%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU248+2 : 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 : n017.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 10:43:40 AM UTC 2026
% Result : Theorem 18.70s 3.35s
% Output : CNFRefutation 18.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 70
% Syntax : Number of formulae : 587 ( 358 unt; 0 typ; 0 def)
% Number of atoms : 2939 ( 874 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 4570 ( 880 ~; 613 |; 66 &;2880 @)
% ( 9 <=>; 122 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 68 usr; 9 con; 0-3 aty)
% Number of variables : 1043 ( 0 ^;1031 !; 12 ?;1043 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $o ).
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_are_equipotent,type,
are_equipotent: $i > $i > $o ).
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cast_to_subset,type,
cast_to_subset: $i > $i ).
thf(tp_complements_of_subsets,type,
complements_of_subsets: $i > $i > $i ).
thf(tp_connected,type,
connected: $i > $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
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_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_fiber,type,
fiber: $i > $i > $i ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_inverse,type,
function_inverse: $i > $i ).
thf(tp_identity_relation,type,
identity_relation: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_is_antisymmetric_in,type,
is_antisymmetric_in: $i > $i > $o ).
thf(tp_is_connected_in,type,
is_connected_in: $i > $i > $o ).
thf(tp_is_reflexive_in,type,
is_reflexive_in: $i > $i > $o ).
thf(tp_is_transitive_in,type,
is_transitive_in: $i > $i > $o ).
thf(tp_is_well_founded_in,type,
is_well_founded_in: $i > $i > $o ).
thf(tp_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_ordinal_subset,type,
ordinal_subset: $i > $i > $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_reflexive,type,
reflexive: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $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_field,type,
relation_field: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_restriction,type,
relation_restriction: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY98,type,
sK2_SY98: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SY151,type,
sK7_SY151: $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_transitive,type,
transitive: $i > $o ).
thf(tp_union,type,
union: $i > $i ).
thf(tp_union_of_subsets,type,
union_of_subsets: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(tp_unordered_triple,type,
unordered_triple: $i > $i > $i > $i ).
thf(tp_well_founded_relation,type,
well_founded_relation: $i > $o ).
thf(tp_well_ordering,type,
well_ordering: $i > $o ).
thf(tp_well_orders,type,
well_orders: $i > $i > $o ).
thf(17,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(24,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(29,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(34,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(36,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(39,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(45,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(47,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(74,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(75,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(81,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(84,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(85,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(86,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(87,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(88,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(90,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(91,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(92,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(93,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(94,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(96,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(98,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(99,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(100,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(101,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(102,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(103,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(104,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(105,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(106,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(107,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(136,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(172,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(187,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
thf(190,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(195,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(203,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(222,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
thf(227,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(236,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(245,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(248,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(261,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t178_relat_1) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_relat_1) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(279,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_relat_1) ).
thf(283,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_relat_1) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
thf(306,conjecture,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l29_wellord1) ).
thf(307,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[306]) ).
thf(308,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_dom @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[307]) ).
thf(309,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(310,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(311,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(312,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(313,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(314,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(315,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(316,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(317,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(318,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(319,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(320,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(321,plain,
$true = $true,
inference(unfold_def,[status(thm)],[74]) ).
thf(322,plain,
$true = $true,
inference(unfold_def,[status(thm)],[75]) ).
thf(323,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(324,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(325,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(326,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(327,plain,
$true = $true,
inference(unfold_def,[status(thm)],[84]) ).
thf(328,plain,
$true = $true,
inference(unfold_def,[status(thm)],[85]) ).
thf(329,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(330,plain,
$true = $true,
inference(unfold_def,[status(thm)],[87]) ).
thf(331,plain,
$true = $true,
inference(unfold_def,[status(thm)],[88]) ).
thf(332,plain,
$true = $true,
inference(unfold_def,[status(thm)],[90]) ).
thf(333,plain,
$true = $true,
inference(unfold_def,[status(thm)],[91]) ).
thf(334,plain,
$true = $true,
inference(unfold_def,[status(thm)],[92]) ).
thf(335,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(336,plain,
$true = $true,
inference(unfold_def,[status(thm)],[94]) ).
thf(337,plain,
$true = $true,
inference(unfold_def,[status(thm)],[96]) ).
thf(338,plain,
$true = $true,
inference(unfold_def,[status(thm)],[98]) ).
thf(339,plain,
$true = $true,
inference(unfold_def,[status(thm)],[99]) ).
thf(340,plain,
$true = $true,
inference(unfold_def,[status(thm)],[100]) ).
thf(341,plain,
$true = $true,
inference(unfold_def,[status(thm)],[101]) ).
thf(342,plain,
$true = $true,
inference(unfold_def,[status(thm)],[102]) ).
thf(343,plain,
$true = $true,
inference(unfold_def,[status(thm)],[103]) ).
thf(344,plain,
$true = $true,
inference(unfold_def,[status(thm)],[104]) ).
thf(345,plain,
$true = $true,
inference(unfold_def,[status(thm)],[105]) ).
thf(346,plain,
$true = $true,
inference(unfold_def,[status(thm)],[106]) ).
thf(347,plain,
$true = $true,
inference(unfold_def,[status(thm)],[107]) ).
thf(348,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(349,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(350,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(351,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(352,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(354,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(355,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(356,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(357,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(358,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(359,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(360,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(361,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(362,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(363,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(364,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(365,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(366,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(367,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(368,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(369,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(370,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(371,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(372,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(373,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(374,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(375,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(376,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(377,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(378,plain,
( ( ! [SY98: $i] :
( ( relation @ SY98 )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ SY98 ) ) @ ( relation_dom @ SY98 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[308]) ).
thf(379,plain,
( ( ( relation @ sK2_SY98 )
=> ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY98 ) ) @ ( relation_dom @ sK2_SY98 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[378]) ).
thf(380,plain,
( ( relation @ sK2_SY98 )
= $true ),
inference(standard_cnf,[status(thm)],[379]) ).
thf(381,plain,
( ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY98 ) ) @ ( relation_dom @ sK2_SY98 ) )
= $false ),
inference(standard_cnf,[status(thm)],[379]) ).
thf(382,plain,
( ( ~ ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY98 ) ) @ ( relation_dom @ sK2_SY98 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[381]) ).
thf(383,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[377]) ).
thf(384,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[376]) ).
thf(385,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[375]) ).
thf(386,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[374]) ).
thf(387,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[373]) ).
thf(388,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[372]) ).
thf(389,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( relation_dom_restriction @ ( relation_rng_restriction @ A @ C ) @ B )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[371]) ).
thf(390,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_inverse_image @ B @ A ) @ ( relation_dom @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[370]) ).
thf(391,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( subset @ A @ B )
=> ( subset @ ( relation_inverse_image @ C @ A ) @ ( relation_inverse_image @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[369]) ).
thf(392,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[368]) ).
thf(393,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[367]) ).
thf(394,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[366]) ).
thf(395,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[365]) ).
thf(396,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[364]) ).
thf(397,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[363]) ).
thf(398,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[362]) ).
thf(399,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[361]) ).
thf(400,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[360]) ).
thf(401,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[359]) ).
thf(402,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom @ ( relation_composition @ A @ B ) ) @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[358]) ).
thf(403,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[357]) ).
thf(404,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[356]) ).
thf(405,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(406,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[354]) ).
thf(407,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(408,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[352]) ).
thf(409,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[351]) ).
thf(410,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(411,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[349]) ).
thf(412,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(413,plain,
$true = $true,
inference(copy,[status(thm)],[347]) ).
thf(414,plain,
$true = $true,
inference(copy,[status(thm)],[346]) ).
thf(415,plain,
$true = $true,
inference(copy,[status(thm)],[345]) ).
thf(416,plain,
$true = $true,
inference(copy,[status(thm)],[344]) ).
thf(417,plain,
$true = $true,
inference(copy,[status(thm)],[343]) ).
thf(418,plain,
$true = $true,
inference(copy,[status(thm)],[342]) ).
thf(419,plain,
$true = $true,
inference(copy,[status(thm)],[341]) ).
thf(420,plain,
$true = $true,
inference(copy,[status(thm)],[340]) ).
thf(421,plain,
$true = $true,
inference(copy,[status(thm)],[339]) ).
thf(422,plain,
$true = $true,
inference(copy,[status(thm)],[338]) ).
thf(423,plain,
$true = $true,
inference(copy,[status(thm)],[337]) ).
thf(424,plain,
$true = $true,
inference(copy,[status(thm)],[336]) ).
thf(425,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(426,plain,
$true = $true,
inference(copy,[status(thm)],[334]) ).
thf(427,plain,
$true = $true,
inference(copy,[status(thm)],[333]) ).
thf(428,plain,
$true = $true,
inference(copy,[status(thm)],[332]) ).
thf(429,plain,
$true = $true,
inference(copy,[status(thm)],[331]) ).
thf(430,plain,
$true = $true,
inference(copy,[status(thm)],[330]) ).
thf(431,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[329]) ).
thf(432,plain,
$true = $true,
inference(copy,[status(thm)],[328]) ).
thf(433,plain,
$true = $true,
inference(copy,[status(thm)],[327]) ).
thf(434,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[326]) ).
thf(435,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[325]) ).
thf(436,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(437,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(438,plain,
$true = $true,
inference(copy,[status(thm)],[322]) ).
thf(439,plain,
$true = $true,
inference(copy,[status(thm)],[321]) ).
thf(440,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[320]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[319]) ).
thf(442,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(443,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(444,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(445,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(446,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(447,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[313]) ).
