel_str @ SY111 )
| ~ ( subrelstr @ SY111 @ SV25 )
| ( subset @ ( the_InternalRel @ SY111 ) @ ( the_InternalRel @ SV25 ) ) ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(285,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK8_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK8_B @ SV26 ) ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(286,plain,
! [SV26: $i] :
( ( ( ~ ( finite @ ( sK8_B @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(287,plain,
! [SV1: $i,SV27: $i] :
( ( ( in @ SV27 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(288,plain,
! [SV28: $i,SV3: $i,SV39: $i] :
( ( ( element @ SV39 @ ( powerset @ ( cartesian_product2 @ SV3 @ SV28 ) ) )
= $false )
| ( ( relation @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(289,plain,
! [SV4: $i,SV43: $i] :
( ( ( ~ ( element @ SV43 @ ( powerset @ SV4 ) ) )
= $true )
| ( ( finite @ SV43 )
= $true )
| ( ( finite @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(290,plain,
! [SV6: $i,SV44: $i] :
( ( ( ~ ( subrelstr @ SV44 @ SV6 ) )
= $true )
| ( ( rel_str @ SV44 )
= $true )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(291,plain,
! [SV29: $i,SV7: $i,SV40: $i] :
( ( ( relation_of2_as_subset @ SV40 @ SV7 @ SV29 )
= $false )
| ( ( element @ SV40 @ ( powerset @ ( cartesian_product2 @ SV7 @ SV29 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(292,plain,
! [SV32: $i,SV13: $i] :
( ( ( finite @ SV13 )
= $false )
| ( ( ~ ( finite @ SV32 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV13 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(293,plain,
! [SV16: $i,SV34: $i] :
( ( ( empty @ SV34 )
= $true )
| ( ( in @ SV16 @ SV34 )
= $true )
| ( ( element @ SV16 @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(294,plain,
! [SV17: $i,SV41: $i,SV35: $i] :
( ( ( ~ ( element @ SV35 @ ( powerset @ SV41 ) ) )
= $true )
| ( ( ~ ( in @ SV17 @ SV35 ) )
= $true )
| ( ( element @ SV17 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(295,plain,
! [SV18: $i,SV42: $i,SV36: $i] :
( ( ( ~ ( element @ SV36 @ ( powerset @ SV42 ) ) )
= $true )
| ( ( ~ ( in @ SV18 @ SV36 ) )
= $true )
| ( ( ~ ( empty @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(296,plain,
! [SV37: $i,SV20: $i] :
( ( ( in @ SV20 @ SV37 )
= $false )
| ( ( empty @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(297,plain,
! [SV38: $i,SV21: $i] :
( ( ( empty @ SV21 )
= $false )
| ( ( SV21 = SV38 )
= $true )
| ( ( ~ ( empty @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(298,plain,
! [SV48: $i,SV45: $i] :
( ( ~ ( element @ SV45 @ ( powerset @ SV48 ) )
| ( subset @ SV45 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(299,plain,
! [SV49: $i,SV46: $i] :
( ( ~ ( subset @ SV46 @ SV49 )
| ( element @ SV46 @ ( powerset @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(300,plain,
! [SV50: $i,SV22: $i] :
( ( ! [SY120: $i] :
( ~ ( relation_of2 @ SY120 @ SV22 @ SV50 )
| ( relation_of2_as_subset @ SY120 @ SV22 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(301,plain,
! [SV51: $i,SV22: $i] :
( ( ! [SY121: $i] :
( ~ ( relation_of2_as_subset @ SY121 @ SV22 @ SV51 )
| ( relation_of2 @ SY121 @ SV22 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(302,plain,
( ( ~ ( element @ sK3_SY74 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(303,plain,
