%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU373+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.58s 0.27s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of formulae : 192 ( 97 unt; 0 typ; 0 def)
% Number of atoms : 1412 ( 408 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 2737 ( 467 ~; 406 |; 12 &;1786 @)
% ( 9 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 7 con; 0-4 aty)
% Number of variables : 356 ( 0 ^; 347 !; 9 ?; 356 :)
% 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_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_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_SY40,type,
sK4_SY40: $i ).
thf(tp_sK5_SY32,type,
sK5_SY32: $i > $i ).
thf(tp_sK6_SY38,type,
sK6_SY38: $i > $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_InternalRel,type,
the_InternalRel: $i > $i ).
thf(tp_the_carrier,type,
the_carrier: $i > $i ).
thf(tp_the_mapping,type,
the_mapping: $i > $i > $i ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(9,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( subnetstr @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_yellow_6) ).
thf(33,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(34,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(37,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(38,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(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/sandbox/benchmark/theBenchmark.p',dt_m1_yellow_6) ).
thf(42,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(43,axiom,
$true,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(45,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(46,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(49,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(50,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(51,axiom,
$true,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',d8_yellow_6) ).
thf(53,axiom,
! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( subrelstr @ B @ A )
<=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_yellow_0) ).
thf(59,conjecture,
! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( subset @ ( the_carrier @ C ) @ ( the_carrier @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_yellow_6) ).
thf(60,negated_conjecture,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( subset @ ( the_carrier @ C ) @ ( the_carrier @ B ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[59]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ! [C: $i] :
( ( subnetstr @ C @ A @ B )
=> ( subset @ ( the_carrier @ C ) @ ( the_carrier @ B ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[60]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(64,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)],[29]) ).
thf(65,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(66,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(67,plain,
$true = $true,
inference(unfold_def,[status(thm)],[37]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(69,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(70,plain,
$true = $true,
inference(unfold_def,[status(thm)],[42]) ).
thf(71,plain,
$true = $true,
inference(unfold_def,[status(thm)],[43]) ).
thf(72,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(73,plain,
$true = $true,
inference(unfold_def,[status(thm)],[45]) ).
thf(74,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(75,plain,
$true = $true,
inference(unfold_def,[status(thm)],[49]) ).
thf(76,plain,
$true = $true,
inference(unfold_def,[status(thm)],[50]) ).
thf(77,plain,
$true = $true,
inference(unfold_def,[status(thm)],[51]) ).
thf(78,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(79,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( subrelstr @ B @ A )
<=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(80,plain,
( ( ( one_sorted_str @ sK1_A )
=> ! [SY25: $i] :
( ( net_str @ SY25 @ sK1_A )
=> ! [SY26: $i] :
( ( subnetstr @ SY26 @ sK1_A @ SY25 )
=> ( subset @ ( the_carrier @ SY26 ) @ ( the_carrier @ SY25 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(81,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(82,plain,
( ( ! [SY25: $i] :
( ( net_str @ SY25 @ sK1_A )
=> ! [SY26: $i] :
( ( subnetstr @ SY26 @ sK1_A @ SY25 )
=> ( subset @ ( the_carrier @ SY26 ) @ ( the_carrier @ SY25 ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[80]) ).
thf(83,plain,
( ( ~ ! [SY25: $i] :
( ( net_str @ SY25 @ sK1_A )
=> ! [SY26: $i] :
( ( subnetstr @ SY26 @ sK1_A @ SY25 )
=> ( subset @ ( the_carrier @ SY26 ) @ ( the_carrier @ SY25 ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[82]) ).
thf(84,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ! [B: $i] :
( ( rel_str @ B )
=> ( ( subrelstr @ B @ A )
<=> ( ( subset @ ( the_carrier @ B ) @ ( the_carrier @ A ) )
& ( subset @ ( the_InternalRel @ B ) @ ( the_InternalRel @ A ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(85,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)],[78]) ).
thf(86,plain,
$true = $true,
inference(copy,[status(thm)],[77]) ).
thf(87,plain,
$true = $true,
inference(copy,[status(thm)],[76]) ).
thf(88,plain,
$true = $true,
inference(copy,[status(thm)],[75]) ).
thf(89,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( one_sorted_str @ A ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(90,plain,
$true = $true,
inference(copy,[status(thm)],[73]) ).
thf(91,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ! [B: $i] :
( ( net_str @ B @ A )
=> ( rel_str @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(92,plain,
$true = $true,
inference(copy,[status(thm)],[71]) ).
thf(93,plain,
$true = $true,
inference(copy,[status(thm)],[70]) ).