thf(448,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(449,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(450,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(451,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(452,plain,
( ( relation @ sK2_SY98 )
= $true ),
inference(copy,[status(thm)],[380]) ).
thf(453,plain,
( ( ~ ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY98 ) ) @ ( relation_dom @ sK2_SY98 ) ) )
= $true ),
inference(copy,[status(thm)],[382]) ).
thf(454,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX1 ) )
| ( subset @ ( set_union2 @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(455,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(456,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(457,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SX0 @ SX1 ) ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(458,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(459,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(460,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(461,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX0 @ SX2 ) )
| ( subset @ SX0 @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(462,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(463,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_intersection2 @ SX0 @ SX2 ) @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(464,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX1 )
| ~ ( function @ SX1 ) )
| ~ ( ~ ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) )
| ~ ( function @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(465,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(466,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(467,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(468,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(469,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(470,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(471,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( proper_subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( proper_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(472,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom @ ( relation_composition @ SX0 @ SX1 ) ) @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(473,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(474,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(475,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(476,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(477,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng_restriction @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(478,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(479,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_inverse_image @ SX1 @ SX0 ) @ ( relation_dom @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(480,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom_restriction @ SX1 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(481,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_difference @ SX0 @ SX2 ) @ ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(482,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_inverse @ ( relation_inverse @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(483,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX3 ) )
| ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(484,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(485,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( relation_dom @ SX0 ) @ ( relation_dom @ SX1 ) )
| ~ ( subset @ ( relation_rng @ SX0 ) @ ( relation_rng @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(486,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SX0 @ SX2 ) @ SX1 )
= ( relation_rng_restriction @ SX0 @ ( relation_dom_restriction @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(487,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( disjoint @ SX1 @ SX2 ) )
| ( disjoint @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(488,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(489,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( relation_inverse_image @ SX2 @ SX0 ) @ ( relation_inverse_image @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(490,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(491,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( proper_subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(492,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(493,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SX0 @ SX1 ) ) @ ( relation_rng @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(494,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(495,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) )
| ~ ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(496,plain,
! [SV1: $i] :
( ( ! [SY99: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY99 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(497,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(498,plain,
! [SV3: $i] :
( ( ! [SY100: $i] : ( subset @ ( set_difference @ SV3 @ SY100 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(499,plain,
! [SV4: $i] :
( ( ! [SY101: $i] : ( subset @ SV4 @ ( set_union2 @ SV4 @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(500,plain,
! [SV5: $i] :
( ( relation @ ( identity_relation @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(501,plain,
! [SV6: $i] :
( ( ! [SY102: $i] : ( subset @ SV6 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(502,plain,
( ( subset @ ( relation_dom @ ( relation_rng_restriction @ sK1_A @ sK2_SY98 ) ) @ ( relation_dom @ sK2_SY98 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(503,plain,
! [SV7: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ~ ~ ( ~ ( subset @ SV7 @ SY103 )
| ~ ( subset @ SY104 @ SY103 ) )
| ( subset @ ( set_union2 @ SV7 @ SY104 ) @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(504,plain,
! [SV8: $i] :
( ( ! [SY105: $i] :
( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( relation @ SY105 ) )
| ( relation @ ( set_difference @ SV8 @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(505,plain,
! [SV9: $i] :
( ( ! [SY106: $i] :
~ ( ~ ( ( SV9 != SY106 )
| ~ ( ~ ( subset @ SV9 @ SY106 )
| ~ ( subset @ SY106 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV9 @ SY106 )
| ~ ( subset @ SY106 @ SV9 ) )
| ( SV9 = SY106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(506,plain,
! [SV10: $i] :
( ( ! [SY107: $i] :
( ~ ( relation @ SY107 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV10 @ SY107 ) ) @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(507,plain,
! [SV11: $i] :
( ( ~ ( subset @ SV11 @ empty_set )
| ( SV11 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(508,plain,
! [SV12: $i] :
( ( ~ ( empty @ SV12 )
| ~ ( ~ ( empty @ ( relation_dom @ SV12 ) )
| ~ ( relation @ ( relation_dom @ SV12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(509,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(510,plain,
! [SV13: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ~ ~ ( ~ ( subset @ SV13 @ SY108 )
| ~ ( subset @ SV13 @ SY109 ) )
| ( subset @ SV13 @ ( set_intersection2 @ SY108 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(511,plain,
! [SV14: $i] :
( ( ! [SY110: $i] :
~ ( ~ ( ~ ( subset @ SV14 @ SY110 )
| ! [SY111: $i] :
( ~ ( in @ SY111 @ SV14 )
| ( in @ SY111 @ SY110 ) ) )
| ~ ( ~ ! [SY112: $i] :
( ~ ( in @ SY112 @ SV14 )
| ( in @ SY112 @ SY110 ) )
| ( subset @ SV14 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(512,plain,
! [SV15: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( subset @ SV15 @ SY113 )
| ( subset @ ( set_intersection2 @ SV15 @ SY114 ) @ ( set_intersection2 @ SY113 @ SY114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(513,plain,
! [SV16: $i] :
( ( ! [SY115: $i] :
( ~ ~ ( ~ ( relation @ SY115 )
| ~ ( function @ SY115 ) )
| ~ ( ~ ( relation @ ( relation_rng_restriction @ SV16 @ SY115 ) )
| ~ ( function @ ( relation_rng_restriction @ SV16 @ SY115 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(514,plain,
! [SV17: $i] :
( ( ! [SY116: $i] :
( ~ ( relation @ SV17 )
| ( relation @ ( relation_dom_restriction @ SV17 @ SY116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(515,plain,
! [SV18: $i] :
( ( ! [SY117: $i] :
( ~ ( subset @ SV18 @ SY117 )
| ( ( set_intersection2 @ SV18 @ SY117 )
= SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(516,plain,
! [SV19: $i] :
( ( ~ ( empty @ SV19 )
| ( relation @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(517,plain,
! [SV20: $i] :
( ( ! [SY118: $i,SY119: $i] :
( ~ ~ ( ~ ( subset @ SV20 @ SY118 )
| ~ ( subset @ SY118 @ SY119 ) )
| ( subset @ SV20 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(518,plain,
! [SV21: $i] :
( ( ! [SY120: $i] :
( ~ ~ ( ~ ( relation @ SV21 )
| ~ ( relation @ SY120 ) )
| ( relation @ ( set_intersection2 @ SV21 @ SY120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(519,plain,
! [SV22: $i] :
( ( ! [SY121: $i] :
( ~ ( subset @ ( singleton @ SV22 ) @ ( singleton @ SY121 ) )
| ( SV22 = SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(520,plain,
! [SV23: $i] :
( ( ! [SY122: $i] :
~ ( ~ ( ~ ( proper_subset @ SV23 @ SY122 )
| ~ ( ~ ( subset @ SV23 @ SY122 )
| ~ ( ( SV23 != SY122 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV23 @ SY122 )
| ~ ( ( SV23 != SY122 ) ) )
| ( proper_subset @ SV23 @ SY122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(521,plain,
! [SV24: $i] :
( ( ~ ( relation @ SV24 )
| ! [SY123: $i] :
( ~ ( relation @ SY123 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV24 @ SY123 ) ) @ ( relation_dom @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(522,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(523,plain,
! [SV25: $i] :
( ( ~ ( relation @ SV25 )
| ( relation @ ( relation_inverse @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(524,plain,
! [SV26: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV26 )
| ~ ( relation @ SV26 ) )
| ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(525,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(526,plain,
! [SV27: $i] :
( ( ! [SY124: $i] :
( ~ ( relation @ SY124 )
| ( subset @ ( relation_rng_restriction @ SV27 @ SY124 ) @ SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(527,plain,
! [SV28: $i] :
( ( ! [SY125: $i] :
( ~ ( subset @ SV28 @ SY125 )
| ( ( set_union2 @ SV28 @ SY125 )
= SY125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(528,plain,
! [SV29: $i] :
( ( ! [SY126: $i] :
( ~ ( relation @ SY126 )
| ( subset @ ( relation_inverse_image @ SY126 @ SV29 ) @ ( relation_dom @ SY126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(529,plain,
! [SV30: $i] :
( ( ! [SY127: $i] :
( ~ ( relation @ SY127 )
| ( subset @ ( relation_dom_restriction @ SY127 @ SV30 ) @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(530,plain,