( ( ~ ~ ( ~ ( element @ sK4_SY78 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(304,plain,
! [SV23: $i,SV47: $i] :
( ( ( ~ ( element @ SV47 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV23 ) )
| ~ ( in @ ( ordered_pair @ SV47 @ SY118 ) @ ( the_InternalRel @ SV23 ) )
| ( related @ SV23 @ SV47 @ SY118 ) )
| ~ ! [SY119: $i] :
( ~ ( element @ SY119 @ ( the_carrier @ SV23 ) )
| ~ ( related @ SV23 @ SV47 @ SY119 )
| ( in @ ( ordered_pair @ SV47 @ SY119 ) @ ( the_InternalRel @ SV23 ) ) ) ) )
= $true )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(305,plain,
! [SV24: $i] :
( ( ( ~ ( ~ ( element @ ( sK7_B @ SV24 ) @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ ( sK7_B @ SV24 ) ) ) )
= $true )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(306,plain,
! [SV24: $i] :
( ( ( finite @ ( sK7_B @ SV24 ) )
= $true )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(307,plain,
! [SV25: $i] :
( ( ( ~ ! [SY109: $i] :
( ~ ( rel_str @ SY109 )
| ~ ( subset @ ( the_carrier @ SY109 ) @ ( the_carrier @ SV25 ) )
| ~ ( subset @ ( the_InternalRel @ SY109 ) @ ( the_InternalRel @ SV25 ) )
| ( subrelstr @ SY109 @ SV25 ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(308,plain,
! [SV25: $i] :
( ( ( ~ ~ ( ~ ! [SY110: $i] :
( ~ ( rel_str @ SY110 )
| ~ ( subrelstr @ SY110 @ SV25 )
| ( subset @ ( the_carrier @ SY110 ) @ ( the_carrier @ SV25 ) ) )
| ~ ! [SY111: $i] :
( ~ ( rel_str @ SY111 )
| ~ ( subrelstr @ SY111 @ SV25 )
| ( subset @ ( the_InternalRel @ SY111 ) @ ( the_InternalRel @ SV25 ) ) ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(309,plain,
! [SV26: $i] :
( ( ( ~ ( ~ ( element @ ( sK8_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK8_B @ SV26 ) ) ) )
= $true )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(310,plain,
! [SV26: $i] :
( ( ( finite @ ( sK8_B @ SV26 ) )
= $true )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(311,plain,
! [SV4: $i,SV43: $i] :
( ( ( element @ SV43 @ ( powerset @ SV4 ) )
= $false )
| ( ( finite @ SV43 )
= $true )
| ( ( finite @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(312,plain,
! [SV6: $i,SV44: $i] :
( ( ( subrelstr @ SV44 @ SV6 )
= $false )
| ( ( rel_str @ SV44 )
= $true )
| ( ( rel_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(313,plain,
! [SV13: $i,SV32: $i] :
( ( ( finite @ SV32 )
= $false )
| ( ( finite @ SV13 )
= $false )
| ( ( finite @ ( cartesian_product2 @ SV13 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(314,plain,
! [SV17: $i,SV41: $i,SV35: $i] :
( ( ( element @ SV35 @ ( powerset @ SV41 ) )
= $false )
| ( ( ~ ( in @ SV17 @ SV35 ) )
= $true )
| ( ( element @ SV17 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(315,plain,
! [SV18: $i,SV42: $i,SV36: $i] :
( ( ( element @ SV36 @ ( powerset @ SV42 ) )
= $false )
| ( ( ~ ( in @ SV18 @ SV36 ) )
= $true )
| ( ( ~ ( empty @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(316,plain,
! [SV21: $i,SV38: $i] :
( ( ( empty @ SV38 )
= $false )
| ( ( SV21 = SV38 )
= $true )
| ( ( empty @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(317,plain,
! [SV48: $i,SV45: $i] :
( ( ( ~ ( element @ SV45 @ ( powerset @ SV48 ) ) )
= $true )
| ( ( subset @ SV45 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(318,plain,
! [SV49: $i,SV46: $i] :
