%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU374+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:44:11 AM UTC 2026
% Result : Theorem 1.11s 0.43s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 26
% Syntax : Number of formulae : 315 ( 177 unt; 0 typ; 0 def)
% Number of atoms : 2434 ( 765 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 4711 ( 932 ~; 741 |; 44 &;2866 @)
% ( 6 <=>; 122 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 37 usr; 11 con; 0-4 aty)
% Number of variables : 774 ( 0 ^; 756 !; 18 ?; 774 :)
% 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_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_net_str,type,
net_str: $i > $i > $o ).
thf(tp_one_sorted_str,type,
one_sorted_str: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_quasi_total,type,
quasi_total: $i > $i > $i > $o ).
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_dom_restr_as_relation_of,type,
relation_dom_restr_as_relation_of: $i > $i > $i > $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $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_SY105,type,
sK10_SY105: $i ).
thf(tp_sK11_SY111,type,
sK11_SY111: $i ).
thf(tp_sK12_SY95,type,
sK12_SY95: $i > $i > $i ).
thf(tp_sK13_SY115,type,
sK13_SY115: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY74,type,
sK4_SY74: $i > $i ).
thf(tp_sK5_SY84,type,
sK5_SY84: $i > $i ).
thf(tp_sK6_SY87,type,
sK6_SY87: $i ).
thf(tp_sK7_SY83,type,
sK7_SY83: $i > $i ).
thf(tp_sK8_SY101,type,
sK8_SY101: $i ).
thf(tp_sK9_SY73,type,
sK9_SY73: $i > $i ).
thf(tp_subnetstr,type,
subnetstr: $i > $i > $i > $o ).
thf(tp_subrelstr,type,
subrelstr: $i > $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_the_mapping,type,
the_mapping: $i > $i > $i ).
thf(4,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',t60_yellow_0) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(16,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(19,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( subnetstr @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_yellow_6) ).
thf(32,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(34,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(35,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(38,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( net_str @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_6) ).
thf(42,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(43,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(44,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(45,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(46,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(49,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(50,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(51,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(52,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( net_str @ C @ A )
=> ( ( subnetstr @ C @ A @ B )
<=> ( ( subrelstr @ C @ B )
& ( ( the_mapping @ A @ C )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_yellow_6) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(58,conjecture,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ C ) )
=> ! [G: $i] :
( ( element @ G @ ( the_carrier @ C ) )
=> ( ( ( D = F )
& ( E = G )
& ( related @ C @ F @ G ) )
=> ( related @ B @ D @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_yellow_6) ).
thf(59,negated_conjecture,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ C ) )
=> ! [G: $i] :
( ( element @ G @ ( the_carrier @ C ) )
=> ( ( ( D = F )
& ( E = G )
& ( related @ C @ F @ G ) )
=> ( related @ B @ D @ E ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[58]) ).
thf(60,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ B ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ B ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ C ) )
=> ! [G: $i] :
( ( element @ G @ ( the_carrier @ C ) )
=> ( ( ( D = F )
& ( E = G )
& ( related @ C @ F @ G ) )
=> ( related @ B @ D @ E ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[59]) ).
thf(61,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 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(62,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(63,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(64,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(67,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(68,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( subnetstr @ C @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(70,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(71,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(72,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(73,plain,
$true = $true,
inference(unfold_def,[status(thm)],[38]) ).
thf(74,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)],[39]) ).
thf(75,plain,
( ( ! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( net_str @ C @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(76,plain,
$true = $true,
inference(unfold_def,[status(thm)],[42]) ).
thf(77,plain,
$true = $true,
inference(unfold_def,[status(thm)],[43]) ).
thf(78,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(79,plain,
$true = $true,
inference(unfold_def,[status(thm)],[45]) ).
thf(80,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(81,plain,
$true = $true,
inference(unfold_def,[status(thm)],[49]) ).
thf(82,plain,
$true = $true,
inference(unfold_def,[status(thm)],[50]) ).
thf(83,plain,
$true = $true,
inference(unfold_def,[status(thm)],[51]) ).
thf(84,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( net_str @ C @ A )
=> ( ( subnetstr @ C @ A @ B )
<=> ( ( subrelstr @ C @ B )
& ( ( the_mapping @ A @ C )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ C ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(85,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(86,plain,
( ( ( one_sorted_str @ sK1_A )
=> ! [SY52: $i] :
( ( net_str @ SY52 @ sK1_A )
=> ! [SY53: $i] :
( ( subnetstr @ SY53 @ sK1_A @ SY52 )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ SY52 ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ SY52 ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ SY53 ) )
=> ! [G: $i] :
( ( element @ G @ ( the_carrier @ SY53 ) )
=> ( ( ( D = F )
& ( E = G )
& ( related @ SY53 @ F @ G ) )
=> ( related @ SY52 @ D @ E ) ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[60]) ).
thf(87,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(88,plain,
( ( ! [SY52: $i] :
( ( net_str @ SY52 @ sK1_A )
=> ! [SY53: $i] :
( ( subnetstr @ SY53 @ sK1_A @ SY52 )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ SY52 ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ SY52 ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ SY53 ) )
=> ! [G: $i] :
( ( element @ G @ ( the_carrier @ SY53 ) )
=> ( ( ( D = F )
& ( E = G )
& ( related @ SY53 @ F @ G ) )
=> ( related @ SY52 @ D @ E ) ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[86]) ).
thf(89,plain,
( ( ~ ! [SY52: $i] :
( ( net_str @ SY52 @ sK1_A )
=> ! [SY53: $i] :
( ( subnetstr @ SY53 @ sK1_A @ SY52 )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ SY52 ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ SY52 ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ SY53 ) )
=> ! [G: $i] :
( ( element @ G @ ( the_carrier @ SY53 ) )
=> ( ( ( D = F )
& ( E = G )
& ( related @ SY53 @ F @ G ) )
=> ( related @ SY52 @ D @ E ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[88]) ).
thf(90,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(91,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( net_str @ C @ A )
=> ( ( subnetstr @ C @ A @ B )
<=> ( ( subrelstr @ C @ B )
& ( ( the_mapping @ A @ C )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ B ) @ ( the_carrier @ A ) @ ( the_mapping @ A @ B ) @ ( the_carrier @ C ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(92,plain,
$true = $true,
inference(copy,[status(thm)],[83]) ).
thf(93,plain,
$true = $true,
inference(copy,[status(thm)],[82]) ).
thf(94,plain,
$true = $true,
inference(copy,[status(thm)],[81]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(96,plain,
$true = $true,
inference(copy,[status(thm)],[79]) ).
thf(97,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(98,plain,
$true = $true,
inference(copy,[status(thm)],[77]) ).
thf(99,plain,
$true = $true,
inference(copy,[status(thm)],[76]) ).
thf(100,plain,
( ( ! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( net_str @ C @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(101,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)],[74]) ).
thf(102,plain,
$true = $true,
inference(copy,[status(thm)],[73]) ).