thf(94,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)],[69]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( rel_str @ A )
=> ( relation_of2_as_subset @ ( the_InternalRel @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(96,plain,
$true = $true,
inference(copy,[status(thm)],[67]) ).
thf(97,plain,
( ( ? [A: $i] : ( one_sorted_str @ A ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(98,plain,
( ( ! [A: $i] :
( ( one_sorted_str @ A )
=> ? [B: $i] : ( net_str @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( ( one_sorted_str @ A )
& ( net_str @ B @ A ) )
=> ? [C: $i] : ( subnetstr @ C @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(100,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(101,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(102,plain,
( ( one_sorted_str @ sK1_A )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(103,plain,
( ( ~ ! [SY25: $i] :
( ( net_str @ SY25 @ sK1_A )
=> ! [SY26: $i] :
( ( subnetstr @ SY26 @ sK1_A @ SY25 )
=> ( subset @ ( the_carrier @ SY26 ) @ ( the_carrier @ SY25 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(104,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SX0 ) @ ( the_carrier @ SX0 ) @ ( the_carrier @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(105,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)],[99]) ).
thf(106,plain,
( ( ~ ! [SX0: $i] :
~ ( one_sorted_str @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(107,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ! [SX1: $i] :
( ~ ( net_str @ SX1 @ SX0 )
| ( rel_str @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(108,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ! [SX1: $i] :
( ~ ( rel_str @ SX1 )
| ~ ( ~ ( ~ ( subrelstr @ SX1 @ SX0 )
| ~ ( ~ ( subset @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) )
| ~ ( subset @ ( the_InternalRel @ SX1 ) @ ( the_InternalRel @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) )
| ~ ( subset @ ( the_InternalRel @ SX1 ) @ ( the_InternalRel @ SX0 ) ) )
| ( subrelstr @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(109,plain,
( ( ! [SX0: $i] :
( ~ ( one_sorted_str @ SX0 )
| ~ ! [SX1: $i] :
~ ( net_str @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(110,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)],[85]) ).
thf(111,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)],[94]) ).
thf(112,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)],[101]) ).
thf(113,plain,
( ( ! [SX0: $i] :
( ~ ( rel_str @ SX0 )
| ( one_sorted_str @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(114,plain,
( ( ~ ! [SX0: $i] :
( ~ ( net_str @ SX0 @ sK1_A )
| ! [SX1: $i] :
( ~ ( subnetstr @ SX1 @ sK1_A @ SX0 )
| ( subset @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(115,plain,
! [SV1: $i] :
( ( ! [SY27: $i] : ( subset @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV2: $i] :
( ( ~ ( rel_str @ SV2 )
| ( relation_of2_as_subset @ ( the_InternalRel @ SV2 ) @ ( the_carrier @ SV2 ) @ ( the_carrier @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV3: $i] :
( ( ! [SY28: $i] :
( ~ ~ ( ~ ( one_sorted_str @ SV3 )
| ~ ( net_str @ SY28 @ SV3 ) )
| ~ ! [SY29: $i] :
~ ( subnetstr @ SY29 @ SV3 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(118,plain,
( ( ! [SX0: $i] :
~ ( one_sorted_str @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(119,plain,
! [SV4: $i] :
( ( ~ ( one_sorted_str @ SV4 )
| ! [SY30: $i] :
( ~ ( net_str @ SY30 @ SV4 )
| ( rel_str @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(120,plain,
! [SV5: $i] :
( ( ~ ( rel_str @ SV5 )
| ! [SY31: $i] :
( ~ ( rel_str @ SY31 )
| ~ ( ~ ( ~ ( subrelstr @ SY31 @ SV5 )
| ~ ( ~ ( subset @ ( the_carrier @ SY31 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SY31 ) @ ( the_InternalRel @ SV5 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SY31 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SY31 ) @ ( the_InternalRel @ SV5 ) ) )
| ( subrelstr @ SY31 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV6: $i] :
( ( ~ ( one_sorted_str @ SV6 )
| ~ ! [SY32: $i] :
~ ( net_str @ SY32 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV7: $i] :
( ( ~ ( one_sorted_str @ SV7 )
| ! [SY33: $i] :
( ~ ( net_str @ SY33 @ SV7 )
| ! [SY34: $i] :
( ~ ( net_str @ SY34 @ SV7 )