( ( ( ~ ( subset @ SV46 @ SV49 ) )
= $true )
| ( ( element @ SV46 @ ( powerset @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(319,plain,
! [SV50: $i,SV22: $i,SV52: $i] :
( ( ~ ( relation_of2 @ SV52 @ SV22 @ SV50 )
| ( relation_of2_as_subset @ SV52 @ SV22 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(320,plain,
! [SV51: $i,SV22: $i,SV53: $i] :
( ( ~ ( relation_of2_as_subset @ SV53 @ SV22 @ SV51 )
| ( relation_of2 @ SV53 @ SV22 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(321,plain,
( ( element @ sK3_SY74 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(322,plain,
( ( ~ ( ~ ( element @ sK4_SY78 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(323,plain,
! [SV23: $i,SV47: $i] :
( ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( ~ ( ~ ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV23 ) )
| ~ ( in @ ( ordered_pair @ SV47 @ SY118 ) @ ( the_InternalRel @ SV23 ) )
| ( related @ SV23 @ SV47 @ SY118 ) )
| ~ ! [SY119: $i] :
( ~ ( element @ SY119 @ ( the_carrier @ SV23 ) )
| ~ ( related @ SV23 @ SV47 @ SY119 )
| ( in @ ( ordered_pair @ SV47 @ SY119 ) @ ( the_InternalRel @ SV23 ) ) ) ) )
= $true )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(324,plain,
! [SV24: $i] :
( ( ( ~ ( element @ ( sK7_B @ SV24 ) @ ( powerset @ SV24 ) )
| ~ ~ ( empty @ ( sK7_B @ SV24 ) ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(325,plain,
! [SV25: $i] :
( ( ( ! [SY109: $i] :
( ~ ( rel_str @ SY109 )
| ~ ( subset @ ( the_carrier @ SY109 ) @ ( the_carrier @ SV25 ) )
| ~ ( subset @ ( the_InternalRel @ SY109 ) @ ( the_InternalRel @ SV25 ) )
| ( subrelstr @ SY109 @ SV25 ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(326,plain,
! [SV25: $i] :
( ( ( ~ ( ~ ! [SY110: $i] :
( ~ ( rel_str @ SY110 )
| ~ ( subrelstr @ SY110 @ SV25 )
| ( subset @ ( the_carrier @ SY110 ) @ ( the_carrier @ SV25 ) ) )
| ~ ! [SY111: $i] :
( ~ ( rel_str @ SY111 )
| ~ ( subrelstr @ SY111 @ SV25 )
| ( subset @ ( the_InternalRel @ SY111 ) @ ( the_InternalRel @ SV25 ) ) ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(327,plain,
! [SV26: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV26 ) @ ( powerset @ SV26 ) )
| ~ ~ ( empty @ ( sK8_B @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(328,plain,
! [SV41: $i,SV35: $i,SV17: $i] :
( ( ( in @ SV17 @ SV35 )
= $false )
| ( ( element @ SV35 @ ( powerset @ SV41 ) )
= $false )
| ( ( element @ SV17 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(329,plain,
! [SV42: $i,SV36: $i,SV18: $i] :
( ( ( in @ SV18 @ SV36 )
= $false )
| ( ( element @ SV36 @ ( powerset @ SV42 ) )
= $false )
| ( ( ~ ( empty @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(330,plain,
! [SV48: $i,SV45: $i] :
( ( ( element @ SV45 @ ( powerset @ SV48 ) )
= $false )
| ( ( subset @ SV45 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(331,plain,
! [SV49: $i,SV46: $i] :
( ( ( subset @ SV46 @ SV49 )
= $false )
| ( ( element @ SV46 @ ( powerset @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(332,plain,
! [SV50: $i,SV22: $i,SV52: $i] :
( ( ( ~ ( relation_of2 @ SV52 @ SV22 @ SV50 ) )
= $true )
| ( ( relation_of2_as_subset @ SV52 @ SV22 @ SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(333,plain,
! [SV51: $i,SV22: $i,SV53: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV53 @ SV22 @ SV51 ) )