! [SV31: $i] :
( ( ! [SY128: $i,SY129: $i] :
( ~ ( subset @ SV31 @ SY128 )
| ( subset @ ( set_difference @ SV31 @ SY129 ) @ ( set_difference @ SY128 @ SY129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(531,plain,
! [SV32: $i] :
( ( ~ ( relation @ SV32 )
| ( ( relation_inverse @ ( relation_inverse @ SV32 ) )
= SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(532,plain,
! [SV33: $i] :
( ( ! [SY130: $i,SY131: $i,SY132: $i] :
( ~ ~ ( ~ ( subset @ SV33 @ SY130 )
| ~ ( subset @ SY131 @ SY132 ) )
| ( subset @ ( cartesian_product2 @ SV33 @ SY131 ) @ ( cartesian_product2 @ SY130 @ SY132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(533,plain,
! [SV34: $i] :
( ( ! [SY133: $i] :
( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( relation @ SY133 ) )
| ( relation @ ( set_union2 @ SV34 @ SY133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(534,plain,
! [SV35: $i] :
( ( ~ ( relation @ SV35 )
| ! [SY134: $i] :
( ~ ( relation @ SY134 )
| ~ ( subset @ SV35 @ SY134 )
| ~ ( ~ ( subset @ ( relation_dom @ SV35 ) @ ( relation_dom @ SY134 ) )
| ~ ( subset @ ( relation_rng @ SV35 ) @ ( relation_rng @ SY134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(535,plain,
! [SV36: $i] :
( ( ! [SY135: $i,SY136: $i] :
( ~ ( relation @ SY136 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV36 @ SY136 ) @ SY135 )
= ( relation_rng_restriction @ SV36 @ ( relation_dom_restriction @ SY136 @ SY135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(536,plain,
! [SV37: $i] :
( ( ! [SY137: $i,SY138: $i] :
( ~ ~ ( ~ ( subset @ SV37 @ SY137 )
| ~ ( disjoint @ SY137 @ SY138 ) )
| ( disjoint @ SV37 @ SY138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(537,plain,
! [SV38: $i] :
( ( ! [SY139: $i] :
( ~ ~ ( ~ ( relation @ SV38 )
| ~ ( relation @ SY139 ) )
| ( relation @ ( relation_composition @ SV38 @ SY139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(538,plain,
! [SV39: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ~ ( relation @ SY141 )
| ~ ( subset @ SV39 @ SY140 )
| ( subset @ ( relation_inverse_image @ SY141 @ SV39 ) @ ( relation_inverse_image @ SY141 @ SY140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(539,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(540,plain,
! [SV40: $i] :
( ( ! [SY142: $i] :
~ ~ ( ~ ( subset @ SV40 @ SY142 )
| ~ ( proper_subset @ SY142 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(541,plain,
! [SV41: $i] :
( ( ! [SY143: $i] :
( ~ ( relation @ SY143 )
| ( relation @ ( relation_rng_restriction @ SV41 @ SY143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(542,plain,
! [SV42: $i] :
( ( ! [SY144: $i] :
( ~ ( relation @ SY144 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV42 @ SY144 ) ) @ ( relation_rng @ SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(543,plain,
! [SV43: $i] :
( ( ! [SY145: $i] :
( ~ ( relation @ SV43 )
| ( relation @ ( relation_restriction @ SV43 @ SY145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(544,plain,
! [SV44: $i] :
( ( ! [SY146: $i,SY147: $i] :
( ~ ( subset @ SV44 @ SY146 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV44 @ SY147 ) @ ( cartesian_product2 @ SY146 @ SY147 ) )
| ~ ( subset @ ( cartesian_product2 @ SY147 @ SV44 ) @ ( cartesian_product2 @ SY147 @ SY146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(545,plain,
! [SV45: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV45 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(546,plain,
! [SV46: $i,SV3: $i] :
( ( subset @ ( set_difference @ SV3 @ SV46 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(547,plain,
! [SV47: $i,SV4: $i] :
( ( subset @ SV4 @ ( set_union2 @ SV4 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(548,plain,
! [SV6: $i] :
( ( subset @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(549,plain,
! [SV49: $i,SV7: $i] :
( ( ! [SY148: $i] :
( ~ ~ ( ~ ( subset @ SV7 @ SV49 )
| ~ ( subset @ SY148 @ SV49 ) )
| ( subset @ ( set_union2 @ SV7 @ SY148 ) @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(550,plain,
! [SV50: $i,SV8: $i] :
( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( relation @ SV50 ) )
| ( relation @ ( set_difference @ SV8 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(551,plain,
! [SV51: $i,SV9: $i] :
( ( ~ ( ~ ( ( SV9 != SV51 )
| ~ ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) )
| ( SV9 = SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(552,plain,
! [SV10: $i,SV52: $i] :
( ( ~ ( relation @ SV52 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV10 @ SV52 ) ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(553,plain,
! [SV11: $i] :
( ( ( ~ ( subset @ SV11 @ empty_set ) )
= $true )
| ( ( SV11 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(554,plain,
! [SV12: $i] :
( ( ( ~ ( empty @ SV12 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV12 ) )
| ~ ( relation @ ( relation_dom @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(555,plain,
( ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( relation_empty_yielding @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[509]) ).
thf(556,plain,
! [SV53: $i,SV13: $i] :
( ( ! [SY149: $i] :
( ~ ~ ( ~ ( subset @ SV13 @ SV53 )
| ~ ( subset @ SV13 @ SY149 ) )
| ( subset @ SV13 @ ( set_intersection2 @ SV53 @ SY149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(557,plain,
! [SV54: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV14 @ SV54 )
| ! [SY150: $i] :
( ~ ( in @ SY150 @ SV14 )
| ( in @ SY150 @ SV54 ) ) )
| ~ ( ~ ! [SY151: $i] :
( ~ ( in @ SY151 @ SV14 )
| ( in @ SY151 @ SV54 ) )
| ( subset @ SV14 @ SV54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(558,plain,
! [SV55: $i,SV15: $i] :
( ( ! [SY152: $i] :
( ~ ( subset @ SV15 @ SV55 )
| ( subset @ ( set_intersection2 @ SV15 @ SY152 ) @ ( set_intersection2 @ SV55 @ SY152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(559,plain,
! [SV16: $i,SV56: $i] :
( ( ~ ~ ( ~ ( relation @ SV56 )
| ~ ( function @ SV56 ) )
| ~ ( ~ ( relation @ ( relation_rng_restriction @ SV16 @ SV56 ) )
| ~ ( function @ ( relation_rng_restriction @ SV16 @ SV56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(560,plain,
! [SV57: $i,SV17: $i] :
( ( ~ ( relation @ SV17 )
| ( relation @ ( relation_dom_restriction @ SV17 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(561,plain,
! [SV58: $i,SV18: $i] :
( ( ~ ( subset @ SV18 @ SV58 )
| ( ( set_intersection2 @ SV18 @ SV58 )
= SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(562,plain,
! [SV19: $i] :
( ( ( ~ ( empty @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(563,plain,
! [SV59: $i,SV20: $i] :
( ( ! [SY153: $i] :
( ~ ~ ( ~ ( subset @ SV20 @ SV59 )
| ~ ( subset @ SV59 @ SY153 ) )
| ( subset @ SV20 @ SY153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(564,plain,
! [SV60: $i,SV21: $i] :
( ( ~ ~ ( ~ ( relation @ SV21 )
| ~ ( relation @ SV60 ) )
| ( relation @ ( set_intersection2 @ SV21 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(565,plain,
! [SV61: $i,SV22: $i] :
( ( ~ ( subset @ ( singleton @ SV22 ) @ ( singleton @ SV61 ) )
| ( SV22 = SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(566,plain,
! [SV62: $i,SV23: $i] :
( ( ~ ( ~ ( ~ ( proper_subset @ SV23 @ SV62 )
| ~ ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) )
| ( proper_subset @ SV23 @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(567,plain,
! [SV24: $i] :
( ( ( ~ ( relation @ SV24 ) )
= $true )
| ( ( ! [SY123: $i] :
( ~ ( relation @ SY123 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV24 @ SY123 ) ) @ ( relation_dom @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(568,plain,
( ( ~ ~ ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[522]) ).
thf(569,plain,
! [SV25: $i] :
( ( ( ~ ( relation @ SV25 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(570,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV26 )
| ~ ( relation @ SV26 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(571,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[525]) ).
thf(572,plain,
! [SV27: $i,SV63: $i] :
( ( ~ ( relation @ SV63 )
| ( subset @ ( relation_rng_restriction @ SV27 @ SV63 ) @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(573,plain,
! [SV64: $i,SV28: $i] :
( ( ~ ( subset @ SV28 @ SV64 )
| ( ( set_union2 @ SV28 @ SV64 )
= SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(574,plain,
! [SV29: $i,SV65: $i] :
( ( ~ ( relation @ SV65 )
| ( subset @ ( relation_inverse_image @ SV65 @ SV29 ) @ ( relation_dom @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(575,plain,
! [SV30: $i,SV66: $i] :
( ( ~ ( relation @ SV66 )
| ( subset @ ( relation_dom_restriction @ SV66 @ SV30 ) @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(576,plain,
! [SV67: $i,SV31: $i] :
( ( ! [SY154: $i] :
( ~ ( subset @ SV31 @ SV67 )
| ( subset @ ( set_difference @ SV31 @ SY154 ) @ ( set_difference @ SV67 @ SY154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(577,plain,
! [SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV32 ) )
= SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(578,plain,
! [SV68: $i,SV33: $i] :
( ( ! [SY155: $i,SY156: $i] :
( ~ ~ ( ~ ( subset @ SV33 @ SV68 )
| ~ ( subset @ SY155 @ SY156 ) )
| ( subset @ ( cartesian_product2 @ SV33 @ SY155 ) @ ( cartesian_product2 @ SV68 @ SY156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(579,plain,
! [SV69: $i,SV34: $i] :
( ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( relation @ SV69 ) )
| ( relation @ ( set_union2 @ SV34 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(580,plain,
! [SV35: $i] :
( ( ( ~ ( relation @ SV35 ) )
= $true )
| ( ( ! [SY134: $i] :
( ~ ( relation @ SY134 )
| ~ ( subset @ SV35 @ SY134 )
| ~ ( ~ ( subset @ ( relation_dom @ SV35 ) @ ( relation_dom @ SY134 ) )
| ~ ( subset @ ( relation_rng @ SV35 ) @ ( relation_rng @ SY134 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(581,plain,
! [SV70: $i,SV36: $i] :
( ( ! [SY157: $i] :
( ~ ( relation @ SY157 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV36 @ SY157 ) @ SV70 )
= ( relation_rng_restriction @ SV36 @ ( relation_dom_restriction @ SY157 @ SV70 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(582,plain,
! [SV71: $i,SV37: $i] :
( ( ! [SY158: $i] :
( ~ ~ ( ~ ( subset @ SV37 @ SV71 )
| ~ ( disjoint @ SV71 @ SY158 ) )
| ( disjoint @ SV37 @ SY158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(583,plain,
! [SV72: $i,SV38: $i] :
( ( ~ ~ ( ~ ( relation @ SV38 )
| ~ ( relation @ SV72 ) )
| ( relation @ ( relation_composition @ SV38 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(584,plain,
! [SV73: $i,SV39: $i] :
( ( ! [SY159: $i] :
( ~ ( relation @ SY159 )
| ~ ( subset @ SV39 @ SV73 )
| ( subset @ ( relation_inverse_image @ SY159 @ SV39 ) @ ( relation_inverse_image @ SY159 @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(585,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[539]) ).