| ~ ( ~ ( ~ ( subnetstr @ SY34 @ SV7 @ SY33 )
| ~ ( ~ ( subrelstr @ SY34 @ SY33 )
| ( ( the_mapping @ SV7 @ SY34 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY33 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SY33 ) @ ( the_carrier @ SY34 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY34 @ SY33 )
| ( ( the_mapping @ SV7 @ SY34 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY33 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SY33 ) @ ( the_carrier @ SY34 ) ) ) )
| ( subnetstr @ SY34 @ SV7 @ SY33 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV8: $i] :
( ( ! [SY35: $i] :
( ~ ~ ( ~ ( one_sorted_str @ SV8 )
| ~ ( net_str @ SY35 @ SV8 ) )
| ! [SY36: $i] :
( ~ ( subnetstr @ SY36 @ SV8 @ SY35 )
| ( net_str @ SY36 @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV9: $i] :
( ( ! [SY37: $i] :
~ ( ~ ( ~ ( element @ SV9 @ ( powerset @ SY37 ) )
| ( subset @ SV9 @ SY37 ) )
| ~ ( ~ ( subset @ SV9 @ SY37 )
| ( element @ SV9 @ ( powerset @ SY37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(125,plain,
! [SV10: $i] :
( ( ~ ( rel_str @ SV10 )
| ( one_sorted_str @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(126,plain,
( ( ! [SX0: $i] :
( ~ ( net_str @ SX0 @ sK1_A )
| ! [SX1: $i] :
( ~ ( subnetstr @ SX1 @ sK1_A @ SX0 )
| ( subset @ ( the_carrier @ SX1 ) @ ( the_carrier @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(127,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV2: $i] :
( ( ( ~ ( rel_str @ SV2 ) )
= $true )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV2 ) @ ( the_carrier @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV12: $i,SV3: $i] :
( ( ~ ~ ( ~ ( one_sorted_str @ SV3 )
| ~ ( net_str @ SV12 @ SV3 ) )
| ~ ! [SY38: $i] :
~ ( subnetstr @ SY38 @ SV3 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(130,plain,
( ( ~ ( one_sorted_str @ sK2_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[118]) ).
thf(131,plain,
! [SV4: $i] :
( ( ( ~ ( one_sorted_str @ SV4 ) )
= $true )
| ( ( ! [SY30: $i] :
( ~ ( net_str @ SY30 @ SV4 )
| ( rel_str @ SY30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV5: $i] :
( ( ( ~ ( rel_str @ SV5 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( rel_str @ SY31 )
| ~ ( ~ ( ~ ( subrelstr @ SY31 @ SV5 )
| ~ ( ~ ( subset @ ( the_carrier @ SY31 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SY31 ) @ ( the_InternalRel @ SV5 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SY31 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SY31 ) @ ( the_InternalRel @ SV5 ) ) )
| ( subrelstr @ SY31 @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(133,plain,
! [SV6: $i] :
( ( ( ~ ( one_sorted_str @ SV6 ) )
= $true )
| ( ( ~ ! [SY32: $i] :
~ ( net_str @ SY32 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV7: $i] :
( ( ( ~ ( one_sorted_str @ SV7 ) )
= $true )
| ( ( ! [SY33: $i] :
( ~ ( net_str @ SY33 @ SV7 )
| ! [SY34: $i] :
( ~ ( net_str @ SY34 @ SV7 )
| ~ ( ~ ( ~ ( subnetstr @ SY34 @ SV7 @ SY33 )
| ~ ( ~ ( subrelstr @ SY34 @ SY33 )
| ( ( the_mapping @ SV7 @ SY34 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY33 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SY33 ) @ ( the_carrier @ SY34 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY34 @ SY33 )
| ( ( the_mapping @ SV7 @ SY34 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY33 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SY33 ) @ ( the_carrier @ SY34 ) ) ) )
| ( subnetstr @ SY34 @ SV7 @ SY33 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV13: $i,SV8: $i] :
( ( ~ ~ ( ~ ( one_sorted_str @ SV8 )
| ~ ( net_str @ SV13 @ SV8 ) )
| ! [SY39: $i] :
( ~ ( subnetstr @ SY39 @ SV8 @ SV13 )
| ( net_str @ SY39 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( ~ ( ~ ( element @ SV9 @ ( powerset @ SV14 ) )
| ( subset @ SV9 @ SV14 ) )
| ~ ( ~ ( subset @ SV9 @ SV14 )
| ( element @ SV9 @ ( powerset @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV10: $i] :
( ( ( ~ ( rel_str @ SV10 ) )
= $true )
| ( ( one_sorted_str @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(138,plain,
( ( ~ ( net_str @ sK3_SX0 @ sK1_A )
| ! [SY40: $i] :
( ~ ( subnetstr @ SY40 @ sK1_A @ sK3_SX0 )
| ( subset @ ( the_carrier @ SY40 ) @ ( the_carrier @ sK3_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[126]) ).