thf(103,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(104,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(105,plain,
( ( ! [A: $i] :
? [B: $i] : ( element @ B @ A ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(106,plain,
( ( ! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( subnetstr @ C @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(107,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(108,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(109,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(110,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(112,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(113,plain,
( ( ! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(114,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 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(115,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(116,plain,
( ( ~ ! [SY52: $i] :
( ( net_str @ SY52 @ sK1_A )
=> ! [SY53: $i] :
( ( subnetstr @ SY53 @ sK1_A @ SY52 )
=> ! [D: $i] :
( ( element @ D @ ( the_carrier @ SY52 ) )
=> ! [E: $i] :
( ( element @ E @ ( the_carrier @ SY52 ) )
=> ! [F: $i] :
( ( element @ F @ ( the_carrier @ SY53 ) )
=> ! [G: $i] :
( ( element @ G @ ( the_carrier @ SY53 ) )
=> ( ( ( D = F )
& ( E = G )
& ( related @ SY53 @ F @ G ) )
=> ( related @ SY52 @ D @ E ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(117,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(118,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( subrelstr @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ! [SX4: $i] :
( ~ ( element @ SX4 @ ( the_carrier @ SX1 ) )
| ! [SX5: $i] :
( ~ ( element @ SX5 @ ( the_carrier @ SX1 ) )
| ~ ~ ( ~ ~ ( ( SX4 != SX2 )
| ( SX5 != SX3 ) )
| ~ ( related @ SX1 @ SX4 @ SX5 ) )
| ( related @ SX0 @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(119,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ! [SX1: $i] :
( ~ ( net_str @ SX1 @ SX0 )
| ( rel_str @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(120,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ! [SX1: $i] :
( ~ ( net_str @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( net_str @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( subnetstr @ SX2 @ SX0 @ SX1 )
| ~ ( ~ ( subrelstr @ SX2 @ SX1 )
| ( ( the_mapping @ SX0 @ SX2 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) @ ( the_mapping @ SX0 @ SX1 ) @ ( the_carrier @ SX2 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SX2 @ SX1 )
| ( ( the_mapping @ SX0 @ SX2 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) @ ( the_mapping @ SX0 @ SX1 ) @ ( the_carrier @ SX2 ) ) ) )
| ( subnetstr @ SX2 @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(121,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ( element @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(122,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( element @ SX1 @ ( powerset @ SX2 ) ) )
| ~ ( empty @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(123,plain,
( ( ~ ! [SX0: $i] :
( ~ ( net_str @ SX0 @ sK1_A )
| ! [SX1: $i] :
( ~ ( subnetstr @ SX1 @ sK1_A @ SX0 )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ! [SX4: $i] :
( ~ ( element @ SX4 @ ( the_carrier @ SX1 ) )
| ! [SX5: $i] :
( ~ ( element @ SX5 @ ( the_carrier @ SX1 ) )
| ~ ~ ( ~ ~ ( ( SX2 != SX4 )
| ( SX3 != SX5 ) )
| ~ ( related @ SX1 @ SX4 @ SX5 ) )
| ( related @ SX0 @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(124,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( element @ SX0 @ SX1 )
| ( empty @ SX1 )
| ( in @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(125,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( element @ SX2 @ ( powerset @ ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ( relation @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(126,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(127,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ( element @ SX1 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(128,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ( net_str @ SX1 @ SX0 ) )
| ! [SX2: $i] :
( ~ ( subnetstr @ SX2 @ SX0 @ SX1 )
| ( net_str @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ( element @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation_of2_as_subset @ SX2 @ SX0 @ SX1 )
| ( element @ SX2 @ ( powerset @ ( cartesian_product2 @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(132,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( one_sorted_str @ SX0 )
| ~ ( net_str @ SX1 @ SX0 ) )
| ~ ! [SX2: $i] :
~ ( subnetstr @ SX2 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(133,plain,
( ( ~ ! [SX0: $i] :
~ ( one_sorted_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(134,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ~ ! [SX1: $i] :
~ ( net_str @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(135,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ( empty @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(136,plain,
! [SV1: $i] :
( ( ~ ( rel_str @ SV1 )
| ( one_sorted_str @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(137,plain,
! [SV2: $i] :
( ( ~ ( rel_str @ SV2 )
| ! [SY58: $i] :
( ~ ( subrelstr @ SY58 @ SV2 )
| ! [SY59: $i] :
( ~ ( element @ SY59 @ ( the_carrier @ SV2 ) )
| ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV2 ) )
| ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SY58 ) )
| ! [SY62: $i] :
( ~ ( element @ SY62 @ ( the_carrier @ SY58 ) )
| ~ ~ ( ~ ~ ( ( SY61 != SY59 )
| ( SY62 != SY60 ) )
| ~ ( related @ SY58 @ SY61 @ SY62 ) )
| ( related @ SV2 @ SY59 @ SY60 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(138,plain,
! [SV3: $i] :
( ( ~ ( one_sorted_str @ SV3 )
| ! [SY63: $i] :
( ~ ( net_str @ SY63 @ SV3 )
| ( rel_str @ SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(139,plain,
! [SV4: $i] :
( ( ~ ( one_sorted_str @ SV4 )
| ! [SY64: $i] :
( ~ ( net_str @ SY64 @ SV4 )
| ! [SY65: $i] :
( ~ ( net_str @ SY65 @ SV4 )
| ~ ( ~ ( ~ ( subnetstr @ SY65 @ SV4 @ SY64 )
| ~ ( ~ ( subrelstr @ SY65 @ SY64 )
| ( ( the_mapping @ SV4 @ SY65 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY64 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SY64 ) @ ( the_carrier @ SY65 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY65 @ SY64 )
| ( ( the_mapping @ SV4 @ SY65 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY64 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SY64 ) @ ( the_carrier @ SY65 ) ) ) )
| ( subnetstr @ SY65 @ SV4 @ SY64 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(140,plain,
! [SV5: $i] :
( ( ! [SY66: $i,SY67: $i] :
( ~ ~ ( ~ ( in @ SV5 @ SY66 )
| ~ ( element @ SY66 @ ( powerset @ SY67 ) ) )
| ( element @ SV5 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(141,plain,
! [SV6: $i] :
( ( ! [SY68: $i,SY69: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV6 @ SY68 )
| ~ ( element @ SY68 @ ( powerset @ SY69 ) ) )
| ~ ( empty @ SY69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(142,plain,
( ( ! [SX0: $i] :
( ~ ( net_str @ SX0 @ sK1_A )
| ! [SX1: $i] :
( ~ ( subnetstr @ SX1 @ sK1_A @ SX0 )
| ! [SX2: $i] :
( ~ ( element @ SX2 @ ( the_carrier @ SX0 ) )
| ! [SX3: $i] :
( ~ ( element @ SX3 @ ( the_carrier @ SX0 ) )
| ! [SX4: $i] :
( ~ ( element @ SX4 @ ( the_carrier @ SX1 ) )
| ! [SX5: $i] :
( ~ ( element @ SX5 @ ( the_carrier @ SX1 ) )
| ~ ~ ( ~ ~ ( ( SX2 != SX4 )
| ( SX3 != SX5 ) )
| ~ ( related @ SX1 @ SX4 @ SX5 ) )
| ( related @ SX0 @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(143,plain,
! [SV7: $i] :
( ( ! [SY70: $i] :
( ~ ( element @ SV7 @ SY70 )
| ( empty @ SY70 )
| ( in @ SV7 @ SY70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(144,plain,
! [SV8: $i] :
( ( ! [SY71: $i,SY72: $i] :
( ~ ( element @ SY72 @ ( powerset @ ( cartesian_product2 @ SV8 @ SY71 ) ) )
| ( relation @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(145,plain,
! [SV9: $i] :
( ( ~ ~ ( empty @ SV9 )
| ~ ! [SY73: $i] :
~ ~ ( ~ ( element @ SY73 @ ( powerset @ SV9 ) )
| ~ ~ ( empty @ SY73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(146,plain,
! [SV10: $i] :
( ( ~ ! [SY74: $i] :
~ ( element @ SY74 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(147,plain,
! [SV11: $i] :
( ( ! [SY75: $i] :
( ~ ~ ( ~ ( one_sorted_str @ SV11 )
| ~ ( net_str @ SY75 @ SV11 ) )
| ! [SY76: $i] :
( ~ ( subnetstr @ SY76 @ SV11 @ SY75 )
| ( net_str @ SY76 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(148,plain,
! [SV12: $i] :
( ( ! [SY77: $i] :
( ~ ( in @ SV12 @ SY77 )
| ( element @ SV12 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(149,plain,
! [SV13: $i] :
( ( ! [SY78: $i,SY79: $i] :
( ~ ( relation_of2_as_subset @ SY79 @ SV13 @ SY78 )
| ( element @ SY79 @ ( powerset @ ( cartesian_product2 @ SV13 @ SY78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(150,plain,
! [SV14: $i] :
( ( ! [SY80: $i] :
~ ( ~ ( ~ ( element @ SV14 @ ( powerset @ SY80 ) )
| ( subset @ SV14 @ SY80 ) )
| ~ ( ~ ( subset @ SV14 @ SY80 )
| ( element @ SV14 @ ( powerset @ SY80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(151,plain,
! [SV15: $i] :
( ( ! [SY81: $i] :
( ~ ~ ( ~ ( one_sorted_str @ SV15 )
| ~ ( net_str @ SY81 @ SV15 ) )
| ~ ! [SY82: $i] :
~ ( subnetstr @ SY82 @ SV15 @ SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(152,plain,
( ( ! [SX0: $i] :
~ ( one_sorted_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(153,plain,
! [SV16: $i] :
( ( ~ ( one_sorted_str @ SV16 )
| ~ ! [SY83: $i] :
~ ( net_str @ SY83 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(154,plain,
! [SV17: $i] :
( ( ~ ! [SY84: $i] :
~ ~ ( ~ ( element @ SY84 @ ( powerset @ SV17 ) )
| ~ ( empty @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(155,plain,
! [SV1: $i] :
( ( ( ~ ( rel_str @ SV1 ) )
= $true )
| ( ( one_sorted_str @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(156,plain,
! [SV2: $i] :
( ( ( ~ ( rel_str @ SV2 ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( subrelstr @ SY58 @ SV2 )
| ! [SY59: $i] :
( ~ ( element @ SY59 @ ( the_carrier @ SV2 ) )
| ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV2 ) )
| ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SY58 ) )
| ! [SY62: $i] :
( ~ ( element @ SY62 @ ( the_carrier @ SY58 ) )
| ~ ~ ( ~ ~ ( ( SY61 != SY59 )
| ( SY62 != SY60 ) )
| ~ ( related @ SY58 @ SY61 @ SY62 ) )
| ( related @ SV2 @ SY59 @ SY60 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(157,plain,
! [SV3: $i] :
( ( ( ~ ( one_sorted_str @ SV3 ) )
= $true )
| ( ( ! [SY63: $i] :
( ~ ( net_str @ SY63 @ SV3 )
| ( rel_str @ SY63 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(158,plain,
! [SV4: $i] :
( ( ( ~ ( one_sorted_str @ SV4 ) )
= $true )
| ( ( ! [SY64: $i] :
( ~ ( net_str @ SY64 @ SV4 )
| ! [SY65: $i] :
( ~ ( net_str @ SY65 @ SV4 )
| ~ ( ~ ( ~ ( subnetstr @ SY65 @ SV4 @ SY64 )
| ~ ( ~ ( subrelstr @ SY65 @ SY64 )
| ( ( the_mapping @ SV4 @ SY65 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY64 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SY64 ) @ ( the_carrier @ SY65 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY65 @ SY64 )
| ( ( the_mapping @ SV4 @ SY65 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY64 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SY64 ) @ ( the_carrier @ SY65 ) ) ) )
| ( subnetstr @ SY65 @ SV4 @ SY64 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(159,plain,
! [SV18: $i,SV5: $i] :
( ( ! [SY85: $i] :
( ~ ~ ( ~ ( in @ SV5 @ SV18 )
| ~ ( element @ SV18 @ ( powerset @ SY85 ) ) )
| ( element @ SV5 @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(160,plain,
! [SV19: $i,SV6: $i] :
( ( ! [SY86: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SV6 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SY86 ) ) )
| ~ ( empty @ SY86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(161,plain,
( ( ~ ( net_str @ sK2_SX0 @ sK1_A )
| ! [SY87: $i] :
( ~ ( subnetstr @ SY87 @ sK1_A @ sK2_SX0 )
| ! [SY88: $i] :
( ~ ( element @ SY88 @ ( the_carrier @ sK2_SX0 ) )
| ! [SY89: $i] :
( ~ ( element @ SY89 @ ( the_carrier @ sK2_SX0 ) )
| ! [SY90: $i] :
( ~ ( element @ SY90 @ ( the_carrier @ SY87 ) )
| ! [SY91: $i] :
( ~ ( element @ SY91 @ ( the_carrier @ SY87 ) )
| ~ ~ ( ~ ~ ( ( SY88 != SY90 )
| ( SY89 != SY91 ) )
| ~ ( related @ SY87 @ SY90 @ SY91 ) )
| ( related @ sK2_SX0 @ SY88 @ SY89 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[142]) ).