thf(586,plain,
! [SV74: $i,SV40: $i] :
( ( ~ ~ ( ~ ( subset @ SV40 @ SV74 )
| ~ ( proper_subset @ SV74 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(587,plain,
! [SV41: $i,SV75: $i] :
( ( ~ ( relation @ SV75 )
| ( relation @ ( relation_rng_restriction @ SV41 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(588,plain,
! [SV42: $i,SV76: $i] :
( ( ~ ( relation @ SV76 )
| ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV42 @ SV76 ) ) @ ( relation_rng @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(589,plain,
! [SV77: $i,SV43: $i] :
( ( ~ ( relation @ SV43 )
| ( relation @ ( relation_restriction @ SV43 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(590,plain,
! [SV78: $i,SV44: $i] :
( ( ! [SY160: $i] :
( ~ ( subset @ SV44 @ SV78 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV44 @ SY160 ) @ ( cartesian_product2 @ SV78 @ SY160 ) )
| ~ ( subset @ ( cartesian_product2 @ SY160 @ SV44 ) @ ( cartesian_product2 @ SY160 @ SV78 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(591,plain,
! [SV79: $i,SV49: $i,SV7: $i] :
( ( ~ ~ ( ~ ( subset @ SV7 @ SV49 )
| ~ ( subset @ SV79 @ SV49 ) )
| ( subset @ ( set_union2 @ SV7 @ SV79 ) @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(592,plain,
! [SV50: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( relation @ SV50 ) ) )
= $true )
| ( ( relation @ ( set_difference @ SV8 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(593,plain,
! [SV51: $i,SV9: $i] :
( ( ~ ( ( SV9 != SV51 )
| ~ ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) )
| ( SV9 = SV51 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(594,plain,
! [SV10: $i,SV52: $i] :
( ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV10 @ SV52 ) ) @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(595,plain,
! [SV11: $i] :
( ( ( subset @ SV11 @ empty_set )
= $false )
| ( ( SV11 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(596,plain,
! [SV12: $i] :
( ( ( empty @ SV12 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV12 ) )
| ~ ( relation @ ( relation_dom @ SV12 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(597,plain,
( ( ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( relation_empty_yielding @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(598,plain,
! [SV80: $i,SV53: $i,SV13: $i] :
( ( ~ ~ ( ~ ( subset @ SV13 @ SV53 )
| ~ ( subset @ SV13 @ SV80 ) )
| ( subset @ SV13 @ ( set_intersection2 @ SV53 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(599,plain,
! [SV54: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ SV14 @ SV54 )
| ! [SY150: $i] :
( ~ ( in @ SY150 @ SV14 )
| ( in @ SY150 @ SV54 ) ) )
| ~ ( ~ ! [SY151: $i] :
( ~ ( in @ SY151 @ SV14 )
| ( in @ SY151 @ SV54 ) )
| ( subset @ SV14 @ SV54 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(600,plain,
! [SV81: $i,SV55: $i,SV15: $i] :
( ( ~ ( subset @ SV15 @ SV55 )
| ( subset @ ( set_intersection2 @ SV15 @ SV81 ) @ ( set_intersection2 @ SV55 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(601,plain,
! [SV16: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV56 )
| ~ ( function @ SV56 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV16 @ SV56 ) )
| ~ ( function @ ( relation_rng_restriction @ SV16 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(602,plain,
! [SV57: $i,SV17: $i] :
( ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( relation @ ( relation_dom_restriction @ SV17 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(603,plain,
! [SV58: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV58 ) )
= $true )
| ( ( ( set_intersection2 @ SV18 @ SV58 )
= SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(604,plain,
! [SV19: $i] :
( ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(605,plain,
! [SV82: $i,SV59: $i,SV20: $i] :
( ( ~ ~ ( ~ ( subset @ SV20 @ SV59 )
| ~ ( subset @ SV59 @ SV82 ) )
| ( subset @ SV20 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(606,plain,
! [SV60: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV21 )
| ~ ( relation @ SV60 ) ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(607,plain,
! [SV61: $i,SV22: $i] :
( ( ( ~ ( subset @ ( singleton @ SV22 ) @ ( singleton @ SV61 ) ) )
= $true )
| ( ( SV22 = SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(608,plain,
! [SV62: $i,SV23: $i] :
( ( ~ ( ~ ( proper_subset @ SV23 @ SV62 )
| ~ ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) )
| ( proper_subset @ SV23 @ SV62 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(609,plain,
! [SV24: $i] :
( ( ( relation @ SV24 )
= $false )
| ( ( ! [SY123: $i] :
( ~ ( relation @ SY123 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV24 @ SY123 ) ) @ ( relation_dom @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(610,plain,
( ( ~ ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(611,plain,
! [SV25: $i] :
( ( ( relation @ SV25 )
= $false )
| ( ( relation @ ( relation_inverse @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(612,plain,
! [SV26: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV26 )
| ~ ( relation @ SV26 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(613,plain,
( ( ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[571]) ).
thf(614,plain,
! [SV27: $i,SV63: $i] :
( ( ( ~ ( relation @ SV63 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV27 @ SV63 ) @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(615,plain,
! [SV64: $i,SV28: $i] :
( ( ( ~ ( subset @ SV28 @ SV64 ) )
= $true )
| ( ( ( set_union2 @ SV28 @ SV64 )
= SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(616,plain,
! [SV29: $i,SV65: $i] :
( ( ( ~ ( relation @ SV65 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV65 @ SV29 ) @ ( relation_dom @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(617,plain,
! [SV30: $i,SV66: $i] :
( ( ( ~ ( relation @ SV66 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV66 @ SV30 ) @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(618,plain,
! [SV83: $i,SV67: $i,SV31: $i] :
( ( ~ ( subset @ SV31 @ SV67 )
| ( subset @ ( set_difference @ SV31 @ SV83 ) @ ( set_difference @ SV67 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(619,plain,
! [SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV32 ) )
= SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(620,plain,
! [SV84: $i,SV68: $i,SV33: $i] :
( ( ! [SY161: $i] :
( ~ ~ ( ~ ( subset @ SV33 @ SV68 )
| ~ ( subset @ SV84 @ SY161 ) )
| ( subset @ ( cartesian_product2 @ SV33 @ SV84 ) @ ( cartesian_product2 @ SV68 @ SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(621,plain,
! [SV69: $i,SV34: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV34 )
| ~ ( relation @ SV69 ) ) )
= $true )
| ( ( relation @ ( set_union2 @ SV34 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(622,plain,
! [SV35: $i] :
( ( ( relation @ SV35 )
= $false )
| ( ( ! [SY134: $i] :
( ~ ( relation @ SY134 )
| ~ ( subset @ SV35 @ SY134 )
| ~ ( ~ ( subset @ ( relation_dom @ SV35 ) @ ( relation_dom @ SY134 ) )
| ~ ( subset @ ( relation_rng @ SV35 ) @ ( relation_rng @ SY134 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(623,plain,
! [SV70: $i,SV36: $i,SV85: $i] :
( ( ~ ( relation @ SV85 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV36 @ SV85 ) @ SV70 )
= ( relation_rng_restriction @ SV36 @ ( relation_dom_restriction @ SV85 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(624,plain,
! [SV86: $i,SV71: $i,SV37: $i] :
( ( ~ ~ ( ~ ( subset @ SV37 @ SV71 )
| ~ ( disjoint @ SV71 @ SV86 ) )
| ( disjoint @ SV37 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(625,plain,
! [SV72: $i,SV38: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV38 )
| ~ ( relation @ SV72 ) ) )
= $true )
| ( ( relation @ ( relation_composition @ SV38 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(626,plain,
! [SV73: $i,SV39: $i,SV87: $i] :
( ( ~ ( relation @ SV87 )
| ~ ( subset @ SV39 @ SV73 )
| ( subset @ ( relation_inverse_image @ SV87 @ SV39 ) @ ( relation_inverse_image @ SV87 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(627,plain,
( ( ~ ( ~ ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(628,plain,
! [SV74: $i,SV40: $i] :
( ( ~ ( ~ ( subset @ SV40 @ SV74 )
| ~ ( proper_subset @ SV74 @ SV40 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(629,plain,
! [SV41: $i,SV75: $i] :
( ( ( ~ ( relation @ SV75 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV41 @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(630,plain,
! [SV42: $i,SV76: $i] :
( ( ( ~ ( relation @ SV76 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV42 @ SV76 ) ) @ ( relation_rng @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(631,plain,
! [SV77: $i,SV43: $i] :
( ( ( ~ ( relation @ SV43 ) )
= $true )
| ( ( relation @ ( relation_restriction @ SV43 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(632,plain,
! [SV88: $i,SV78: $i,SV44: $i] :
( ( ~ ( subset @ SV44 @ SV78 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV44 @ SV88 ) @ ( cartesian_product2 @ SV78 @ SV88 ) )
| ~ ( subset @ ( cartesian_product2 @ SV88 @ SV44 ) @ ( cartesian_product2 @ SV88 @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(633,plain,
! [SV79: $i,SV49: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV7 @ SV49 )
| ~ ( subset @ SV79 @ SV49 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV7 @ SV79 ) @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(634,plain,
! [SV50: $i,SV8: $i] :
( ( ( ~ ( ~ ( relation @ SV8 )
| ~ ( relation @ SV50 ) ) )
= $false )
| ( ( relation @ ( set_difference @ SV8 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(635,plain,
! [SV51: $i,SV9: $i] :
( ( ~ ( ( SV9 != SV51 )
| ~ ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[593]) ).