thf(139,plain,
! [SV2: $i] :
( ( ( rel_str @ SV2 )
= $false )
| ( ( relation_of2_as_subset @ ( the_InternalRel @ SV2 ) @ ( the_carrier @ SV2 ) @ ( the_carrier @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(140,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( one_sorted_str @ SV3 )
| ~ ( net_str @ SV12 @ SV3 ) ) )
= $true )
| ( ( ~ ! [SY38: $i] :
~ ( subnetstr @ SY38 @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(141,plain,
( ( one_sorted_str @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(142,plain,
! [SV4: $i] :
( ( ( one_sorted_str @ SV4 )
= $false )
| ( ( ! [SY30: $i] :
( ~ ( net_str @ SY30 @ SV4 )
| ( rel_str @ SY30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(143,plain,
! [SV5: $i] :
( ( ( rel_str @ SV5 )
= $false )
| ( ( ! [SY31: $i] :
( ~ ( rel_str @ SY31 )
| ~ ( ~ ( ~ ( subrelstr @ SY31 @ SV5 )
| ~ ( ~ ( subset @ ( the_carrier @ SY31 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SY31 ) @ ( the_InternalRel @ SV5 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SY31 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SY31 ) @ ( the_InternalRel @ SV5 ) ) )
| ( subrelstr @ SY31 @ SV5 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(144,plain,
! [SV6: $i] :
( ( ( one_sorted_str @ SV6 )
= $false )
| ( ( ~ ! [SY32: $i] :
~ ( net_str @ SY32 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(145,plain,
! [SV7: $i] :
( ( ( one_sorted_str @ SV7 )
= $false )
| ( ( ! [SY33: $i] :
( ~ ( net_str @ SY33 @ SV7 )
| ! [SY34: $i] :
( ~ ( net_str @ SY34 @ SV7 )
| ~ ( ~ ( ~ ( subnetstr @ SY34 @ SV7 @ SY33 )
| ~ ( ~ ( subrelstr @ SY34 @ SY33 )
| ( ( the_mapping @ SV7 @ SY34 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY33 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SY33 ) @ ( the_carrier @ SY34 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY34 @ SY33 )
| ( ( the_mapping @ SV7 @ SY34 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SY33 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SY33 ) @ ( the_carrier @ SY34 ) ) ) )
| ( subnetstr @ SY34 @ SV7 @ SY33 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(146,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( one_sorted_str @ SV8 )
| ~ ( net_str @ SV13 @ SV8 ) ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( subnetstr @ SY39 @ SV8 @ SV13 )
| ( net_str @ SY39 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(147,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( ~ ( element @ SV9 @ ( powerset @ SV14 ) )
| ( subset @ SV9 @ SV14 ) )
| ~ ( ~ ( subset @ SV9 @ SV14 )
| ( element @ SV9 @ ( powerset @ SV14 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(148,plain,
! [SV10: $i] :
( ( ( rel_str @ SV10 )
= $false )
| ( ( one_sorted_str @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(149,plain,
( ( ~ ( net_str @ sK3_SX0 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(150,plain,
( ( ! [SY40: $i] :
( ~ ( subnetstr @ SY40 @ sK1_A @ sK3_SX0 )
| ( subset @ ( the_carrier @ SY40 ) @ ( the_carrier @ sK3_SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(151,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ( ~ ( one_sorted_str @ SV3 )
| ~ ( net_str @ SV12 @ SV3 ) ) )
= $false )
| ( ( ~ ! [SY38: $i] :
~ ( subnetstr @ SY38 @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV4: $i,SV15: $i] :
( ( ( ~ ( net_str @ SV15 @ SV4 )
| ( rel_str @ SV15 ) )
= $true )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(153,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( rel_str @ SV16 )
| ~ ( ~ ( ~ ( subrelstr @ SV16 @ SV5 )
| ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) )
| ( subrelstr @ SV16 @ SV5 ) ) ) )
= $true )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(154,plain,
! [SV6: $i] :
( ( ( ! [SY32: $i] :
~ ( net_str @ SY32 @ SV6 ) )
= $false )
| ( ( one_sorted_str @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(155,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( net_str @ SV17 @ SV7 )
| ! [SY41: $i] :
( ~ ( net_str @ SY41 @ SV7 )
| ~ ( ~ ( ~ ( subnetstr @ SY41 @ SV7 @ SV17 )
| ~ ( ~ ( subrelstr @ SY41 @ SV17 )
| ( ( the_mapping @ SV7 @ SY41 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SY41 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY41 @ SV17 )
| ( ( the_mapping @ SV7 @ SY41 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SY41 ) ) ) )
| ( subnetstr @ SY41 @ SV7 @ SV17 ) ) ) ) )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(156,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( ~ ( one_sorted_str @ SV8 )
| ~ ( net_str @ SV13 @ SV8 ) ) )
= $false )
| ( ( ! [SY39: $i] :
( ~ ( subnetstr @ SY39 @ SV8 @ SV13 )
| ( net_str @ SY39 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(157,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( ~ ( element @ SV9 @ ( powerset @ SV14 ) )
| ( subset @ SV9 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(158,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( ~ ( subset @ SV9 @ SV14 )
| ( element @ SV9 @ ( powerset @ SV14 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(159,plain,
( ( net_str @ sK3_SX0 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(160,plain,
( ( ~ ( subnetstr @ sK4_SY40 @ sK1_A @ sK3_SX0 )
| ( subset @ ( the_carrier @ sK4_SY40 ) @ ( the_carrier @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[150]) ).