thf(162,plain,
! [SV20: $i,SV7: $i] :
( ( ~ ( element @ SV7 @ SV20 )
| ( empty @ SV20 )
| ( in @ SV7 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(163,plain,
! [SV21: $i,SV8: $i] :
( ( ! [SY92: $i] :
( ~ ( element @ SY92 @ ( powerset @ ( cartesian_product2 @ SV8 @ SV21 ) ) )
| ( relation @ SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(164,plain,
! [SV9: $i] :
( ( ( ~ ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( element @ SY73 @ ( powerset @ SV9 ) )
| ~ ~ ( empty @ SY73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(165,plain,
! [SV10: $i] :
( ( ! [SY74: $i] :
~ ( element @ SY74 @ SV10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(166,plain,
! [SV22: $i,SV11: $i] :
( ( ~ ~ ( ~ ( one_sorted_str @ SV11 )
| ~ ( net_str @ SV22 @ SV11 ) )
| ! [SY93: $i] :
( ~ ( subnetstr @ SY93 @ SV11 @ SV22 )
| ( net_str @ SY93 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(167,plain,
! [SV23: $i,SV12: $i] :
( ( ~ ( in @ SV12 @ SV23 )
| ( element @ SV12 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(168,plain,
! [SV24: $i,SV13: $i] :
( ( ! [SY94: $i] :
( ~ ( relation_of2_as_subset @ SY94 @ SV13 @ SV24 )
| ( element @ SY94 @ ( powerset @ ( cartesian_product2 @ SV13 @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(169,plain,
! [SV25: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( element @ SV14 @ ( powerset @ SV25 ) )
| ( subset @ SV14 @ SV25 ) )
| ~ ( ~ ( subset @ SV14 @ SV25 )
| ( element @ SV14 @ ( powerset @ SV25 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(170,plain,
! [SV26: $i,SV15: $i] :
( ( ~ ~ ( ~ ( one_sorted_str @ SV15 )
| ~ ( net_str @ SV26 @ SV15 ) )
| ~ ! [SY95: $i] :
~ ( subnetstr @ SY95 @ SV15 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(171,plain,
( ( ~ ( one_sorted_str @ sK3_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[152]) ).
thf(172,plain,
! [SV16: $i] :
( ( ( ~ ( one_sorted_str @ SV16 ) )
= $true )
| ( ( ~ ! [SY83: $i] :
~ ( net_str @ SY83 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(173,plain,
! [SV17: $i] :
( ( ! [SY84: $i] :
~ ~ ( ~ ( element @ SY84 @ ( powerset @ SV17 ) )
| ~ ( empty @ SY84 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(174,plain,
! [SV1: $i] :
( ( ( rel_str @ SV1 )
= $false )
| ( ( one_sorted_str @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(175,plain,
! [SV2: $i] :
( ( ( rel_str @ SV2 )
= $false )
| ( ( ! [SY58: $i] :
( ~ ( subrelstr @ SY58 @ SV2 )
| ! [SY59: $i] :
( ~ ( element @ SY59 @ ( the_carrier @ SV2 ) )
| ! [SY60: $i] :
( ~ ( element @ SY60 @ ( the_carrier @ SV2 ) )
| ! [SY61: $i] :
( ~ ( element @ SY61 @ ( the_carrier @ SY58 ) )
| ! [SY62: $i] :
( ~ ( element @ SY62 @ ( the_carrier @ SY58 ) )
| ~ ~ ( ~ ~ ( ( SY61 != SY59 )
| ( SY62 != SY60 ) )
| ~ ( related @ SY58 @ SY61 @ SY62 ) )
| ( related @ SV2 @ SY59 @ SY60 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(176,plain,
! [SV3: $i] :
( ( ( one_sorted_str @ SV3 )
= $false )
| ( ( ! [SY63: $i] :
( ~ ( net_str @ SY63 @ SV3 )
| ( rel_str @ SY63 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(177,plain,
! [SV4: $i] :
( ( ( one_sorted_str @ SV4 )
= $false )
| ( ( ! [SY64: $i] :
( ~ ( net_str @ SY64 @ SV4 )
| ! [SY65: $i] :
( ~ ( net_str @ SY65 @ SV4 )
| ~ ( ~ ( ~ ( subnetstr @ SY65 @ SV4 @ SY64 )
| ~ ( ~ ( subrelstr @ SY65 @ SY64 )
| ( ( the_mapping @ SV4 @ SY65 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY64 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SY64 ) @ ( the_carrier @ SY65 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY65 @ SY64 )
| ( ( the_mapping @ SV4 @ SY65 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY64 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SY64 ) @ ( the_carrier @ SY65 ) ) ) )
| ( subnetstr @ SY65 @ SV4 @ SY64 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(178,plain,
! [SV27: $i,SV18: $i,SV5: $i] :
( ( ~ ~ ( ~ ( in @ SV5 @ SV18 )
| ~ ( element @ SV18 @ ( powerset @ SV27 ) ) )
| ( element @ SV5 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(179,plain,
! [SV28: $i,SV19: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( in @ SV6 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV28 ) ) )
| ~ ( empty @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(180,plain,
( ( ~ ( net_str @ sK2_SX0 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(181,plain,
( ( ! [SY87: $i] :
( ~ ( subnetstr @ SY87 @ sK1_A @ sK2_SX0 )
| ! [SY88: $i] :
( ~ ( element @ SY88 @ ( the_carrier @ sK2_SX0 ) )
| ! [SY89: $i] :
( ~ ( element @ SY89 @ ( the_carrier @ sK2_SX0 ) )
| ! [SY90: $i] :
( ~ ( element @ SY90 @ ( the_carrier @ SY87 ) )
| ! [SY91: $i] :
( ~ ( element @ SY91 @ ( the_carrier @ SY87 ) )
| ~ ~ ( ~ ~ ( ( SY88 != SY90 )
| ( SY89 != SY91 ) )
| ~ ( related @ SY87 @ SY90 @ SY91 ) )
| ( related @ sK2_SX0 @ SY88 @ SY89 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(182,plain,
! [SV20: $i,SV7: $i] :
( ( ( ~ ( element @ SV7 @ SV20 ) )
= $true )
| ( ( ( empty @ SV20 )
| ( in @ SV7 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(183,plain,
! [SV21: $i,SV8: $i,SV29: $i] :
( ( ~ ( element @ SV29 @ ( powerset @ ( cartesian_product2 @ SV8 @ SV21 ) ) )
| ( relation @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(184,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $false )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( element @ SY73 @ ( powerset @ SV9 ) )
| ~ ~ ( empty @ SY73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(185,plain,
! [SV10: $i] :
( ( ~ ( element @ ( sK4_SY74 @ SV10 ) @ SV10 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[165]) ).
thf(186,plain,
! [SV22: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( one_sorted_str @ SV11 )
| ~ ( net_str @ SV22 @ SV11 ) ) )
= $true )
| ( ( ! [SY93: $i] :
( ~ ( subnetstr @ SY93 @ SV11 @ SV22 )
| ( net_str @ SY93 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(187,plain,
! [SV23: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV23 ) )
= $true )
| ( ( element @ SV12 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(188,plain,
! [SV24: $i,SV13: $i,SV30: $i] :
( ( ~ ( relation_of2_as_subset @ SV30 @ SV13 @ SV24 )
| ( element @ SV30 @ ( powerset @ ( cartesian_product2 @ SV13 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(189,plain,
! [SV25: $i,SV14: $i] :
( ( ~ ( ~ ( element @ SV14 @ ( powerset @ SV25 ) )
| ( subset @ SV14 @ SV25 ) )
| ~ ( ~ ( subset @ SV14 @ SV25 )
| ( element @ SV14 @ ( powerset @ SV25 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(190,plain,
! [SV26: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( one_sorted_str @ SV15 )
| ~ ( net_str @ SV26 @ SV15 ) ) )
= $true )
| ( ( ~ ! [SY95: $i] :
~ ( subnetstr @ SY95 @ SV15 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(191,plain,
( ( one_sorted_str @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(192,plain,
! [SV16: $i] :
( ( ( one_sorted_str @ SV16 )
= $false )
| ( ( ~ ! [SY83: $i] :
~ ( net_str @ SY83 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(193,plain,
! [SV17: $i] :
( ( ~ ~ ( ~ ( element @ ( sK5_SY84 @ SV17 ) @ ( powerset @ SV17 ) )
| ~ ( empty @ ( sK5_SY84 @ SV17 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[173]) ).