= $true )
| ( ( relation_of2 @ SV53 @ SV22 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(334,plain,
( ( ~ ( element @ sK4_SY78 @ ( the_carrier @ sK1_A ) )
| ~ ~ ( ~ ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(335,plain,
! [SV47: $i,SV23: $i] :
( ( ( ~ ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV23 ) )
| ~ ( in @ ( ordered_pair @ SV47 @ SY118 ) @ ( the_InternalRel @ SV23 ) )
| ( related @ SV23 @ SV47 @ SY118 ) )
| ~ ! [SY119: $i] :
( ~ ( element @ SY119 @ ( the_carrier @ SV23 ) )
| ~ ( related @ SV23 @ SV47 @ SY119 )
| ( in @ ( ordered_pair @ SV47 @ SY119 ) @ ( the_InternalRel @ SV23 ) ) ) )
= $false )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(336,plain,
! [SV24: $i] :
( ( ( ~ ( element @ ( sK7_B @ SV24 ) @ ( powerset @ SV24 ) ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(337,plain,
! [SV24: $i] :
( ( ( ~ ~ ( empty @ ( sK7_B @ SV24 ) ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[324]) ).
thf(338,plain,
! [SV25: $i,SV54: $i] :
( ( ( ~ ( rel_str @ SV54 )
| ~ ( subset @ ( the_carrier @ SV54 ) @ ( the_carrier @ SV25 ) )
| ~ ( subset @ ( the_InternalRel @ SV54 ) @ ( the_InternalRel @ SV25 ) )
| ( subrelstr @ SV54 @ SV25 ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(339,plain,
! [SV25: $i] :
( ( ( ~ ! [SY110: $i] :
( ~ ( rel_str @ SY110 )
| ~ ( subrelstr @ SY110 @ SV25 )
| ( subset @ ( the_carrier @ SY110 ) @ ( the_carrier @ SV25 ) ) )
| ~ ! [SY111: $i] :
( ~ ( rel_str @ SY111 )
| ~ ( subrelstr @ SY111 @ SV25 )
| ( subset @ ( the_InternalRel @ SY111 ) @ ( the_InternalRel @ SV25 ) ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(340,plain,
! [SV26: $i] :
( ( ( ~ ( element @ ( sK8_B @ SV26 ) @ ( powerset @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(341,plain,
! [SV26: $i] :
( ( ( ~ ~ ( empty @ ( sK8_B @ SV26 ) ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[327]) ).
thf(342,plain,
! [SV18: $i,SV36: $i,SV42: $i] :
( ( ( empty @ SV42 )
= $false )
| ( ( element @ SV36 @ ( powerset @ SV42 ) )
= $false )
| ( ( in @ SV18 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(343,plain,
! [SV50: $i,SV22: $i,SV52: $i] :
( ( ( relation_of2 @ SV52 @ SV22 @ SV50 )
= $false )
| ( ( relation_of2_as_subset @ SV52 @ SV22 @ SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(344,plain,
! [SV51: $i,SV22: $i,SV53: $i] :
( ( ( relation_of2_as_subset @ SV53 @ SV22 @ SV51 )
= $false )
| ( ( relation_of2 @ SV53 @ SV22 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(345,plain,
( ( ~ ( element @ sK4_SY78 @ ( the_carrier @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(346,plain,
( ( ~ ~ ( ~ ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(347,plain,
! [SV47: $i,SV23: $i] :
( ( ( ~ ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV23 ) )
| ~ ( in @ ( ordered_pair @ SV47 @ SY118 ) @ ( the_InternalRel @ SV23 ) )
| ( related @ SV23 @ SV47 @ SY118 ) ) )
= $false )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(348,plain,
! [SV47: $i,SV23: $i] :
( ( ( ~ ! [SY119: $i] :
( ~ ( element @ SY119 @ ( the_carrier @ SV23 ) )
| ~ ( related @ SV23 @ SV47 @ SY119 )
| ( in @ ( ordered_pair @ SV47 @ SY119 ) @ ( the_InternalRel @ SV23 ) ) ) )
= $false )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[335]) ).