thf(161,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ( one_sorted_str @ SV3 )
| ~ ( net_str @ SV12 @ SV3 ) )
= $true )
| ( ( ~ ! [SY38: $i] :
~ ( subnetstr @ SY38 @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(162,plain,
! [SV4: $i,SV15: $i] :
( ( ( ~ ( net_str @ SV15 @ SV4 ) )
= $true )
| ( ( rel_str @ SV15 )
= $true )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( rel_str @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subrelstr @ SV16 @ SV5 )
| ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) )
| ( subrelstr @ SV16 @ SV5 ) ) ) )
= $true )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(164,plain,
! [SV6: $i] :
( ( ( ~ ( net_str @ ( sK5_SY32 @ SV6 ) @ SV6 ) )
= $false )
| ( ( one_sorted_str @ SV6 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[154]) ).
thf(165,plain,
! [SV7: $i,SV17: $i] :
( ( ( ~ ( net_str @ SV17 @ SV7 ) )
= $true )
| ( ( ! [SY41: $i] :
( ~ ( net_str @ SY41 @ SV7 )
| ~ ( ~ ( ~ ( subnetstr @ SY41 @ SV7 @ SV17 )
| ~ ( ~ ( subrelstr @ SY41 @ SV17 )
| ( ( the_mapping @ SV7 @ SY41 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SY41 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY41 @ SV17 )
| ( ( the_mapping @ SV7 @ SY41 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SY41 ) ) ) )
| ( subnetstr @ SY41 @ SV7 @ SV17 ) ) ) ) )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( one_sorted_str @ SV8 )
| ~ ( net_str @ SV13 @ SV8 ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( subnetstr @ SY39 @ SV8 @ SV13 )
| ( net_str @ SY39 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(167,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( element @ SV9 @ ( powerset @ SV14 ) )
| ( subset @ SV9 @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(168,plain,
! [SV14: $i,SV9: $i] :
( ( ~ ( subset @ SV9 @ SV14 )
| ( element @ SV9 @ ( powerset @ SV14 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(169,plain,
( ( ~ ( subnetstr @ sK4_SY40 @ sK1_A @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(170,plain,
( ( subset @ ( the_carrier @ sK4_SY40 ) @ ( the_carrier @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(171,plain,
! [SV12: $i,SV3: $i] :
( ( ( ~ ( one_sorted_str @ SV3 ) )
= $true )
| ( ( ~ ( net_str @ SV12 @ SV3 ) )
= $true )
| ( ( ~ ! [SY38: $i] :
~ ( subnetstr @ SY38 @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV4: $i,SV15: $i] :
( ( ( net_str @ SV15 @ SV4 )
= $false )
| ( ( rel_str @ SV15 )
= $true )
| ( ( one_sorted_str @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(173,plain,
! [SV5: $i,SV16: $i] :
( ( ( rel_str @ SV16 )
= $false )
| ( ( ~ ( ~ ( ~ ( subrelstr @ SV16 @ SV5 )
| ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) )
| ( subrelstr @ SV16 @ SV5 ) ) ) )
= $true )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(174,plain,
! [SV6: $i] :
( ( ( net_str @ ( sK5_SY32 @ SV6 ) @ SV6 )
= $true )
| ( ( one_sorted_str @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(175,plain,
! [SV7: $i,SV17: $i] :
( ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( ! [SY41: $i] :
( ~ ( net_str @ SY41 @ SV7 )
| ~ ( ~ ( ~ ( subnetstr @ SY41 @ SV7 @ SV17 )
| ~ ( ~ ( subrelstr @ SY41 @ SV17 )
| ( ( the_mapping @ SV7 @ SY41 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SY41 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SY41 @ SV17 )
| ( ( the_mapping @ SV7 @ SY41 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SY41 ) ) ) )
| ( subnetstr @ SY41 @ SV7 @ SV17 ) ) ) ) )
= $true )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(176,plain,
! [SV13: $i,SV8: $i] :
( ( ( ~ ( one_sorted_str @ SV8 ) )
= $true )
| ( ( ~ ( net_str @ SV13 @ SV8 ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( subnetstr @ SY39 @ SV8 @ SV13 )
| ( net_str @ SY39 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV14: $i,SV9: $i] :
( ( ( ~ ( element @ SV9 @ ( powerset @ SV14 ) ) )
= $true )
| ( ( subset @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV14: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV14 ) )
= $true )
| ( ( element @ SV9 @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(179,plain,