thf(194,plain,
! [SV2: $i,SV31: $i] :
( ( ( ~ ( subrelstr @ SV31 @ SV2 )
| ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV2 ) )
| ! [SY97: $i] :
( ~ ( element @ SY97 @ ( the_carrier @ SV2 ) )
| ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV31 ) )
| ! [SY99: $i] :
( ~ ( element @ SY99 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SY98 != SY96 )
| ( SY99 != SY97 ) )
| ~ ( related @ SV31 @ SY98 @ SY99 ) )
| ( related @ SV2 @ SY96 @ SY97 ) ) ) ) ) )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(195,plain,
! [SV3: $i,SV32: $i] :
( ( ( ~ ( net_str @ SV32 @ SV3 )
| ( rel_str @ SV32 ) )
= $true )
| ( ( one_sorted_str @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(196,plain,
! [SV4: $i,SV33: $i] :
( ( ( ~ ( net_str @ SV33 @ SV4 )
| ! [SY100: $i] :
( ~ ( net_str @ SY100 @ SV4 )
| ~ ( ~ ( ~ ( subnetstr @ SY100 @ SV4 @ SV33 )
| ~ ( ~ ( subrelstr @ SY100 @ SV33 )
| ( ( the_mapping @ SV4 @ SY100 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SY100 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY100 @ SV33 )
| ( ( the_mapping @ SV4 @ SY100 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SY100 ) ) ) )
| ( subnetstr @ SY100 @ SV4 @ SV33 ) ) ) ) )
= $true )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(197,plain,
! [SV27: $i,SV18: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( in @ SV5 @ SV18 )
| ~ ( element @ SV18 @ ( powerset @ SV27 ) ) ) )
= $true )
| ( ( element @ SV5 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(198,plain,
! [SV28: $i,SV19: $i,SV6: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ SV6 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV28 ) ) )
| ~ ( empty @ SV28 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(199,plain,
( ( net_str @ sK2_SX0 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(200,plain,
( ( ~ ( subnetstr @ sK6_SY87 @ sK1_A @ sK2_SX0 )
| ! [SY101: $i] :
( ~ ( element @ SY101 @ ( the_carrier @ sK2_SX0 ) )
| ! [SY102: $i] :
( ~ ( element @ SY102 @ ( the_carrier @ sK2_SX0 ) )
| ! [SY103: $i] :
( ~ ( element @ SY103 @ ( the_carrier @ sK6_SY87 ) )
| ! [SY104: $i] :
( ~ ( element @ SY104 @ ( the_carrier @ sK6_SY87 ) )
| ~ ~ ( ~ ~ ( ( SY101 != SY103 )
| ( SY102 != SY104 ) )
| ~ ( related @ sK6_SY87 @ SY103 @ SY104 ) )
| ( related @ sK2_SX0 @ SY101 @ SY102 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[181]) ).
thf(201,plain,
! [SV20: $i,SV7: $i] :
( ( ( element @ SV7 @ SV20 )
= $false )
| ( ( ( empty @ SV20 )
| ( in @ SV7 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(202,plain,
! [SV21: $i,SV8: $i,SV29: $i] :
( ( ( ~ ( element @ SV29 @ ( powerset @ ( cartesian_product2 @ SV8 @ SV21 ) ) ) )
= $true )
| ( ( relation @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(203,plain,
! [SV9: $i] :
( ( ( empty @ SV9 )
= $true )
| ( ( ~ ! [SY73: $i] :
~ ~ ( ~ ( element @ SY73 @ ( powerset @ SV9 ) )
| ~ ~ ( empty @ SY73 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(204,plain,
! [SV10: $i] :
( ( element @ ( sK4_SY74 @ SV10 ) @ SV10 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(205,plain,
! [SV22: $i,SV11: $i] :
( ( ( ~ ( ~ ( one_sorted_str @ SV11 )
| ~ ( net_str @ SV22 @ SV11 ) ) )
= $false )
| ( ( ! [SY93: $i] :
( ~ ( subnetstr @ SY93 @ SV11 @ SV22 )
| ( net_str @ SY93 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(206,plain,
! [SV23: $i,SV12: $i] :
( ( ( in @ SV12 @ SV23 )
= $false )
| ( ( element @ SV12 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(207,plain,
! [SV24: $i,SV13: $i,SV30: $i] :
( ( ( ~ ( relation_of2_as_subset @ SV30 @ SV13 @ SV24 ) )
= $true )
| ( ( element @ SV30 @ ( powerset @ ( cartesian_product2 @ SV13 @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(208,plain,
! [SV25: $i,SV14: $i] :
( ( ~ ( ~ ( element @ SV14 @ ( powerset @ SV25 ) )
| ( subset @ SV14 @ SV25 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(209,plain,
! [SV25: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ SV14 @ SV25 )
| ( element @ SV14 @ ( powerset @ SV25 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(210,plain,
! [SV26: $i,SV15: $i] :
( ( ( ~ ( ~ ( one_sorted_str @ SV15 )
| ~ ( net_str @ SV26 @ SV15 ) ) )
= $false )
| ( ( ~ ! [SY95: $i] :
~ ( subnetstr @ SY95 @ SV15 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(211,plain,
! [SV16: $i] :
( ( ( ! [SY83: $i] :
~ ( net_str @ SY83 @ SV16 ) )
= $false )
| ( ( one_sorted_str @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(212,plain,
! [SV17: $i] :
( ( ~ ( ~ ( element @ ( sK5_SY84 @ SV17 ) @ ( powerset @ SV17 ) )
| ~ ( empty @ ( sK5_SY84 @ SV17 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(213,plain,
! [SV2: $i,SV31: $i] :
( ( ( ~ ( subrelstr @ SV31 @ SV2 ) )
= $true )
| ( ( ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV2 ) )
| ! [SY97: $i] :
( ~ ( element @ SY97 @ ( the_carrier @ SV2 ) )
| ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV31 ) )
| ! [SY99: $i] :
( ~ ( element @ SY99 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SY98 != SY96 )
| ( SY99 != SY97 ) )
| ~ ( related @ SV31 @ SY98 @ SY99 ) )
| ( related @ SV2 @ SY96 @ SY97 ) ) ) ) ) )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(214,plain,
! [SV3: $i,SV32: $i] :
( ( ( ~ ( net_str @ SV32 @ SV3 ) )
= $true )
| ( ( rel_str @ SV32 )
= $true )
| ( ( one_sorted_str @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(215,plain,
! [SV4: $i,SV33: $i] :
( ( ( ~ ( net_str @ SV33 @ SV4 ) )
= $true )
| ( ( ! [SY100: $i] :
( ~ ( net_str @ SY100 @ SV4 )
| ~ ( ~ ( ~ ( subnetstr @ SY100 @ SV4 @ SV33 )
| ~ ( ~ ( subrelstr @ SY100 @ SV33 )
| ( ( the_mapping @ SV4 @ SY100 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SY100 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY100 @ SV33 )
| ( ( the_mapping @ SV4 @ SY100 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SY100 ) ) ) )
| ( subnetstr @ SY100 @ SV4 @ SV33 ) ) ) ) )
= $true )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(216,plain,
! [SV27: $i,SV18: $i,SV5: $i] :
( ( ( ~ ( ~ ( in @ SV5 @ SV18 )
| ~ ( element @ SV18 @ ( powerset @ SV27 ) ) ) )
= $false )
| ( ( element @ SV5 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(217,plain,
! [SV28: $i,SV19: $i,SV6: $i] :
( ( ~ ~ ( ~ ( in @ SV6 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV28 ) ) )
| ~ ( empty @ SV28 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(218,plain,
( ( ~ ( subnetstr @ sK6_SY87 @ sK1_A @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(219,plain,
( ( ! [SY101: $i] :
( ~ ( element @ SY101 @ ( the_carrier @ sK2_SX0 ) )
| ! [SY102: $i] :
( ~ ( element @ SY102 @ ( the_carrier @ sK2_SX0 ) )
| ! [SY103: $i] :
( ~ ( element @ SY103 @ ( the_carrier @ sK6_SY87 ) )
| ! [SY104: $i] :
( ~ ( element @ SY104 @ ( the_carrier @ sK6_SY87 ) )
| ~ ~ ( ~ ~ ( ( SY101 != SY103 )
| ( SY102 != SY104 ) )
| ~ ( related @ sK6_SY87 @ SY103 @ SY104 ) )
| ( related @ sK2_SX0 @ SY101 @ SY102 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(220,plain,
! [SV7: $i,SV20: $i] :
( ( ( empty @ SV20 )
= $true )
| ( ( in @ SV7 @ SV20 )
= $true )
| ( ( element @ SV7 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(221,plain,
! [SV21: $i,SV8: $i,SV29: $i] :
( ( ( element @ SV29 @ ( powerset @ ( cartesian_product2 @ SV8 @ SV21 ) ) )
= $false )
| ( ( relation @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(222,plain,
! [SV9: $i] :
( ( ( ! [SY73: $i] :
~ ~ ( ~ ( element @ SY73 @ ( powerset @ SV9 ) )
| ~ ~ ( empty @ SY73 ) ) )
= $false )
| ( ( empty @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(223,plain,
! [SV22: $i,SV11: $i] :
( ( ( ~ ( one_sorted_str @ SV11 )
| ~ ( net_str @ SV22 @ SV11 ) )
= $true )
| ( ( ! [SY93: $i] :
( ~ ( subnetstr @ SY93 @ SV11 @ SV22 )
| ( net_str @ SY93 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(224,plain,
! [SV24: $i,SV13: $i,SV30: $i] :
( ( ( relation_of2_as_subset @ SV30 @ SV13 @ SV24 )
= $false )
| ( ( element @ SV30 @ ( powerset @ ( cartesian_product2 @ SV13 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(225,plain,
! [SV25: $i,SV14: $i] :
( ( ~ ( element @ SV14 @ ( powerset @ SV25 ) )
| ( subset @ SV14 @ SV25 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(226,plain,
! [SV25: $i,SV14: $i] :
( ( ~ ( subset @ SV14 @ SV25 )
| ( element @ SV14 @ ( powerset @ SV25 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(227,plain,
! [SV26: $i,SV15: $i] :
( ( ( ~ ( one_sorted_str @ SV15 )
| ~ ( net_str @ SV26 @ SV15 ) )
= $true )
| ( ( ~ ! [SY95: $i] :
~ ( subnetstr @ SY95 @ SV15 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(228,plain,
! [SV16: $i] :
( ( ( ~ ( net_str @ ( sK7_SY83 @ SV16 ) @ SV16 ) )
= $false )
| ( ( one_sorted_str @ SV16 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[211]) ).