thf(636,plain,
! [SV51: $i,SV9: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) )
| ( SV9 = SV51 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[593]) ).
thf(637,plain,
! [SV10: $i,SV52: $i] :
( ( ( relation @ SV52 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV10 @ SV52 ) ) @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(638,plain,
! [SV12: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV12 ) )
| ~ ( relation @ ( relation_dom @ SV12 ) ) )
= $false )
| ( ( empty @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(639,plain,
( ( ~ ( relation @ sK3_SX0 )
| ~ ( relation_empty_yielding @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(640,plain,
! [SV80: $i,SV53: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV13 @ SV53 )
| ~ ( subset @ SV13 @ SV80 ) ) )
= $true )
| ( ( subset @ SV13 @ ( set_intersection2 @ SV53 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(641,plain,
! [SV54: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ SV14 @ SV54 )
| ! [SY150: $i] :
( ~ ( in @ SY150 @ SV14 )
| ( in @ SY150 @ SV54 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[599]) ).
thf(642,plain,
! [SV54: $i,SV14: $i] :
( ( ~ ( ~ ! [SY151: $i] :
( ~ ( in @ SY151 @ SV14 )
| ( in @ SY151 @ SV54 ) )
| ( subset @ SV14 @ SV54 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[599]) ).
thf(643,plain,
! [SV81: $i,SV55: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV55 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV15 @ SV81 ) @ ( set_intersection2 @ SV55 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(644,plain,
! [SV16: $i,SV56: $i] :
( ( ( ~ ( ~ ( relation @ SV56 )
| ~ ( function @ SV56 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV16 @ SV56 ) )
| ~ ( function @ ( relation_rng_restriction @ SV16 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(645,plain,
! [SV57: $i,SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( relation @ ( relation_dom_restriction @ SV17 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(646,plain,
! [SV58: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV58 )
= $false )
| ( ( ( set_intersection2 @ SV18 @ SV58 )
= SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(647,plain,
! [SV82: $i,SV59: $i,SV20: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV20 @ SV59 )
| ~ ( subset @ SV59 @ SV82 ) ) )
= $true )
| ( ( subset @ SV20 @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(648,plain,
! [SV60: $i,SV21: $i] :
( ( ( ~ ( ~ ( relation @ SV21 )
| ~ ( relation @ SV60 ) ) )
= $false )
| ( ( relation @ ( set_intersection2 @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(649,plain,
! [SV61: $i,SV22: $i] :
( ( ( subset @ ( singleton @ SV22 ) @ ( singleton @ SV61 ) )
= $false )
| ( ( SV22 = SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(650,plain,
! [SV62: $i,SV23: $i] :
( ( ~ ( ~ ( proper_subset @ SV23 @ SV62 )
| ~ ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[608]) ).
thf(651,plain,
! [SV62: $i,SV23: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) )
| ( proper_subset @ SV23 @ SV62 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[608]) ).
thf(652,plain,
! [SV24: $i,SV89: $i] :
( ( ( ~ ( relation @ SV89 )
| ( subset @ ( relation_dom @ ( relation_composition @ SV24 @ SV89 ) ) @ ( relation_dom @ SV24 ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(653,plain,
( ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(654,plain,
! [SV26: $i] :
( ( ( ~ ~ ( empty @ SV26 )
| ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[612]) ).
thf(655,plain,
( ( ~ ( relation @ sK5_SX0 )
| ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(656,plain,
! [SV27: $i,SV63: $i] :
( ( ( relation @ SV63 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV27 @ SV63 ) @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(657,plain,
! [SV64: $i,SV28: $i] :
( ( ( subset @ SV28 @ SV64 )
= $false )
| ( ( ( set_union2 @ SV28 @ SV64 )
= SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(658,plain,
! [SV29: $i,SV65: $i] :
( ( ( relation @ SV65 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV65 @ SV29 ) @ ( relation_dom @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(659,plain,
! [SV30: $i,SV66: $i] :
( ( ( relation @ SV66 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV66 @ SV30 ) @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(660,plain,
! [SV83: $i,SV67: $i,SV31: $i] :
( ( ( ~ ( subset @ SV31 @ SV67 ) )
= $true )
| ( ( subset @ ( set_difference @ SV31 @ SV83 ) @ ( set_difference @ SV67 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(661,plain,
! [SV90: $i,SV84: $i,SV68: $i,SV33: $i] :
( ( ~ ~ ( ~ ( subset @ SV33 @ SV68 )
| ~ ( subset @ SV84 @ SV90 ) )
| ( subset @ ( cartesian_product2 @ SV33 @ SV84 ) @ ( cartesian_product2 @ SV68 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(662,plain,
! [SV69: $i,SV34: $i] :
( ( ( ~ ( ~ ( relation @ SV34 )
| ~ ( relation @ SV69 ) ) )
= $false )
| ( ( relation @ ( set_union2 @ SV34 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(663,plain,
! [SV35: $i,SV91: $i] :
( ( ( ~ ( relation @ SV91 )
| ~ ( subset @ SV35 @ SV91 )
| ~ ( ~ ( subset @ ( relation_dom @ SV35 ) @ ( relation_dom @ SV91 ) )
| ~ ( subset @ ( relation_rng @ SV35 ) @ ( relation_rng @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(664,plain,
! [SV70: $i,SV36: $i,SV85: $i] :
( ( ( ~ ( relation @ SV85 ) )
= $true )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV36 @ SV85 ) @ SV70 )
= ( relation_rng_restriction @ SV36 @ ( relation_dom_restriction @ SV85 @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(665,plain,
! [SV86: $i,SV71: $i,SV37: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV37 @ SV71 )
| ~ ( disjoint @ SV71 @ SV86 ) ) )
= $true )
| ( ( disjoint @ SV37 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(666,plain,
! [SV72: $i,SV38: $i] :
( ( ( ~ ( ~ ( relation @ SV38 )
| ~ ( relation @ SV72 ) ) )
= $false )
| ( ( relation @ ( relation_composition @ SV38 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(667,plain,
! [SV73: $i,SV39: $i,SV87: $i] :
( ( ( ~ ( relation @ SV87 ) )
= $true )
| ( ( ~ ( subset @ SV39 @ SV73 )
| ( subset @ ( relation_inverse_image @ SV87 @ SV39 ) @ ( relation_inverse_image @ SV87 @ SV73 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(668,plain,
( ( ~ ~ ( empty @ sK6_SX0 )
| ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(669,plain,
! [SV74: $i,SV40: $i] :
( ( ~ ( subset @ SV40 @ SV74 )
| ~ ( proper_subset @ SV74 @ SV40 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(670,plain,
! [SV41: $i,SV75: $i] :
( ( ( relation @ SV75 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV41 @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[629]) ).
thf(671,plain,
! [SV42: $i,SV76: $i] :
( ( ( relation @ SV76 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_rng_restriction @ SV42 @ SV76 ) ) @ ( relation_rng @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(672,plain,
! [SV77: $i,SV43: $i] :
( ( ( relation @ SV43 )
= $false )
| ( ( relation @ ( relation_restriction @ SV43 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(673,plain,
! [SV88: $i,SV78: $i,SV44: $i] :
( ( ( ~ ( subset @ SV44 @ SV78 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( cartesian_product2 @ SV44 @ SV88 ) @ ( cartesian_product2 @ SV78 @ SV88 ) )
| ~ ( subset @ ( cartesian_product2 @ SV88 @ SV44 ) @ ( cartesian_product2 @ SV88 @ SV78 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(674,plain,
! [SV79: $i,SV49: $i,SV7: $i] :
( ( ( ~ ( ~ ( subset @ SV7 @ SV49 )
| ~ ( subset @ SV79 @ SV49 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV7 @ SV79 ) @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[633]) ).
thf(675,plain,
! [SV50: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 )
| ~ ( relation @ SV50 ) )
= $true )
| ( ( relation @ ( set_difference @ SV8 @ SV50 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[634]) ).
thf(676,plain,
! [SV51: $i,SV9: $i] :
( ( ( SV9 != SV51 )
| ~ ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[635]) ).
thf(677,plain,
! [SV51: $i,SV9: $i] :
( ( ~ ~ ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) )
| ( SV9 = SV51 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[636]) ).
thf(678,plain,
! [SV12: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV12 ) ) )
= $false )
| ( ( empty @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(679,plain,
! [SV12: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV12 ) ) )
= $false )
| ( ( empty @ SV12 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(680,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(681,plain,
( ( ~ ( relation_empty_yielding @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(682,plain,
! [SV80: $i,SV53: $i,SV13: $i] :
( ( ( ~ ( ~ ( subset @ SV13 @ SV53 )
| ~ ( subset @ SV13 @ SV80 ) ) )
= $false )
| ( ( subset @ SV13 @ ( set_intersection2 @ SV53 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(683,plain,
! [SV54: $i,SV14: $i] :
( ( ~ ( subset @ SV14 @ SV54 )
| ! [SY150: $i] :
( ~ ( in @ SY150 @ SV14 )
| ( in @ SY150 @ SV54 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(684,plain,
! [SV54: $i,SV14: $i] :
( ( ~ ! [SY151: $i] :
( ~ ( in @ SY151 @ SV14 )
| ( in @ SY151 @ SV54 ) )
| ( subset @ SV14 @ SV54 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(685,plain,
! [SV81: $i,SV55: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV55 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV15 @ SV81 ) @ ( set_intersection2 @ SV55 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(686,plain,
! [SV16: $i,SV56: $i] :
( ( ( ~ ( relation @ SV56 )
| ~ ( function @ SV56 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV16 @ SV56 ) )
| ~ ( function @ ( relation_rng_restriction @ SV16 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[644]) ).