( ( subnetstr @ sK4_SY40 @ sK1_A @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(180,plain,
! [SV12: $i,SV3: $i] :
( ( ( one_sorted_str @ SV3 )
= $false )
| ( ( ~ ( net_str @ SV12 @ SV3 ) )
= $true )
| ( ( ~ ! [SY38: $i] :
~ ( subnetstr @ SY38 @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(181,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( ~ ( subrelstr @ SV16 @ SV5 )
| ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) )
| ( subrelstr @ SV16 @ SV5 ) ) )
= $false )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(182,plain,
! [SV17: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( net_str @ SV18 @ SV7 )
| ~ ( ~ ( ~ ( subnetstr @ SV18 @ SV7 @ SV17 )
| ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) )
| ( subnetstr @ SV18 @ SV7 @ SV17 ) ) ) )
= $true )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(183,plain,
! [SV13: $i,SV8: $i] :
( ( ( one_sorted_str @ SV8 )
= $false )
| ( ( ~ ( net_str @ SV13 @ SV8 ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( subnetstr @ SY39 @ SV8 @ SV13 )
| ( net_str @ SY39 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(184,plain,
! [SV14: $i,SV9: $i] :
( ( ( element @ SV9 @ ( powerset @ SV14 ) )
= $false )
| ( ( subset @ SV9 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(185,plain,
! [SV14: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV14 )
= $false )
| ( ( element @ SV9 @ ( powerset @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(186,plain,
! [SV3: $i,SV12: $i] :
( ( ( net_str @ SV12 @ SV3 )
= $false )
| ( ( one_sorted_str @ SV3 )
= $false )
| ( ( ~ ! [SY38: $i] :
~ ( subnetstr @ SY38 @ SV3 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(187,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( ~ ( subrelstr @ SV16 @ SV5 )
| ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) ) ) )
= $false )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(188,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) )
| ( subrelstr @ SV16 @ SV5 ) ) )
= $false )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(189,plain,
! [SV17: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( net_str @ SV18 @ SV7 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( subnetstr @ SV18 @ SV7 @ SV17 )
| ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) )
| ( subnetstr @ SV18 @ SV7 @ SV17 ) ) ) )
= $true )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(190,plain,
! [SV8: $i,SV13: $i] :
( ( ( net_str @ SV13 @ SV8 )
= $false )
| ( ( one_sorted_str @ SV8 )
= $false )
| ( ( ! [SY39: $i] :
( ~ ( subnetstr @ SY39 @ SV8 @ SV13 )
| ( net_str @ SY39 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(191,plain,
! [SV12: $i,SV3: $i] :
( ( ( ! [SY38: $i] :
~ ( subnetstr @ SY38 @ SV3 @ SV12 ) )
= $false )
| ( ( one_sorted_str @ SV3 )
= $false )
| ( ( net_str @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(192,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( subrelstr @ SV16 @ SV5 )
| ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) ) )
= $true )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(193,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) )
| ( subrelstr @ SV16 @ SV5 ) )
= $true )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(194,plain,
! [SV17: $i,SV7: $i,SV18: $i] :
( ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( ~ ( ~ ( ~ ( subnetstr @ SV18 @ SV7 @ SV17 )
| ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) )
| ( subnetstr @ SV18 @ SV7 @ SV17 ) ) ) )
= $true )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(195,plain,
! [SV13: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( subnetstr @ SV19 @ SV8 @ SV13 )
| ( net_str @ SV19 @ SV8 ) )
= $true )
| ( ( one_sorted_str @ SV8 )
= $false )
| ( ( net_str @ SV13 @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(196,plain,
! [SV3: $i,SV12: $i] :
( ( ( ~ ( subnetstr @ ( sK6_SY38 @ SV12 @ SV3 ) @ SV3 @ SV12 ) )
= $false )
| ( ( one_sorted_str @ SV3 )
= $false )
| ( ( net_str @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[191]) ).