thf(229,plain,
! [SV17: $i] :
( ( ~ ( element @ ( sK5_SY84 @ SV17 ) @ ( powerset @ SV17 ) )
| ~ ( empty @ ( sK5_SY84 @ SV17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(230,plain,
! [SV2: $i,SV31: $i] :
( ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( ! [SY96: $i] :
( ~ ( element @ SY96 @ ( the_carrier @ SV2 ) )
| ! [SY97: $i] :
( ~ ( element @ SY97 @ ( the_carrier @ SV2 ) )
| ! [SY98: $i] :
( ~ ( element @ SY98 @ ( the_carrier @ SV31 ) )
| ! [SY99: $i] :
( ~ ( element @ SY99 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SY98 != SY96 )
| ( SY99 != SY97 ) )
| ~ ( related @ SV31 @ SY98 @ SY99 ) )
| ( related @ SV2 @ SY96 @ SY97 ) ) ) ) ) )
= $true )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(231,plain,
! [SV3: $i,SV32: $i] :
( ( ( net_str @ SV32 @ SV3 )
= $false )
| ( ( rel_str @ SV32 )
= $true )
| ( ( one_sorted_str @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(232,plain,
! [SV4: $i,SV33: $i] :
( ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( ! [SY100: $i] :
( ~ ( net_str @ SY100 @ SV4 )
| ~ ( ~ ( ~ ( subnetstr @ SY100 @ SV4 @ SV33 )
| ~ ( ~ ( subrelstr @ SY100 @ SV33 )
| ( ( the_mapping @ SV4 @ SY100 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SY100 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY100 @ SV33 )
| ( ( the_mapping @ SV4 @ SY100 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SY100 ) ) ) )
| ( subnetstr @ SY100 @ SV4 @ SV33 ) ) ) ) )
= $true )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(233,plain,
! [SV27: $i,SV18: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV18 )
| ~ ( element @ SV18 @ ( powerset @ SV27 ) ) )
= $true )
| ( ( element @ SV5 @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[216]) ).
thf(234,plain,
! [SV28: $i,SV19: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( in @ SV6 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV28 ) ) ) )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(235,plain,
( ( subnetstr @ sK6_SY87 @ sK1_A @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(236,plain,
( ( ~ ( element @ sK8_SY101 @ ( the_carrier @ sK2_SX0 ) )
| ! [SY105: $i] :
( ~ ( element @ SY105 @ ( the_carrier @ sK2_SX0 ) )
| ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ sK6_SY87 ) )
| ! [SY107: $i] :
( ~ ( element @ SY107 @ ( the_carrier @ sK6_SY87 ) )
| ~ ~ ( ~ ~ ( ( sK8_SY101 != SY106 )
| ( SY105 != SY107 ) )
| ~ ( related @ sK6_SY87 @ SY106 @ SY107 ) )
| ( related @ sK2_SX0 @ sK8_SY101 @ SY105 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[219]) ).
thf(237,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK9_SY73 @ SV9 ) @ ( powerset @ SV9 ) )
| ~ ~ ( empty @ ( sK9_SY73 @ SV9 ) ) ) )
= $false )
| ( ( empty @ SV9 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[222]) ).
thf(238,plain,
! [SV22: $i,SV11: $i] :
( ( ( ~ ( one_sorted_str @ SV11 ) )
= $true )
| ( ( ~ ( net_str @ SV22 @ SV11 ) )
= $true )
| ( ( ! [SY93: $i] :
( ~ ( subnetstr @ SY93 @ SV11 @ SV22 )
| ( net_str @ SY93 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(239,plain,
! [SV25: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ ( powerset @ SV25 ) ) )
= $true )
| ( ( subset @ SV14 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(240,plain,
! [SV25: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV25 ) )
= $true )
| ( ( element @ SV14 @ ( powerset @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(241,plain,
! [SV26: $i,SV15: $i] :
( ( ( ~ ( one_sorted_str @ SV15 ) )
= $true )
| ( ( ~ ( net_str @ SV26 @ SV15 ) )
= $true )
| ( ( ~ ! [SY95: $i] :
~ ( subnetstr @ SY95 @ SV15 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(242,plain,
! [SV16: $i] :
( ( ( net_str @ ( sK7_SY83 @ SV16 ) @ SV16 )
= $true )
| ( ( one_sorted_str @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(243,plain,
! [SV17: $i] :
( ( ~ ( element @ ( sK5_SY84 @ SV17 ) @ ( powerset @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(244,plain,
! [SV17: $i] :
( ( ~ ( empty @ ( sK5_SY84 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(245,plain,
! [SV31: $i,SV2: $i,SV34: $i] :
( ( ( ~ ( element @ SV34 @ ( the_carrier @ SV2 ) )
| ! [SY108: $i] :
( ~ ( element @ SY108 @ ( the_carrier @ SV2 ) )
| ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV31 ) )
| ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SY109 != SV34 )
| ( SY110 != SY108 ) )
| ~ ( related @ SV31 @ SY109 @ SY110 ) )
| ( related @ SV2 @ SV34 @ SY108 ) ) ) ) )
= $true )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(246,plain,
! [SV33: $i,SV4: $i,SV35: $i] :
( ( ( ~ ( net_str @ SV35 @ SV4 )
| ~ ( ~ ( ~ ( subnetstr @ SV35 @ SV4 @ SV33 )
| ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) )
| ( subnetstr @ SV35 @ SV4 @ SV33 ) ) ) )
= $true )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(247,plain,
! [SV27: $i,SV18: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ SV18 ) )
= $true )
| ( ( ~ ( element @ SV18 @ ( powerset @ SV27 ) ) )
= $true )
| ( ( element @ SV5 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(248,plain,
! [SV28: $i,SV19: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ SV6 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV28 ) ) ) )
= $false )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(249,plain,
( ( ~ ( element @ sK8_SY101 @ ( the_carrier @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(250,plain,
( ( ! [SY105: $i] :
( ~ ( element @ SY105 @ ( the_carrier @ sK2_SX0 ) )
| ! [SY106: $i] :
( ~ ( element @ SY106 @ ( the_carrier @ sK6_SY87 ) )
| ! [SY107: $i] :
( ~ ( element @ SY107 @ ( the_carrier @ sK6_SY87 ) )
| ~ ~ ( ~ ~ ( ( sK8_SY101 != SY106 )
| ( SY105 != SY107 ) )
| ~ ( related @ sK6_SY87 @ SY106 @ SY107 ) )
| ( related @ sK2_SX0 @ sK8_SY101 @ SY105 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(251,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( element @ ( sK9_SY73 @ SV9 ) @ ( powerset @ SV9 ) )
| ~ ~ ( empty @ ( sK9_SY73 @ SV9 ) ) ) )
= $true )
| ( ( empty @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(252,plain,
! [SV22: $i,SV11: $i] :
( ( ( one_sorted_str @ SV11 )
= $false )
| ( ( ~ ( net_str @ SV22 @ SV11 ) )
= $true )
| ( ( ! [SY93: $i] :
( ~ ( subnetstr @ SY93 @ SV11 @ SV22 )
| ( net_str @ SY93 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(253,plain,
! [SV25: $i,SV14: $i] :
( ( ( element @ SV14 @ ( powerset @ SV25 ) )
= $false )
| ( ( subset @ SV14 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(254,plain,
! [SV25: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV25 )
= $false )
| ( ( element @ SV14 @ ( powerset @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(255,plain,
! [SV26: $i,SV15: $i] :
( ( ( one_sorted_str @ SV15 )
= $false )
| ( ( ~ ( net_str @ SV26 @ SV15 ) )
= $true )
| ( ( ~ ! [SY95: $i] :
~ ( subnetstr @ SY95 @ SV15 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(256,plain,
! [SV17: $i] :
( ( element @ ( sK5_SY84 @ SV17 ) @ ( powerset @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[243]) ).