thf(687,plain,
! [SV82: $i,SV59: $i,SV20: $i] :
( ( ( ~ ( ~ ( subset @ SV20 @ SV59 )
| ~ ( subset @ SV59 @ SV82 ) ) )
= $false )
| ( ( subset @ SV20 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(688,plain,
! [SV60: $i,SV21: $i] :
( ( ( ~ ( relation @ SV21 )
| ~ ( relation @ SV60 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[648]) ).
thf(689,plain,
! [SV62: $i,SV23: $i] :
( ( ~ ( proper_subset @ SV23 @ SV62 )
| ~ ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(690,plain,
! [SV62: $i,SV23: $i] :
( ( ~ ~ ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) )
| ( proper_subset @ SV23 @ SV62 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(691,plain,
! [SV24: $i,SV89: $i] :
( ( ( ~ ( relation @ SV89 ) )
= $true )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV24 @ SV89 ) ) @ ( relation_dom @ SV24 ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(692,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(693,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[653]) ).
thf(694,plain,
! [SV26: $i] :
( ( ( ~ ~ ( empty @ SV26 ) )
= $true )
| ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(695,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[655]) ).
thf(696,plain,
( ( ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[655]) ).
thf(697,plain,
! [SV83: $i,SV67: $i,SV31: $i] :
( ( ( subset @ SV31 @ SV67 )
= $false )
| ( ( subset @ ( set_difference @ SV31 @ SV83 ) @ ( set_difference @ SV67 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(698,plain,
! [SV90: $i,SV84: $i,SV68: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV33 @ SV68 )
| ~ ( subset @ SV84 @ SV90 ) ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV33 @ SV84 ) @ ( cartesian_product2 @ SV68 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(699,plain,
! [SV69: $i,SV34: $i] :
( ( ( ~ ( relation @ SV34 )
| ~ ( relation @ SV69 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV34 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[662]) ).
thf(700,plain,
! [SV35: $i,SV91: $i] :
( ( ( ~ ( relation @ SV91 ) )
= $true )
| ( ( ~ ( subset @ SV35 @ SV91 )
| ~ ( ~ ( subset @ ( relation_dom @ SV35 ) @ ( relation_dom @ SV91 ) )
| ~ ( subset @ ( relation_rng @ SV35 ) @ ( relation_rng @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[663]) ).
thf(701,plain,
! [SV70: $i,SV36: $i,SV85: $i] :
( ( ( relation @ SV85 )
= $false )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV36 @ SV85 ) @ SV70 )
= ( relation_rng_restriction @ SV36 @ ( relation_dom_restriction @ SV85 @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(702,plain,
! [SV86: $i,SV71: $i,SV37: $i] :
( ( ( ~ ( ~ ( subset @ SV37 @ SV71 )
| ~ ( disjoint @ SV71 @ SV86 ) ) )
= $false )
| ( ( disjoint @ SV37 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(703,plain,
! [SV72: $i,SV38: $i] :
( ( ( ~ ( relation @ SV38 )
| ~ ( relation @ SV72 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV38 @ SV72 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[666]) ).
thf(704,plain,
! [SV73: $i,SV39: $i,SV87: $i] :
( ( ( relation @ SV87 )
= $false )
| ( ( ~ ( subset @ SV39 @ SV73 )
| ( subset @ ( relation_inverse_image @ SV87 @ SV39 ) @ ( relation_inverse_image @ SV87 @ SV73 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(705,plain,
( ( ~ ~ ( empty @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[668]) ).
thf(706,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[668]) ).
thf(707,plain,
! [SV74: $i,SV40: $i] :
( ( ( ~ ( subset @ SV40 @ SV74 ) )
= $true )
| ( ( ~ ( proper_subset @ SV74 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(708,plain,
! [SV88: $i,SV78: $i,SV44: $i] :
( ( ( subset @ SV44 @ SV78 )
= $false )
| ( ( ~ ( ~ ( subset @ ( cartesian_product2 @ SV44 @ SV88 ) @ ( cartesian_product2 @ SV78 @ SV88 ) )
| ~ ( subset @ ( cartesian_product2 @ SV88 @ SV44 ) @ ( cartesian_product2 @ SV88 @ SV78 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[673]) ).
thf(709,plain,
! [SV79: $i,SV49: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV49 )
| ~ ( subset @ SV79 @ SV49 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV7 @ SV79 ) @ SV49 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[674]) ).
thf(710,plain,
! [SV50: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ~ ( relation @ SV50 ) )
= $true )
| ( ( relation @ ( set_difference @ SV8 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(711,plain,
! [SV51: $i,SV9: $i] :
( ( ( SV9 != SV51 )
= $true )
| ( ( ~ ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(712,plain,
! [SV51: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) ) )
= $true )
| ( ( SV9 = SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(713,plain,
! [SV12: $i] :
( ( ( empty @ ( relation_dom @ SV12 ) )
= $true )
| ( ( empty @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[678]) ).
thf(714,plain,
! [SV12: $i] :
( ( ( relation @ ( relation_dom @ SV12 ) )
= $true )
| ( ( empty @ SV12 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[679]) ).
thf(715,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[680]) ).
thf(716,plain,
( ( relation_empty_yielding @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[681]) ).
thf(717,plain,
! [SV80: $i,SV53: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV53 )
| ~ ( subset @ SV13 @ SV80 ) )
= $true )
| ( ( subset @ SV13 @ ( set_intersection2 @ SV53 @ SV80 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[682]) ).
thf(718,plain,
! [SV54: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV54 ) )
= $true )
| ( ( ! [SY150: $i] :
( ~ ( in @ SY150 @ SV14 )
| ( in @ SY150 @ SV54 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(719,plain,
! [SV54: $i,SV14: $i] :
( ( ( ~ ! [SY151: $i] :
( ~ ( in @ SY151 @ SV14 )
| ( in @ SY151 @ SV54 ) ) )
= $true )
| ( ( subset @ SV14 @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(720,plain,
! [SV16: $i,SV56: $i] :
( ( ( ~ ( relation @ SV56 ) )
= $true )
| ( ( ~ ( function @ SV56 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV16 @ SV56 ) )
| ~ ( function @ ( relation_rng_restriction @ SV16 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(721,plain,
! [SV82: $i,SV59: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV59 )
| ~ ( subset @ SV59 @ SV82 ) )
= $true )
| ( ( subset @ SV20 @ SV82 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[687]) ).
thf(722,plain,
! [SV60: $i,SV21: $i] :
( ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( ~ ( relation @ SV60 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(723,plain,
! [SV62: $i,SV23: $i] :
( ( ( ~ ( proper_subset @ SV23 @ SV62 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(724,plain,
! [SV62: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) ) )
= $true )
| ( ( proper_subset @ SV23 @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[690]) ).
thf(725,plain,
! [SV24: $i,SV89: $i] :
( ( ( relation @ SV89 )
= $false )
| ( ( subset @ ( relation_dom @ ( relation_composition @ SV24 @ SV89 ) ) @ ( relation_dom @ SV24 ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(726,plain,
( ( empty @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(727,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(728,plain,
! [SV26: $i] :
( ( ( ~ ( empty @ SV26 ) )
= $false )
| ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(729,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[695]) ).
thf(730,plain,
( ( function @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[696]) ).
thf(731,plain,
! [SV90: $i,SV84: $i,SV68: $i,SV33: $i] :
( ( ( ~ ( ~ ( subset @ SV33 @ SV68 )
| ~ ( subset @ SV84 @ SV90 ) ) )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV33 @ SV84 ) @ ( cartesian_product2 @ SV68 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(732,plain,
! [SV69: $i,SV34: $i] :
( ( ( ~ ( relation @ SV34 ) )
= $true )
| ( ( ~ ( relation @ SV69 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV34 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(733,plain,
! [SV35: $i,SV91: $i] :
( ( ( relation @ SV91 )
= $false )
| ( ( ~ ( subset @ SV35 @ SV91 )
| ~ ( ~ ( subset @ ( relation_dom @ SV35 ) @ ( relation_dom @ SV91 ) )
| ~ ( subset @ ( relation_rng @ SV35 ) @ ( relation_rng @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(734,plain,
! [SV86: $i,SV71: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV71 )
| ~ ( disjoint @ SV71 @ SV86 ) )
= $true )
| ( ( disjoint @ SV37 @ SV86 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[702]) ).
thf(735,plain,
! [SV72: $i,SV38: $i] :
( ( ( ~ ( relation @ SV38 ) )
= $true )
| ( ( ~ ( relation @ SV72 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV38 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(736,plain,
! [SV87: $i,SV73: $i,SV39: $i] :
( ( ( ~ ( subset @ SV39 @ SV73 ) )
= $true )
| ( ( subset @ ( relation_inverse_image @ SV87 @ SV39 ) @ ( relation_inverse_image @ SV87 @ SV73 ) )
= $true )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(737,plain,
( ( ~ ( empty @ sK6_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[705]) ).
thf(738,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[706]) ).