thf(349,plain,
! [SV24: $i] :
( ( ( element @ ( sK7_B @ SV24 ) @ ( powerset @ SV24 ) )
= $true )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(350,plain,
! [SV24: $i] :
( ( ( ~ ( empty @ ( sK7_B @ SV24 ) ) )
= $true )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(351,plain,
! [SV25: $i,SV54: $i] :
( ( ( ~ ( rel_str @ SV54 ) )
= $true )
| ( ( ~ ( subset @ ( the_carrier @ SV54 ) @ ( the_carrier @ SV25 ) )
| ~ ( subset @ ( the_InternalRel @ SV54 ) @ ( the_InternalRel @ SV25 ) )
| ( subrelstr @ SV54 @ SV25 ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(352,plain,
! [SV25: $i] :
( ( ( ~ ! [SY110: $i] :
( ~ ( rel_str @ SY110 )
| ~ ( subrelstr @ SY110 @ SV25 )
| ( subset @ ( the_carrier @ SY110 ) @ ( the_carrier @ SV25 ) ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(353,plain,
! [SV25: $i] :
( ( ( ~ ! [SY111: $i] :
( ~ ( rel_str @ SY111 )
| ~ ( subrelstr @ SY111 @ SV25 )
| ( subset @ ( the_InternalRel @ SY111 ) @ ( the_InternalRel @ SV25 ) ) ) )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[339]) ).
thf(354,plain,
! [SV26: $i] :
( ( ( element @ ( sK8_B @ SV26 ) @ ( powerset @ SV26 ) )
= $true )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(355,plain,
! [SV26: $i] :
( ( ( ~ ( empty @ ( sK8_B @ SV26 ) ) )
= $true )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(356,plain,
( ( element @ sK4_SY78 @ ( the_carrier @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(357,plain,
( ( ~ ( ~ ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(358,plain,
! [SV47: $i,SV23: $i] :
( ( ( ! [SY118: $i] :
( ~ ( element @ SY118 @ ( the_carrier @ SV23 ) )
| ~ ( in @ ( ordered_pair @ SV47 @ SY118 ) @ ( the_InternalRel @ SV23 ) )
| ( related @ SV23 @ SV47 @ SY118 ) ) )
= $true )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(359,plain,
! [SV47: $i,SV23: $i] :
( ( ( ! [SY119: $i] :
( ~ ( element @ SY119 @ ( the_carrier @ SV23 ) )
| ~ ( related @ SV23 @ SV47 @ SY119 )
| ( in @ ( ordered_pair @ SV47 @ SY119 ) @ ( the_InternalRel @ SV23 ) ) ) )
= $true )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(360,plain,
! [SV24: $i] :
( ( ( empty @ ( sK7_B @ SV24 ) )
= $false )
| ( ( empty @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(361,plain,
! [SV25: $i,SV54: $i] :
( ( ( rel_str @ SV54 )
= $false )
| ( ( ~ ( subset @ ( the_carrier @ SV54 ) @ ( the_carrier @ SV25 ) )
| ~ ( subset @ ( the_InternalRel @ SV54 ) @ ( the_InternalRel @ SV25 ) )
| ( subrelstr @ SV54 @ SV25 ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(362,plain,
! [SV25: $i] :
( ( ( ! [SY110: $i] :
( ~ ( rel_str @ SY110 )
| ~ ( subrelstr @ SY110 @ SV25 )
| ( subset @ ( the_carrier @ SY110 ) @ ( the_carrier @ SV25 ) ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(363,plain,
! [SV25: $i] :
( ( ( ! [SY111: $i] :
( ~ ( rel_str @ SY111 )
| ~ ( subrelstr @ SY111 @ SV25 )
| ( subset @ ( the_InternalRel @ SY111 ) @ ( the_InternalRel @ SV25 ) ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(364,plain,
! [SV26: $i] :
( ( ( empty @ ( sK8_B @ SV26 ) )
= $false )
| ( ( empty @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(365,plain,
( ( ~ ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(366,plain,
! [SV47: $i,SV23: $i,SV55: $i] :
( ( ( ~ ( element @ SV55 @ ( the_carrier @ SV23 ) )
| ~ ( in @ ( ordered_pair @ SV47 @ SV55 ) @ ( the_InternalRel @ SV23 ) )
| ( related @ SV23 @ SV47 @ SV55 ) )