thf(257,plain,
! [SV17: $i] :
( ( empty @ ( sK5_SY84 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(258,plain,
! [SV31: $i,SV2: $i,SV34: $i] :
( ( ( ~ ( element @ SV34 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ! [SY108: $i] :
( ~ ( element @ SY108 @ ( the_carrier @ SV2 ) )
| ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV31 ) )
| ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SY109 != SV34 )
| ( SY110 != SY108 ) )
| ~ ( related @ SV31 @ SY109 @ SY110 ) )
| ( related @ SV2 @ SV34 @ SY108 ) ) ) ) )
= $true )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(259,plain,
! [SV33: $i,SV4: $i,SV35: $i] :
( ( ( ~ ( net_str @ SV35 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subnetstr @ SV35 @ SV4 @ SV33 )
| ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) )
| ( subnetstr @ SV35 @ SV4 @ SV33 ) ) ) )
= $true )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(260,plain,
! [SV27: $i,SV18: $i,SV5: $i] :
( ( ( in @ SV5 @ SV18 )
= $false )
| ( ( ~ ( element @ SV18 @ ( powerset @ SV27 ) ) )
= $true )
| ( ( element @ SV5 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(261,plain,
! [SV28: $i,SV19: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV19 )
| ~ ( element @ SV19 @ ( powerset @ SV28 ) ) )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(262,plain,
( ( element @ sK8_SY101 @ ( the_carrier @ sK2_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(263,plain,
( ( ~ ( element @ sK10_SY105 @ ( the_carrier @ sK2_SX0 ) )
| ! [SY111: $i] :
( ~ ( element @ SY111 @ ( the_carrier @ sK6_SY87 ) )
| ! [SY112: $i] :
( ~ ( element @ SY112 @ ( the_carrier @ sK6_SY87 ) )
| ~ ~ ( ~ ~ ( ( sK8_SY101 != SY111 )
| ( sK10_SY105 != SY112 ) )
| ~ ( related @ sK6_SY87 @ SY111 @ SY112 ) )
| ( related @ sK2_SX0 @ sK8_SY101 @ sK10_SY105 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[250]) ).
thf(264,plain,
! [SV9: $i] :
( ( ( ~ ( element @ ( sK9_SY73 @ SV9 ) @ ( powerset @ SV9 ) )
| ~ ~ ( empty @ ( sK9_SY73 @ SV9 ) ) )
= $false )
| ( ( empty @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(265,plain,
! [SV11: $i,SV22: $i] :
( ( ( net_str @ SV22 @ SV11 )
= $false )
| ( ( one_sorted_str @ SV11 )
= $false )
| ( ( ! [SY93: $i] :
( ~ ( subnetstr @ SY93 @ SV11 @ SV22 )
| ( net_str @ SY93 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(266,plain,
! [SV15: $i,SV26: $i] :
( ( ( net_str @ SV26 @ SV15 )
= $false )
| ( ( one_sorted_str @ SV15 )
= $false )
| ( ( ~ ! [SY95: $i] :
~ ( subnetstr @ SY95 @ SV15 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(267,plain,
! [SV31: $i,SV2: $i,SV34: $i] :
( ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ! [SY108: $i] :
( ~ ( element @ SY108 @ ( the_carrier @ SV2 ) )
| ! [SY109: $i] :
( ~ ( element @ SY109 @ ( the_carrier @ SV31 ) )
| ! [SY110: $i] :
( ~ ( element @ SY110 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SY109 != SV34 )
| ( SY110 != SY108 ) )
| ~ ( related @ SV31 @ SY109 @ SY110 ) )
| ( related @ SV2 @ SV34 @ SY108 ) ) ) ) )
= $true )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(268,plain,
! [SV33: $i,SV4: $i,SV35: $i] :
( ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( ~ ( ~ ( ~ ( subnetstr @ SV35 @ SV4 @ SV33 )
| ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) )
| ( subnetstr @ SV35 @ SV4 @ SV33 ) ) ) )
= $true )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(269,plain,
! [SV5: $i,SV27: $i,SV18: $i] :
( ( ( element @ SV18 @ ( powerset @ SV27 ) )
= $false )
| ( ( in @ SV5 @ SV18 )
= $false )
| ( ( element @ SV5 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(270,plain,
! [SV28: $i,SV19: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV19 ) )
= $true )
| ( ( ~ ( element @ SV19 @ ( powerset @ SV28 ) ) )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(271,plain,
( ( ~ ( element @ sK10_SY105 @ ( the_carrier @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(272,plain,
( ( ! [SY111: $i] :
( ~ ( element @ SY111 @ ( the_carrier @ sK6_SY87 ) )
| ! [SY112: $i] :
( ~ ( element @ SY112 @ ( the_carrier @ sK6_SY87 ) )
| ~ ~ ( ~ ~ ( ( sK8_SY101 != SY111 )
| ( sK10_SY105 != SY112 ) )
| ~ ( related @ sK6_SY87 @ SY111 @ SY112 ) )
| ( related @ sK2_SX0 @ sK8_SY101 @ sK10_SY105 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(273,plain,
! [SV9: $i] :
( ( ( ~ ( element @ ( sK9_SY73 @ SV9 ) @ ( powerset @ SV9 ) ) )
= $false )
| ( ( empty @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(274,plain,
! [SV9: $i] :
( ( ( ~ ~ ( empty @ ( sK9_SY73 @ SV9 ) ) )
= $false )
| ( ( empty @ SV9 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[264]) ).
thf(275,plain,
! [SV22: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( subnetstr @ SV36 @ SV11 @ SV22 )
| ( net_str @ SV36 @ SV11 ) )
= $true )
| ( ( one_sorted_str @ SV11 )
= $false )
| ( ( net_str @ SV22 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(276,plain,
! [SV26: $i,SV15: $i] :
( ( ( ! [SY95: $i] :
~ ( subnetstr @ SY95 @ SV15 @ SV26 ) )
= $false )
| ( ( one_sorted_str @ SV15 )
= $false )
| ( ( net_str @ SV26 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(277,plain,
! [SV34: $i,SV31: $i,SV2: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( the_carrier @ SV2 ) )
| ! [SY113: $i] :
( ~ ( element @ SY113 @ ( the_carrier @ SV31 ) )
| ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SY113 != SV34 )
| ( SY114 != SV37 ) )
| ~ ( related @ SV31 @ SY113 @ SY114 ) )
| ( related @ SV2 @ SV34 @ SV37 ) ) ) )
= $true )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(278,plain,
! [SV33: $i,SV4: $i,SV35: $i] :
( ( ( ~ ( ~ ( subnetstr @ SV35 @ SV4 @ SV33 )
| ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) )
| ( subnetstr @ SV35 @ SV4 @ SV33 ) ) )
= $false )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(279,plain,
! [SV28: $i,SV19: $i,SV6: $i] :
( ( ( in @ SV6 @ SV19 )
= $false )
| ( ( ~ ( element @ SV19 @ ( powerset @ SV28 ) ) )
= $true )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(280,plain,
( ( element @ sK10_SY105 @ ( the_carrier @ sK2_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(281,plain,
( ( ~ ( element @ sK11_SY111 @ ( the_carrier @ sK6_SY87 ) )
| ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ sK6_SY87 ) )
| ~ ~ ( ~ ~ ( ( sK8_SY101 != sK11_SY111 )
| ( sK10_SY105 != SY115 ) )
| ~ ( related @ sK6_SY87 @ sK11_SY111 @ SY115 ) )
| ( related @ sK2_SX0 @ sK8_SY101 @ sK10_SY105 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[272]) ).
thf(282,plain,
! [SV9: $i] :
( ( ( element @ ( sK9_SY73 @ SV9 ) @ ( powerset @ SV9 ) )
= $true )
| ( ( empty @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(283,plain,
! [SV9: $i] :
( ( ( ~ ( empty @ ( sK9_SY73 @ SV9 ) ) )
= $true )
| ( ( empty @ SV9 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(284,plain,
! [SV22: $i,SV11: $i,SV36: $i] :
( ( ( ~ ( subnetstr @ SV36 @ SV11 @ SV22 ) )
= $true )
| ( ( net_str @ SV36 @ SV11 )
= $true )
| ( ( one_sorted_str @ SV11 )
= $false )
| ( ( net_str @ SV22 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(285,plain,
! [SV15: $i,SV26: $i] :
( ( ( ~ ( subnetstr @ ( sK12_SY95 @ SV26 @ SV15 ) @ SV15 @ SV26 ) )
= $false )
| ( ( one_sorted_str @ SV15 )
= $false )
| ( ( net_str @ SV26 @ SV15 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[276]) ).