thf(739,plain,
! [SV74: $i,SV40: $i] :
( ( ( subset @ SV40 @ SV74 )
= $false )
| ( ( ~ ( proper_subset @ SV74 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(740,plain,
! [SV78: $i,SV88: $i,SV44: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV44 @ SV88 ) @ ( cartesian_product2 @ SV78 @ SV88 ) )
| ~ ( subset @ ( cartesian_product2 @ SV88 @ SV44 ) @ ( cartesian_product2 @ SV88 @ SV78 ) ) )
= $false )
| ( ( subset @ SV44 @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(741,plain,
! [SV79: $i,SV49: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV49 ) )
= $true )
| ( ( ~ ( subset @ SV79 @ SV49 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV7 @ SV79 ) @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(742,plain,
! [SV50: $i,SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ~ ( relation @ SV50 ) )
= $true )
| ( ( relation @ ( set_difference @ SV8 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(743,plain,
! [SV51: $i,SV9: $i] :
( ( ( SV9 = SV51 )
= $false )
| ( ( ~ ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(744,plain,
! [SV51: $i,SV9: $i] :
( ( ( ~ ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) ) )
= $false )
| ( ( SV9 = SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(745,plain,
! [SV80: $i,SV53: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV53 ) )
= $true )
| ( ( ~ ( subset @ SV13 @ SV80 ) )
= $true )
| ( ( subset @ SV13 @ ( set_intersection2 @ SV53 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[717]) ).
thf(746,plain,
! [SV54: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV54 )
= $false )
| ( ( ! [SY150: $i] :
( ~ ( in @ SY150 @ SV14 )
| ( in @ SY150 @ SV54 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(747,plain,
! [SV54: $i,SV14: $i] :
( ( ( ! [SY151: $i] :
( ~ ( in @ SY151 @ SV14 )
| ( in @ SY151 @ SV54 ) ) )
= $false )
| ( ( subset @ SV14 @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(748,plain,
! [SV16: $i,SV56: $i] :
( ( ( relation @ SV56 )
= $false )
| ( ( ~ ( function @ SV56 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV16 @ SV56 ) )
| ~ ( function @ ( relation_rng_restriction @ SV16 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(749,plain,
! [SV82: $i,SV59: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV59 ) )
= $true )
| ( ( ~ ( subset @ SV59 @ SV82 ) )
= $true )
| ( ( subset @ SV20 @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(750,plain,
! [SV60: $i,SV21: $i] :
( ( ( relation @ SV21 )
= $false )
| ( ( ~ ( relation @ SV60 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(751,plain,
! [SV62: $i,SV23: $i] :
( ( ( proper_subset @ SV23 @ SV62 )
= $false )
| ( ( ~ ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(752,plain,
! [SV62: $i,SV23: $i] :
( ( ( ~ ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) ) )
= $false )
| ( ( proper_subset @ SV23 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(753,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
= $true )
| ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[728]) ).
thf(754,plain,
! [SV90: $i,SV84: $i,SV68: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV68 )
| ~ ( subset @ SV84 @ SV90 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV33 @ SV84 ) @ ( cartesian_product2 @ SV68 @ SV90 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[731]) ).
thf(755,plain,
! [SV69: $i,SV34: $i] :
( ( ( relation @ SV34 )
= $false )
| ( ( ~ ( relation @ SV69 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV34 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(756,plain,
! [SV91: $i,SV35: $i] :
( ( ( ~ ( subset @ SV35 @ SV91 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV35 ) @ ( relation_dom @ SV91 ) )
| ~ ( subset @ ( relation_rng @ SV35 ) @ ( relation_rng @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(757,plain,
! [SV86: $i,SV71: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV71 ) )
= $true )
| ( ( ~ ( disjoint @ SV71 @ SV86 ) )
= $true )
| ( ( disjoint @ SV37 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(758,plain,
! [SV72: $i,SV38: $i] :
( ( ( relation @ SV38 )
= $false )
| ( ( ~ ( relation @ SV72 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV38 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(759,plain,
! [SV87: $i,SV73: $i,SV39: $i] :
( ( ( subset @ SV39 @ SV73 )
= $false )
| ( ( subset @ ( relation_inverse_image @ SV87 @ SV39 ) @ ( relation_inverse_image @ SV87 @ SV73 ) )
= $true )
| ( ( relation @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(760,plain,
( ( empty @ sK6_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(761,plain,
! [SV40: $i,SV74: $i] :
( ( ( proper_subset @ SV74 @ SV40 )
= $false )
| ( ( subset @ SV40 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(762,plain,
! [SV78: $i,SV88: $i,SV44: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV44 @ SV88 ) @ ( cartesian_product2 @ SV78 @ SV88 ) ) )
= $false )
| ( ( subset @ SV44 @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(763,plain,
! [SV78: $i,SV44: $i,SV88: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV88 @ SV44 ) @ ( cartesian_product2 @ SV88 @ SV78 ) ) )
= $false )
| ( ( subset @ SV44 @ SV78 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[740]) ).
thf(764,plain,
! [SV79: $i,SV49: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV49 )
= $false )
| ( ( ~ ( subset @ SV79 @ SV49 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV7 @ SV79 ) @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(765,plain,
! [SV8: $i,SV50: $i] :
( ( ( relation @ SV50 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( relation @ ( set_difference @ SV8 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(766,plain,
! [SV51: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) )
= $false )
| ( ( SV9 = SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(767,plain,
! [SV51: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV51 )
| ~ ( subset @ SV51 @ SV9 ) )
= $true )
| ( ( SV9 = SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[744]) ).
thf(768,plain,
! [SV80: $i,SV53: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV53 )
= $false )
| ( ( ~ ( subset @ SV13 @ SV80 ) )
= $true )
| ( ( subset @ SV13 @ ( set_intersection2 @ SV53 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(769,plain,
! [SV54: $i,SV14: $i,SV92: $i] :
( ( ( ~ ( in @ SV92 @ SV14 )
| ( in @ SV92 @ SV54 ) )
= $true )
| ( ( subset @ SV14 @ SV54 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(770,plain,
! [SV14: $i,SV54: $i] :
( ( ( ~ ( in @ ( sK7_SY151 @ SV54 @ SV14 ) @ SV14 )
| ( in @ ( sK7_SY151 @ SV54 @ SV14 ) @ SV54 ) )
= $false )
| ( ( subset @ SV14 @ SV54 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[747]) ).
thf(771,plain,
! [SV16: $i,SV56: $i] :
( ( ( function @ SV56 )
= $false )
| ( ( relation @ SV56 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV16 @ SV56 ) )
| ~ ( function @ ( relation_rng_restriction @ SV16 @ SV56 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(772,plain,
! [SV82: $i,SV59: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV59 )
= $false )
| ( ( ~ ( subset @ SV59 @ SV82 ) )
= $true )
| ( ( subset @ SV20 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(773,plain,
! [SV21: $i,SV60: $i] :
( ( ( relation @ SV60 )
= $false )
| ( ( relation @ SV21 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV21 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(774,plain,
! [SV62: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) )
= $false )
| ( ( proper_subset @ SV23 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(775,plain,
! [SV62: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV62 )
| ~ ( ( SV23 != SV62 ) ) )
= $true )
| ( ( proper_subset @ SV23 @ SV62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[752]) ).
thf(776,plain,
! [SV26: $i] :
( ( ( relation @ SV26 )
= $false )
| ( ( empty @ SV26 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(777,plain,
! [SV90: $i,SV84: $i,SV68: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV68 ) )
= $true )
| ( ( ~ ( subset @ SV84 @ SV90 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV33 @ SV84 ) @ ( cartesian_product2 @ SV68 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(778,plain,
! [SV34: $i,SV69: $i] :
( ( ( relation @ SV69 )
= $false )
| ( ( relation @ SV34 )
= $false )
| ( ( relation @ ( set_union2 @ SV34 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(779,plain,
! [SV91: $i,SV35: $i] :
( ( ( subset @ SV35 @ SV91 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV35 ) @ ( relation_dom @ SV91 ) )
| ~ ( subset @ ( relation_rng @ SV35 ) @ ( relation_rng @ SV91 ) ) ) )
= $true )
| ( ( relation @ SV91 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(780,plain,
! [SV86: $i,SV71: $i,SV37: $i] :
( ( ( subset @ SV37 @ SV71 )
= $false )
| ( ( ~ ( disjoint @ SV71 @ SV86 ) )
= $true )
| ( ( disjoint @ SV37 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(781,plain,
! [SV38: $i,SV72: $i] :
( ( ( relation @ SV72 )
= $false )
| ( ( relation @ SV38 )
= $false )
| ( ( relation @ ( relation_composition @ SV38 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(782,plain,
! [SV78: $i,SV88: $i,SV44: $i] :
( ( ( subset @ ( cartesian_product2 @ SV44 @ SV88 ) @ ( cartesian_product2 @ SV78 @ SV88 ) )
= $true )
| ( ( subset @ SV44 @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[762]) ).
thf(783,plain,
! [SV78: $i,SV44: $i,SV88: $i] :
( ( ( subset @ ( cartesian_product2 @ SV88 @ SV44 ) @ ( cartesian_product2 @ SV88 @ SV78 ) )
= $true )
| ( ( subset @ SV44 @ SV78 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[763]) ).
thf(784,plain,
! [SV7: $i,SV49: $i,SV79: $i] :
( ( ( subset @ SV79 @ SV49 )
= $false )
| ( ( subset @ SV7 @ SV49 )
= $false )
| ( ( subset @ ( set_union2 @ SV7 @ SV79 ) @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(785,plain,
! [SV51: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV51 ) )
= $false )
| ( ( SV9 = SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[766]) ).