thf(197,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( subrelstr @ SV16 @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) ) )
= $true )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(198,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) ) )
= $true )
| ( ( subrelstr @ SV16 @ SV5 )
= $true )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(199,plain,
! [SV17: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( ~ ( subnetstr @ SV18 @ SV7 @ SV17 )
| ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) ) )
| ~ ( ~ ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) )
| ( subnetstr @ SV18 @ SV7 @ SV17 ) ) )
= $false )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(200,plain,
! [SV13: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( subnetstr @ SV19 @ SV8 @ SV13 ) )
= $true )
| ( ( net_str @ SV19 @ SV8 )
= $true )
| ( ( one_sorted_str @ SV8 )
= $false )
| ( ( net_str @ SV13 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(201,plain,
! [SV3: $i,SV12: $i] :
( ( ( subnetstr @ ( sK6_SY38 @ SV12 @ SV3 ) @ SV3 @ SV12 )
= $true )
| ( ( one_sorted_str @ SV3 )
= $false )
| ( ( net_str @ SV12 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(202,plain,
! [SV5: $i,SV16: $i] :
( ( ( subrelstr @ SV16 @ SV5 )
= $false )
| ( ( ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) ) )
= $true )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(203,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) ) )
= $false )
| ( ( subrelstr @ SV16 @ SV5 )
= $true )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(204,plain,
! [SV17: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( ~ ( subnetstr @ SV18 @ SV7 @ SV17 )
| ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) ) ) )
= $false )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(205,plain,
! [SV7: $i,SV17: $i,SV18: $i] :
( ( ( ~ ( ~ ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) )
| ( subnetstr @ SV18 @ SV7 @ SV17 ) ) )
= $false )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(206,plain,
! [SV13: $i,SV8: $i,SV19: $i] :
( ( ( subnetstr @ SV19 @ SV8 @ SV13 )
= $false )
| ( ( net_str @ SV19 @ SV8 )
= $true )
| ( ( one_sorted_str @ SV8 )
= $false )
| ( ( net_str @ SV13 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(207,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) )
= $false )
| ( ( subrelstr @ SV16 @ SV5 )
= $false )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(208,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
| ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) )
= $true )
| ( ( subrelstr @ SV16 @ SV5 )
= $true )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(209,plain,
! [SV17: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( subnetstr @ SV18 @ SV7 @ SV17 )
| ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) ) )
= $true )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(210,plain,
! [SV7: $i,SV17: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) )
| ( subnetstr @ SV18 @ SV7 @ SV17 ) )
= $true )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(211,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) ) )
= $false )
| ( ( subrelstr @ SV16 @ SV5 )
= $false )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(212,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) )
= $false )
| ( ( subrelstr @ SV16 @ SV5 )
= $false )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(213,plain,
! [SV5: $i,SV16: $i] :
( ( ( ~ ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) ) )
= $true )
| ( ( ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) )
= $true )
| ( ( subrelstr @ SV16 @ SV5 )
= $true )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(214,plain,
! [SV17: $i,SV7: $i,SV18: $i] :
( ( ( ~ ( subnetstr @ SV18 @ SV7 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) ) )
= $true )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(215,plain,
! [SV7: $i,SV17: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) ) )
= $true )
| ( ( subnetstr @ SV18 @ SV7 @ SV17 )
= $true )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(216,plain,
! [SV5: $i,SV16: $i] :
( ( ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
= $true )
| ( ( subrelstr @ SV16 @ SV5 )
= $false )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(217,plain,
! [SV5: $i,SV16: $i] :
( ( ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) )
= $true )
| ( ( subrelstr @ SV16 @ SV5 )
= $false )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(218,plain,
! [SV5: $i,SV16: $i] :
( ( ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
= $false )
| ( ( ~ ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) ) )