thf(286,plain,
! [SV34: $i,SV31: $i,SV2: $i,SV37: $i] :
( ( ( ~ ( element @ SV37 @ ( the_carrier @ SV2 ) ) )
= $true )
| ( ( ! [SY113: $i] :
( ~ ( element @ SY113 @ ( the_carrier @ SV31 ) )
| ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SY113 != SV34 )
| ( SY114 != SV37 ) )
| ~ ( related @ SV31 @ SY113 @ SY114 ) )
| ( related @ SV2 @ SV34 @ SV37 ) ) ) )
= $true )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(287,plain,
! [SV33: $i,SV4: $i,SV35: $i] :
( ( ( ~ ( ~ ( subnetstr @ SV35 @ SV4 @ SV33 )
| ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) ) ) )
= $false )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(288,plain,
! [SV4: $i,SV33: $i,SV35: $i] :
( ( ( ~ ( ~ ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) )
| ( subnetstr @ SV35 @ SV4 @ SV33 ) ) )
= $false )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[278]) ).
thf(289,plain,
! [SV6: $i,SV28: $i,SV19: $i] :
( ( ( element @ SV19 @ ( powerset @ SV28 ) )
= $false )
| ( ( in @ SV6 @ SV19 )
= $false )
| ( ( ~ ( empty @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(290,plain,
( ( ~ ( element @ sK11_SY111 @ ( the_carrier @ sK6_SY87 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(291,plain,
( ( ! [SY115: $i] :
( ~ ( element @ SY115 @ ( the_carrier @ sK6_SY87 ) )
| ~ ~ ( ~ ~ ( ( sK8_SY101 != sK11_SY111 )
| ( sK10_SY105 != SY115 ) )
| ~ ( related @ sK6_SY87 @ sK11_SY111 @ SY115 ) )
| ( related @ sK2_SX0 @ sK8_SY101 @ sK10_SY105 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[281]) ).
thf(292,plain,
! [SV9: $i] :
( ( ( empty @ ( sK9_SY73 @ SV9 ) )
= $false )
| ( ( empty @ SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(293,plain,
! [SV22: $i,SV11: $i,SV36: $i] :
( ( ( subnetstr @ SV36 @ SV11 @ SV22 )
= $false )
| ( ( net_str @ SV36 @ SV11 )
= $true )
| ( ( one_sorted_str @ SV11 )
= $false )
| ( ( net_str @ SV22 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(294,plain,
! [SV15: $i,SV26: $i] :
( ( ( subnetstr @ ( sK12_SY95 @ SV26 @ SV15 ) @ SV15 @ SV26 )
= $true )
| ( ( one_sorted_str @ SV15 )
= $false )
| ( ( net_str @ SV26 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(295,plain,
! [SV34: $i,SV31: $i,SV2: $i,SV37: $i] :
( ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( ! [SY113: $i] :
( ~ ( element @ SY113 @ ( the_carrier @ SV31 ) )
| ! [SY114: $i] :
( ~ ( element @ SY114 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SY113 != SV34 )
| ( SY114 != SV37 ) )
| ~ ( related @ SV31 @ SY113 @ SY114 ) )
| ( related @ SV2 @ SV34 @ SV37 ) ) ) )
= $true )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(296,plain,
! [SV33: $i,SV4: $i,SV35: $i] :
( ( ( ~ ( subnetstr @ SV35 @ SV4 @ SV33 )
| ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) ) )
= $true )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(297,plain,
! [SV4: $i,SV33: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) )
| ( subnetstr @ SV35 @ SV4 @ SV33 ) )
= $true )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(298,plain,
! [SV19: $i,SV6: $i,SV28: $i] :
( ( ( empty @ SV28 )
= $false )
| ( ( in @ SV6 @ SV19 )
= $false )
| ( ( element @ SV19 @ ( powerset @ SV28 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(299,plain,
( ( element @ sK11_SY111 @ ( the_carrier @ sK6_SY87 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(300,plain,
( ( ~ ( element @ sK13_SY115 @ ( the_carrier @ sK6_SY87 ) )
| ~ ~ ( ~ ~ ( ( sK8_SY101 != sK11_SY111 )
| ( sK10_SY105 != sK13_SY115 ) )
| ~ ( related @ sK6_SY87 @ sK11_SY111 @ sK13_SY115 ) )
| ( related @ sK2_SX0 @ sK8_SY101 @ sK10_SY105 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[291]) ).
thf(301,plain,
! [SV2: $i,SV37: $i,SV34: $i,SV31: $i,SV38: $i] :
( ( ( ~ ( element @ SV38 @ ( the_carrier @ SV31 ) )
| ! [SY116: $i] :
( ~ ( element @ SY116 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SV38 != SV34 )
| ( SY116 != SV37 ) )
| ~ ( related @ SV31 @ SV38 @ SY116 ) )
| ( related @ SV2 @ SV34 @ SV37 ) ) )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(302,plain,
! [SV33: $i,SV4: $i,SV35: $i] :
( ( ( ~ ( subnetstr @ SV35 @ SV4 @ SV33 ) )
= $true )
| ( ( ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) ) )
= $true )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(303,plain,
! [SV4: $i,SV33: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) ) )
= $true )
| ( ( subnetstr @ SV35 @ SV4 @ SV33 )
= $true )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(304,plain,
( ( ~ ( element @ sK13_SY115 @ ( the_carrier @ sK6_SY87 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(305,plain,
( ( ~ ~ ( ~ ~ ( ( sK8_SY101 != sK11_SY111 )
| ( sK10_SY105 != sK13_SY115 ) )
| ~ ( related @ sK6_SY87 @ sK11_SY111 @ sK13_SY115 ) )
| ( related @ sK2_SX0 @ sK8_SY101 @ sK10_SY105 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[300]) ).
thf(306,plain,
! [SV2: $i,SV37: $i,SV34: $i,SV31: $i,SV38: $i] :
( ( ( ~ ( element @ SV38 @ ( the_carrier @ SV31 ) ) )
= $true )
| ( ( ! [SY116: $i] :
( ~ ( element @ SY116 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SV38 != SV34 )
| ( SY116 != SV37 ) )
| ~ ( related @ SV31 @ SV38 @ SY116 ) )
| ( related @ SV2 @ SV34 @ SV37 ) ) )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(307,plain,
! [SV33: $i,SV4: $i,SV35: $i] :
( ( ( subnetstr @ SV35 @ SV4 @ SV33 )
= $false )
| ( ( ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) ) )
= $true )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(308,plain,
! [SV4: $i,SV33: $i,SV35: $i] :
( ( ( ~ ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) ) )
= $false )
| ( ( subnetstr @ SV35 @ SV4 @ SV33 )
= $true )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(309,plain,
( ( element @ sK13_SY115 @ ( the_carrier @ sK6_SY87 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(310,plain,
( ( ~ ~ ( ~ ~ ( ( sK8_SY101 != sK11_SY111 )
| ( sK10_SY105 != sK13_SY115 ) )
| ~ ( related @ sK6_SY87 @ sK11_SY111 @ sK13_SY115 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(311,plain,
( ( related @ sK2_SX0 @ sK8_SY101 @ sK10_SY105 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(312,plain,
! [SV2: $i,SV37: $i,SV34: $i,SV31: $i,SV38: $i] :
( ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( ! [SY116: $i] :
( ~ ( element @ SY116 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SV38 != SV34 )
| ( SY116 != SV37 ) )
| ~ ( related @ SV31 @ SV38 @ SY116 ) )
| ( related @ SV2 @ SV34 @ SV37 ) ) )
= $true )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(313,plain,
! [SV4: $i,SV33: $i,SV35: $i] :
( ( ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) )
= $false )
| ( ( subnetstr @ SV35 @ SV4 @ SV33 )
= $false )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(314,plain,
! [SV4: $i,SV33: $i,SV35: $i] :
( ( ( ~ ( subrelstr @ SV35 @ SV33 )
| ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) ) )
= $true )
| ( ( subnetstr @ SV35 @ SV4 @ SV33 )
= $true )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(315,plain,
( ( ~ ( ~ ~ ( ( sK8_SY101 != sK11_SY111 )
| ( sK10_SY105 != sK13_SY115 ) )
| ~ ( related @ sK6_SY87 @ sK11_SY111 @ sK13_SY115 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(316,plain,
! [SV2: $i,SV37: $i,SV34: $i,SV38: $i,SV31: $i,SV39: $i] :
( ( ( ~ ( element @ SV39 @ ( the_carrier @ SV31 ) )
| ~ ~ ( ~ ~ ( ( SV38 != SV34 )
| ( SV39 != SV37 ) )
| ~ ( related @ SV31 @ SV38 @ SV39 ) )
| ( related @ SV2 @ SV34 @ SV37 ) )
= $true )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(317,plain,
! [SV4: $i,SV33: $i,SV35: $i] :
( ( ( ~ ( subrelstr @ SV35 @ SV33 ) )
= $false )
| ( ( subnetstr @ SV35 @ SV4 @ SV33 )
= $false )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(318,plain,
! [SV33: $i,SV35: $i,SV4: $i] :
( ( ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) )
= $false )
| ( ( subnetstr @ SV35 @ SV4 @ SV33 )