= $true )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(367,plain,
! [SV47: $i,SV23: $i,SV56: $i] :
( ( ( ~ ( element @ SV56 @ ( the_carrier @ SV23 ) )
| ~ ( related @ SV23 @ SV47 @ SV56 )
| ( in @ ( ordered_pair @ SV47 @ SV56 ) @ ( the_InternalRel @ SV23 ) ) )
= $true )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(368,plain,
! [SV25: $i,SV54: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV54 ) @ ( the_carrier @ SV25 ) )
| ~ ( subset @ ( the_InternalRel @ SV54 ) @ ( the_InternalRel @ SV25 ) ) )
= $true )
| ( ( subrelstr @ SV54 @ SV25 )
= $true )
| ( ( rel_str @ SV54 )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(369,plain,
! [SV25: $i,SV57: $i] :
( ( ( ~ ( rel_str @ SV57 )
| ~ ( subrelstr @ SV57 @ SV25 )
| ( subset @ ( the_carrier @ SV57 ) @ ( the_carrier @ SV25 ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(370,plain,
! [SV25: $i,SV58: $i] :
( ( ( ~ ( rel_str @ SV58 )
| ~ ( subrelstr @ SV58 @ SV25 )
| ( subset @ ( the_InternalRel @ SV58 ) @ ( the_InternalRel @ SV25 ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(371,plain,
( ( ~ ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(372,plain,
( ( ~ ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[365]) ).
thf(373,plain,
! [SV47: $i,SV23: $i,SV55: $i] :
( ( ( ~ ( element @ SV55 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV55 ) @ ( the_InternalRel @ SV23 ) )
| ( related @ SV23 @ SV47 @ SV55 ) )
= $true )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(374,plain,
! [SV47: $i,SV23: $i,SV56: $i] :
( ( ( ~ ( element @ SV56 @ ( the_carrier @ SV23 ) ) )
= $true )
| ( ( ~ ( related @ SV23 @ SV47 @ SV56 )
| ( in @ ( ordered_pair @ SV47 @ SV56 ) @ ( the_InternalRel @ SV23 ) ) )
= $true )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(375,plain,
! [SV25: $i,SV54: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV54 ) @ ( the_carrier @ SV25 ) ) )
= $true )
| ( ( ~ ( subset @ ( the_InternalRel @ SV54 ) @ ( the_InternalRel @ SV25 ) ) )
= $true )
| ( ( subrelstr @ SV54 @ SV25 )
= $true )
| ( ( rel_str @ SV54 )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(376,plain,
! [SV25: $i,SV57: $i] :
( ( ( ~ ( rel_str @ SV57 ) )
= $true )
| ( ( ~ ( subrelstr @ SV57 @ SV25 )
| ( subset @ ( the_carrier @ SV57 ) @ ( the_carrier @ SV25 ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(377,plain,
! [SV25: $i,SV58: $i] :
( ( ( ~ ( rel_str @ SV58 ) )
= $true )
| ( ( ~ ( subrelstr @ SV58 @ SV25 )
| ( subset @ ( the_InternalRel @ SV58 ) @ ( the_InternalRel @ SV25 ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(378,plain,
( ( element @ sK5_SY81 @ ( the_carrier @ sK2_SY69 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(379,plain,
( ( ~ ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(380,plain,
! [SV47: $i,SV23: $i,SV55: $i] :
( ( ( element @ SV55 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV55 ) @ ( the_InternalRel @ SV23 ) )
| ( related @ SV23 @ SV47 @ SV55 ) )
= $true )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(381,plain,
! [SV47: $i,SV23: $i,SV56: $i] :
( ( ( element @ SV56 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( ~ ( related @ SV23 @ SV47 @ SV56 )
| ( in @ ( ordered_pair @ SV47 @ SV56 ) @ ( the_InternalRel @ SV23 ) ) )
= $true )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(382,plain,
! [SV25: $i,SV54: $i] :