= $true )
| ( ( subrelstr @ SV16 @ SV5 )
= $true )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(219,plain,
! [SV17: $i,SV7: $i,SV18: $i] :
( ( ( subnetstr @ SV18 @ SV7 @ SV17 )
= $false )
| ( ( ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) ) )
= $true )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(220,plain,
! [SV7: $i,SV17: $i,SV18: $i] :
( ( ( ~ ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) ) )
= $false )
| ( ( subnetstr @ SV18 @ SV7 @ SV17 )
= $true )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(221,plain,
! [SV5: $i,SV16: $i] :
( ( ( subset @ ( the_InternalRel @ SV16 ) @ ( the_InternalRel @ SV5 ) )
= $false )
| ( ( subset @ ( the_carrier @ SV16 ) @ ( the_carrier @ SV5 ) )
= $false )
| ( ( subrelstr @ SV16 @ SV5 )
= $true )
| ( ( rel_str @ SV16 )
= $false )
| ( ( rel_str @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(222,plain,
! [SV7: $i,SV17: $i,SV18: $i] :
( ( ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) )
= $false )
| ( ( subnetstr @ SV18 @ SV7 @ SV17 )
= $false )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(223,plain,
! [SV7: $i,SV17: $i,SV18: $i] :
( ( ( ~ ( subrelstr @ SV18 @ SV17 )
| ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) ) )
= $true )
| ( ( subnetstr @ SV18 @ SV7 @ SV17 )
= $true )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(224,plain,
! [SV7: $i,SV17: $i,SV18: $i] :
( ( ( ~ ( subrelstr @ SV18 @ SV17 ) )
= $false )
| ( ( subnetstr @ SV18 @ SV7 @ SV17 )
= $false )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(225,plain,
! [SV17: $i,SV18: $i,SV7: $i] :
( ( ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) )
= $false )
| ( ( subnetstr @ SV18 @ SV7 @ SV17 )
= $false )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(226,plain,
! [SV7: $i,SV17: $i,SV18: $i] :
( ( ( ~ ( subrelstr @ SV18 @ SV17 ) )
= $true )
| ( ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) )
= $true )
| ( ( subnetstr @ SV18 @ SV7 @ SV17 )
= $true )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(227,plain,
! [SV7: $i,SV17: $i,SV18: $i] :
( ( ( subrelstr @ SV18 @ SV17 )
= $true )
| ( ( subnetstr @ SV18 @ SV7 @ SV17 )
= $false )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(228,plain,
! [SV17: $i,SV18: $i,SV7: $i] :
( ( ( ( the_mapping @ SV7 @ SV18 )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) )
= $true )
| ( ( subnetstr @ SV18 @ SV7 @ SV17 )
= $false )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(229,plain,
! [SV7: $i,SV17: $i,SV18: $i] :
( ( ( subrelstr @ SV18 @ SV17 )
= $false )
| ( ( ( the_mapping @ SV7 @ SV18 )
!= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) )
= $true )
| ( ( subnetstr @ SV18 @ SV7 @ SV17 )
= $true )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(230,plain,
! [SV17: $i,SV18: $i,SV7: $i] :
( ( ( ( the_mapping @ SV7 @ SV18 )
= ( relation_dom_restr_as_relation_of @ ( the_carrier @ SV17 ) @ ( the_carrier @ SV7 ) @ ( the_mapping @ SV7 @ SV17 ) @ ( the_carrier @ SV18 ) ) )
= $false )
| ( ( subrelstr @ SV18 @ SV17 )
= $false )
| ( ( subnetstr @ SV18 @ SV7 @ SV17 )
= $true )
| ( ( net_str @ SV18 @ SV7 )
= $false )
| ( ( net_str @ SV17 @ SV7 )
= $false )
| ( ( one_sorted_str @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(231,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[86,230,228,227,221,217,216,206,201,185,184,179,174,172,170,159,148,141,139,127,102,96,93,92,90,88,87]) ).
thf(232,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU373+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n010.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 15:17:03 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.58/0.27
% 0.58/0.27 No.of.Axioms: 18
% 0.58/0.27
% 0.58/0.27 Length.of.Defs: 0
% 0.58/0.27
% 0.58/0.27 Contains.Choice.Funs: false
% 0.58/0.27 .....
% 0.58/0.27
% 0.58/0.27 ********************************
% 0.58/0.27 * All subproblems solved! *
% 0.58/0.27 ********************************
% 0.58/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:19,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:231,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.58/0.27
% 0.58/0.27 %**** Beginning of derivation protocol ****
% 0.58/0.27 % SZS output start CNFRefutation
% See solution above
% 0.58/0.27
% 0.58/0.27 %**** End of derivation protocol ****
% 0.58/0.27 %**** no. of clauses in derivation: 192 ****
% 0.58/0.27 %**** clause counter: 231 ****
% 0.58/0.27
% 0.58/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:19,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:231,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------