thf(786,plain,
! [SV9: $i,SV51: $i] :
( ( ( ~ ( subset @ SV51 @ SV9 ) )
= $false )
| ( ( SV9 = SV51 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[766]) ).
thf(787,plain,
! [SV51: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV51 ) )
= $true )
| ( ( ~ ( subset @ SV51 @ SV9 ) )
= $true )
| ( ( SV9 = SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(788,plain,
! [SV53: $i,SV80: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV80 )
= $false )
| ( ( subset @ SV13 @ SV53 )
= $false )
| ( ( subset @ SV13 @ ( set_intersection2 @ SV53 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(789,plain,
! [SV54: $i,SV14: $i,SV92: $i] :
( ( ( ~ ( in @ SV92 @ SV14 ) )
= $true )
| ( ( in @ SV92 @ SV54 )
= $true )
| ( ( subset @ SV14 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(790,plain,
! [SV14: $i,SV54: $i] :
( ( ( ~ ( in @ ( sK7_SY151 @ SV54 @ SV14 ) @ SV14 ) )
= $false )
| ( ( subset @ SV14 @ SV54 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[770]) ).
thf(791,plain,
! [SV14: $i,SV54: $i] :
( ( ( in @ ( sK7_SY151 @ SV54 @ SV14 ) @ SV54 )
= $false )
| ( ( subset @ SV14 @ SV54 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[770]) ).
thf(792,plain,
! [SV56: $i,SV16: $i] :
( ( ( ~ ( relation @ ( relation_rng_restriction @ SV16 @ SV56 ) )
| ~ ( function @ ( relation_rng_restriction @ SV16 @ SV56 ) ) )
= $false )
| ( ( relation @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[771]) ).
thf(793,plain,
! [SV20: $i,SV82: $i,SV59: $i] :
( ( ( subset @ SV59 @ SV82 )
= $false )
| ( ( subset @ SV20 @ SV59 )
= $false )
| ( ( subset @ SV20 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(794,plain,
! [SV62: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV62 ) )
= $false )
| ( ( proper_subset @ SV23 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[774]) ).
thf(795,plain,
! [SV62: $i,SV23: $i] :
( ( ( ~ ( ( SV23 != SV62 ) ) )
= $false )
| ( ( proper_subset @ SV23 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[774]) ).
thf(796,plain,
! [SV62: $i,SV23: $i] :
( ( ( ~ ( subset @ SV23 @ SV62 ) )
= $true )
| ( ( ~ ( ( SV23 != SV62 ) ) )
= $true )
| ( ( proper_subset @ SV23 @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(797,plain,
! [SV26: $i] :
( ( ( empty @ ( relation_dom @ SV26 ) )
= $false )
| ( ( empty @ SV26 )
= $true )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(798,plain,
! [SV90: $i,SV84: $i,SV68: $i,SV33: $i] :
( ( ( subset @ SV33 @ SV68 )
= $false )
| ( ( ~ ( subset @ SV84 @ SV90 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV33 @ SV84 ) @ ( cartesian_product2 @ SV68 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[777]) ).
thf(799,plain,
! [SV91: $i,SV35: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV35 ) @ ( relation_dom @ SV91 ) )
| ~ ( subset @ ( relation_rng @ SV35 ) @ ( relation_rng @ SV91 ) ) )
= $false )
| ( ( subset @ SV35 @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(800,plain,
! [SV37: $i,SV86: $i,SV71: $i] :
( ( ( disjoint @ SV71 @ SV86 )
= $false )
| ( ( subset @ SV37 @ SV71 )
= $false )
| ( ( disjoint @ SV37 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[780]) ).
thf(801,plain,
! [SV51: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV51 )
= $true )
| ( ( SV9 = SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[785]) ).
thf(802,plain,
! [SV9: $i,SV51: $i] :
( ( ( subset @ SV51 @ SV9 )
= $true )
| ( ( SV9 = SV51 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[786]) ).
thf(803,plain,
! [SV51: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV51 )
= $false )
| ( ( ~ ( subset @ SV51 @ SV9 ) )
= $true )
| ( ( SV9 = SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(804,plain,
! [SV54: $i,SV14: $i,SV92: $i] :
( ( ( in @ SV92 @ SV14 )
= $false )
| ( ( in @ SV92 @ SV54 )
= $true )
| ( ( subset @ SV14 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(805,plain,
! [SV14: $i,SV54: $i] :
( ( ( in @ ( sK7_SY151 @ SV54 @ SV14 ) @ SV14 )
= $true )
| ( ( subset @ SV14 @ SV54 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(806,plain,
! [SV56: $i,SV16: $i] :
( ( ( ~ ( relation @ ( relation_rng_restriction @ SV16 @ SV56 ) ) )
= $false )
| ( ( relation @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[792]) ).
thf(807,plain,
! [SV56: $i,SV16: $i] :
( ( ( ~ ( function @ ( relation_rng_restriction @ SV16 @ SV56 ) ) )
= $false )
| ( ( relation @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[792]) ).
thf(808,plain,
! [SV62: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV62 )
= $true )
| ( ( proper_subset @ SV23 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[794]) ).
thf(809,plain,
! [SV62: $i,SV23: $i] :
( ( ( SV23 != SV62 )
= $true )
| ( ( proper_subset @ SV23 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(810,plain,
! [SV62: $i,SV23: $i] :
( ( ( subset @ SV23 @ SV62 )
= $false )
| ( ( ~ ( ( SV23 != SV62 ) ) )
= $true )
| ( ( proper_subset @ SV23 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(811,plain,
! [SV68: $i,SV33: $i,SV90: $i,SV84: $i] :
( ( ( subset @ SV84 @ SV90 )
= $false )
| ( ( subset @ SV33 @ SV68 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV33 @ SV84 ) @ ( cartesian_product2 @ SV68 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(812,plain,
! [SV91: $i,SV35: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV35 ) @ ( relation_dom @ SV91 ) ) )
= $false )
| ( ( subset @ SV35 @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[799]) ).
thf(813,plain,
! [SV91: $i,SV35: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV35 ) @ ( relation_rng @ SV91 ) ) )
= $false )
| ( ( subset @ SV35 @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[799]) ).
thf(814,plain,
! [SV9: $i,SV51: $i] :
( ( ( subset @ SV51 @ SV9 )
= $false )
| ( ( subset @ SV9 @ SV51 )
= $false )
| ( ( SV9 = SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[803]) ).
thf(815,plain,
! [SV56: $i,SV16: $i] :
( ( ( relation @ ( relation_rng_restriction @ SV16 @ SV56 ) )
= $true )
| ( ( relation @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(816,plain,
! [SV56: $i,SV16: $i] :
( ( ( function @ ( relation_rng_restriction @ SV16 @ SV56 ) )
= $true )
| ( ( relation @ SV56 )
= $false )
| ( ( function @ SV56 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(817,plain,
! [SV62: $i,SV23: $i] :
( ( ( SV23 = SV62 )
= $false )
| ( ( proper_subset @ SV23 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[809]) ).
thf(818,plain,
! [SV62: $i,SV23: $i] :
( ( ( SV23 != SV62 )
= $false )
| ( ( subset @ SV23 @ SV62 )
= $false )
| ( ( proper_subset @ SV23 @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[810]) ).
thf(819,plain,
! [SV91: $i,SV35: $i] :
( ( ( subset @ ( relation_dom @ SV35 ) @ ( relation_dom @ SV91 ) )
= $true )
| ( ( subset @ SV35 @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(820,plain,
! [SV91: $i,SV35: $i] :
( ( ( subset @ ( relation_rng @ SV35 ) @ ( relation_rng @ SV91 ) )
= $true )
| ( ( subset @ SV35 @ SV91 )
= $false )
| ( ( relation @ SV91 )
= $false )
| ( ( relation @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(821,plain,
! [SV62: $i,SV23: $i] :
( ( ( SV23 = SV62 )
= $true )
| ( ( subset @ SV23 @ SV62 )
= $false )
| ( ( proper_subset @ SV23 @ SV62 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[818]) ).
thf(822,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[413,821,820,819,817,816,815,814,811,808,805,804,802,801,800,797,793,791,788,784,783,782,781,778,773,765,761,760,759,738,730,729,727,726,725,716,715,714,713,701,697,685,672,671,670,659,658,657,656,649,646,645,637,619,611,604,595,548,547,546,545,502,500,497,452,439,438,433,432,430,429,428,427,426,424,423,422,421,420,419,418,417,416,415,414]) ).
thf(823,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[822]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU248+2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n017.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 15:04:45 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.70/3.35 ..
% 18.70/3.35
% 18.70/3.35 No.of.Axioms: 69
% 18.70/3.35
% 18.70/3.35 Length.of.Defs: 0
% 18.70/3.35
% 18.70/3.35 Contains.Choice.Funs: false
% 18.70/3.35 ................
% 18.70/3.35
% 18.70/3.35 ********************************
% 18.70/3.35 * All subproblems solved! *
% 18.70/3.35 ********************************
% 18.70/3.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:70,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:822,loop_count:0,foatp_calls:1,translation:fof_full)
% 18.70/3.35
% 18.70/3.35 %**** Beginning of derivation protocol ****
% 18.70/3.35 % SZS output start CNFRefutation
% See solution above
% 18.70/3.36
% 18.70/3.36 %**** End of derivation protocol ****
% 18.70/3.36 %**** no. of clauses in derivation: 587 ****
% 18.70/3.36 %**** clause counter: 822 ****
% 18.70/3.36
% 18.70/3.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:70,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:822,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------