( ( ( subset @ ( the_carrier @ SV54 ) @ ( the_carrier @ SV25 ) )
= $false )
| ( ( ~ ( subset @ ( the_InternalRel @ SV54 ) @ ( the_InternalRel @ SV25 ) ) )
= $true )
| ( ( subrelstr @ SV54 @ SV25 )
= $true )
| ( ( rel_str @ SV54 )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(383,plain,
! [SV25: $i,SV57: $i] :
( ( ( rel_str @ SV57 )
= $false )
| ( ( ~ ( subrelstr @ SV57 @ SV25 )
| ( subset @ ( the_carrier @ SV57 ) @ ( the_carrier @ SV25 ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(384,plain,
! [SV25: $i,SV58: $i] :
( ( ( rel_str @ SV58 )
= $false )
| ( ( ~ ( subrelstr @ SV58 @ SV25 )
| ( subset @ ( the_InternalRel @ SV58 ) @ ( the_InternalRel @ SV25 ) ) )
= $true )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(385,plain,
( ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
| ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(386,plain,
! [SV23: $i,SV55: $i,SV47: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV47 @ SV55 ) @ ( the_InternalRel @ SV23 ) ) )
= $true )
| ( ( related @ SV23 @ SV47 @ SV55 )
= $true )
| ( ( element @ SV55 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(387,plain,
! [SV56: $i,SV47: $i,SV23: $i] :
( ( ( ~ ( related @ SV23 @ SV47 @ SV56 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV47 @ SV56 ) @ ( the_InternalRel @ SV23 ) )
= $true )
| ( ( element @ SV56 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(388,plain,
! [SV25: $i,SV54: $i] :
( ( ( subset @ ( the_InternalRel @ SV54 ) @ ( the_InternalRel @ SV25 ) )
= $false )
| ( ( subset @ ( the_carrier @ SV54 ) @ ( the_carrier @ SV25 ) )
= $false )
| ( ( subrelstr @ SV54 @ SV25 )
= $true )
| ( ( rel_str @ SV54 )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(389,plain,
! [SV25: $i,SV57: $i] :
( ( ( ~ ( subrelstr @ SV57 @ SV25 ) )
= $true )
| ( ( subset @ ( the_carrier @ SV57 ) @ ( the_carrier @ SV25 ) )
= $true )
| ( ( rel_str @ SV57 )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(390,plain,
! [SV25: $i,SV58: $i] :
( ( ( ~ ( subrelstr @ SV58 @ SV25 ) )
= $true )
| ( ( subset @ ( the_InternalRel @ SV58 ) @ ( the_InternalRel @ SV25 ) )
= $true )
| ( ( rel_str @ SV58 )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(391,plain,
( ( ~ ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(392,plain,
( ( ~ ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(393,plain,
! [SV23: $i,SV55: $i,SV47: $i] :
( ( ( in @ ( ordered_pair @ SV47 @ SV55 ) @ ( the_InternalRel @ SV23 ) )
= $false )
| ( ( related @ SV23 @ SV47 @ SV55 )
= $true )
| ( ( element @ SV55 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(394,plain,
! [SV56: $i,SV47: $i,SV23: $i] :
( ( ( related @ SV23 @ SV47 @ SV56 )
= $false )
| ( ( in @ ( ordered_pair @ SV47 @ SV56 ) @ ( the_InternalRel @ SV23 ) )
= $true )
| ( ( element @ SV56 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( element @ SV47 @ ( the_carrier @ SV23 ) )
= $false )
| ( ( rel_str @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(395,plain,
! [SV25: $i,SV57: $i] :
( ( ( subrelstr @ SV57 @ SV25 )
= $false )
| ( ( subset @ ( the_carrier @ SV57 ) @ ( the_carrier @ SV25 ) )
= $true )
| ( ( rel_str @ SV57 )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(396,plain,
! [SV25: $i,SV58: $i] :
( ( ( subrelstr @ SV58 @ SV25 )
= $false )
| ( ( subset @ ( the_InternalRel @ SV58 ) @ ( the_InternalRel @ SV25 ) )
= $true )
| ( ( rel_str @ SV58 )