= $false )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(319,plain,
! [SV4: $i,SV33: $i,SV35: $i] :
( ( ( ~ ( subrelstr @ SV35 @ SV33 ) )
= $true )
| ( ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( subnetstr @ SV35 @ SV4 @ SV33 )
= $true )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(320,plain,
( ( ~ ~ ( ( sK8_SY101 != sK11_SY111 )
| ( sK10_SY105 != sK13_SY115 ) )
| ~ ( related @ sK6_SY87 @ sK11_SY111 @ sK13_SY115 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(321,plain,
! [SV2: $i,SV37: $i,SV34: $i,SV38: $i,SV31: $i,SV39: $i] :
( ( ( ~ ( element @ SV39 @ ( the_carrier @ SV31 ) ) )
= $true )
| ( ( ~ ~ ( ~ ~ ( ( SV38 != SV34 )
| ( SV39 != SV37 ) )
| ~ ( related @ SV31 @ SV38 @ SV39 ) )
| ( related @ SV2 @ SV34 @ SV37 ) )
= $true )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(322,plain,
! [SV4: $i,SV33: $i,SV35: $i] :
( ( ( subrelstr @ SV35 @ SV33 )
= $true )
| ( ( subnetstr @ SV35 @ SV4 @ SV33 )
= $false )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(323,plain,
! [SV33: $i,SV35: $i,SV4: $i] :
( ( ( ( the_mapping @ SV4 @ SV35 )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( subnetstr @ SV35 @ SV4 @ SV33 )
= $false )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(324,plain,
! [SV4: $i,SV33: $i,SV35: $i] :
( ( ( subrelstr @ SV35 @ SV33 )
= $false )
| ( ( ( the_mapping @ SV4 @ SV35 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) )
= $true )
| ( ( subnetstr @ SV35 @ SV4 @ SV33 )
= $true )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(325,plain,
( ( ~ ~ ( ( sK8_SY101 != sK11_SY111 )
| ( sK10_SY105 != sK13_SY115 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(326,plain,
( ( ~ ( related @ sK6_SY87 @ sK11_SY111 @ sK13_SY115 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(327,plain,
! [SV2: $i,SV37: $i,SV34: $i,SV38: $i,SV31: $i,SV39: $i] :
( ( ( element @ SV39 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( ~ ~ ( ~ ~ ( ( SV38 != SV34 )
| ( SV39 != SV37 ) )
| ~ ( related @ SV31 @ SV38 @ SV39 ) )
| ( related @ SV2 @ SV34 @ SV37 ) )
= $true )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(328,plain,
! [SV33: $i,SV35: $i,SV4: $i] :
( ( ( ( the_mapping @ SV4 @ SV35 )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV33 ) @ ( the_carrier @ SV4 ) @ ( the_mapping @ SV4 @ SV33 ) @ ( the_carrier @ SV35 ) ) )
= $false )
| ( ( subrelstr @ SV35 @ SV33 )
= $false )
| ( ( subnetstr @ SV35 @ SV4 @ SV33 )
= $true )
| ( ( net_str @ SV35 @ SV4 )
= $false )
| ( ( net_str @ SV33 @ SV4 )
= $false )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(329,plain,
( ( ~ ( ( sK8_SY101 != sK11_SY111 )
| ( sK10_SY105 != sK13_SY115 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(330,plain,
( ( related @ sK6_SY87 @ sK11_SY111 @ sK13_SY115 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(331,plain,
! [SV2: $i,SV31: $i,SV37: $i,SV39: $i,SV34: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ~ ( ( SV38 != SV34 )
| ( SV39 != SV37 ) )
| ~ ( related @ SV31 @ SV38 @ SV39 ) ) )
= $true )
| ( ( related @ SV2 @ SV34 @ SV37 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(332,plain,
( ( ( sK8_SY101 != sK11_SY111 )
| ( sK10_SY105 != sK13_SY115 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(333,plain,
! [SV2: $i,SV31: $i,SV37: $i,SV39: $i,SV34: $i,SV38: $i] :
( ( ( ~ ( ~ ~ ( ( SV38 != SV34 )
| ( SV39 != SV37 ) )
| ~ ( related @ SV31 @ SV38 @ SV39 ) ) )
= $false )
| ( ( related @ SV2 @ SV34 @ SV37 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(334,plain,
( ( sK8_SY101 != sK11_SY111 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[332]) ).
thf(335,plain,
( ( sK10_SY105 != sK13_SY115 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[332]) ).
thf(336,plain,
! [SV2: $i,SV31: $i,SV37: $i,SV39: $i,SV34: $i,SV38: $i] :
( ( ( ~ ~ ( ( SV38 != SV34 )
| ( SV39 != SV37 ) )
| ~ ( related @ SV31 @ SV38 @ SV39 ) )
= $true )
| ( ( related @ SV2 @ SV34 @ SV37 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(337,plain,
( ( sK8_SY101 = sK11_SY111 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(338,plain,
( ( sK10_SY105 = sK13_SY115 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(339,plain,
! [SV2: $i,SV31: $i,SV37: $i,SV39: $i,SV34: $i,SV38: $i] :
( ( ( ~ ~ ( ( SV38 != SV34 )
| ( SV39 != SV37 ) ) )
= $true )
| ( ( ~ ( related @ SV31 @ SV38 @ SV39 ) )
= $true )
| ( ( related @ SV2 @ SV34 @ SV37 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(340,plain,
! [SV2: $i,SV31: $i,SV37: $i,SV39: $i,SV34: $i,SV38: $i] :
( ( ( ~ ( ( SV38 != SV34 )
| ( SV39 != SV37 ) ) )
= $false )
| ( ( ~ ( related @ SV31 @ SV38 @ SV39 ) )
= $true )
| ( ( related @ SV2 @ SV34 @ SV37 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(341,plain,
! [SV2: $i,SV31: $i,SV37: $i,SV39: $i,SV34: $i,SV38: $i] :
( ( ( ( SV38 != SV34 )
| ( SV39 != SV37 ) )
= $true )
| ( ( ~ ( related @ SV31 @ SV38 @ SV39 ) )
= $true )
| ( ( related @ SV2 @ SV34 @ SV37 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(342,plain,
! [SV2: $i,SV31: $i,SV37: $i,SV39: $i,SV34: $i,SV38: $i] :
( ( ( SV38 != SV34 )
= $true )
| ( ( SV39 != SV37 )
= $true )
| ( ( ~ ( related @ SV31 @ SV38 @ SV39 ) )
= $true )
| ( ( related @ SV2 @ SV34 @ SV37 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(343,plain,
! [SV2: $i,SV31: $i,SV37: $i,SV39: $i,SV34: $i,SV38: $i] :
( ( ( SV38 = SV34 )
= $false )
| ( ( SV39 != SV37 )
= $true )
| ( ( ~ ( related @ SV31 @ SV38 @ SV39 ) )
= $true )
| ( ( related @ SV2 @ SV34 @ SV37 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(344,plain,
! [SV2: $i,SV31: $i,SV34: $i,SV38: $i,SV37: $i,SV39: $i] :
( ( ( SV39 = SV37 )
= $false )
| ( ( SV38 = SV34 )
= $false )
| ( ( ~ ( related @ SV31 @ SV38 @ SV39 ) )
= $true )
| ( ( related @ SV2 @ SV34 @ SV37 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(345,plain,
! [SV2: $i,SV37: $i,SV34: $i,SV39: $i,SV38: $i,SV31: $i] :
( ( ( related @ SV31 @ SV38 @ SV39 )
= $false )
| ( ( SV38 = SV34 )
= $false )
| ( ( SV39 = SV37 )
= $false )
| ( ( related @ SV2 @ SV34 @ SV37 )
= $true )
| ( ( element @ SV39 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV38 @ ( the_carrier @ SV31 ) )
= $false )
| ( ( element @ SV37 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( element @ SV34 @ ( the_carrier @ SV2 ) )
= $false )
| ( ( subrelstr @ SV31 @ SV2 )
= $false )
| ( ( rel_str @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(346,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[92,345,338,337,330,328,323,322,311,309,299,298,294,293,292,282,280,269,262,257,256,254,253,242,235,231,224,221,220,206,204,199,191,174,115,102,99,98,96,94,93]) ).
thf(347,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU374+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n004.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 15:17:35 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.11/0.43
% 1.11/0.43 No.of.Axioms: 25
% 1.11/0.43
% 1.11/0.43 Length.of.Defs: 0
% 1.11/0.43
% 1.11/0.43 Contains.Choice.Funs: false
% 1.11/0.43 ...........
% 1.11/0.43
% 1.11/0.43 ********************************
% 1.11/0.43 * All subproblems solved! *
% 1.11/0.43 ********************************
% 1.11/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:26,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:346,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.11/0.43
% 1.11/0.43 %**** Beginning of derivation protocol ****
% 1.11/0.43 % SZS output start CNFRefutation
% See solution above
% 1.11/0.43
% 1.11/0.43 %**** End of derivation protocol ****
% 1.11/0.43 %**** no. of clauses in derivation: 315 ****
% 1.11/0.43 %**** clause counter: 346 ****
% 1.11/0.43
% 1.11/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:26,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:346,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------