= $false )
| ( ( rel_str @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(397,plain,
( ( element @ sK6_SY83 @ ( the_carrier @ sK2_SY69 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(398,plain,
( ( ~ ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(399,plain,
( ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
| ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(400,plain,
( ( ~ ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(401,plain,
( ( ~ ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(402,plain,
( ( ~ ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(403,plain,
( ( ~ ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(404,plain,
( ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
| ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(405,plain,
( ( related @ sK1_A @ sK3_SY74 @ sK4_SY78 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(406,plain,
( ( ~ ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(407,plain,
( ( ~ ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(408,plain,
( ( ~ ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[406]) ).
thf(409,plain,
( ( related @ sK2_SY69 @ sK5_SY81 @ sK6_SY83 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[407]) ).
thf(410,plain,
( ( ( sK5_SY81 != sK3_SY74 )
| ( sK6_SY83 != sK4_SY78 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(411,plain,
( ( ( sK5_SY81 != sK3_SY74 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(412,plain,
( ( ( sK6_SY83 != sK4_SY78 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(413,plain,
( ( sK5_SY81 = sK3_SY74 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(414,plain,
( ( sK6_SY83 = sK4_SY78 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(415,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[129,414,413,409,405,397,396,395,394,393,388,378,364,360,356,354,349,344,343,342,331,330,328,321,316,313,312,311,310,306,296,293,291,288,287,275,269,257,252,248,242,241,238,235,214,212,188,187,183,164,150,148,142,141,140,136,135,134,132,131,130]) ).
thf(416,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU362+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 00:27:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.37
% 0.13/0.37 No.of.Axioms: 41
% 0.13/0.37
% 0.13/0.37 Length.of.Defs: 0
% 0.13/0.37
% 0.13/0.37 Contains.Choice.Funs: false
% 0.13/0.38 .
% 0.13/0.39 (rf:0,axioms:41,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:43,loop_count:0,foatp_calls:0,translation:fof_full)....................
% 35.79/36.03
% 35.79/36.03 ********************************
% 35.79/36.03 * All subproblems solved! *
% 35.79/36.03 ********************************
% 35.79/36.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:42,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:415,loop_count:0,foatp_calls:1,translation:fof_full)
% 35.89/36.08
% 35.89/36.08 %**** Beginning of derivation protocol ****
% 35.89/36.08 % SZS output start CNFRefutation
% See solution above
% 35.89/36.08
% 35.89/36.08 %**** End of derivation protocol ****
% 35.89/36.08 %**** no. of clauses in derivation: 416 ****
% 35.89/36.08 %**** clause counter: 415 ****
% 35.89/36.08
% 35.89/36.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:42,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:415,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------