%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU247+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 : n001.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 2.53s 0.69s
% Output : CNFRefutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 44
% Syntax : Number of formulae : 306 ( 207 unt; 0 typ; 0 def)
% Number of atoms : 1406 ( 407 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 1874 ( 391 ~; 254 |; 42 &;1131 @)
% ( 0 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 67 usr; 9 con; 0-3 aty)
% Number of variables : 373 ( 0 ^; 361 !; 12 ?; 373 :)
% 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_SY39,type,
sK2_SY39: $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_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(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(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(52,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_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(69,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_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(172,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_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(261,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_dom_restriction @ ( relation_rng_restriction @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_wellord1) ).
thf(275,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(282,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(305,conjecture,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_wellord1) ).
thf(306,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ B @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[305]) ).
thf(307,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_rng_restriction @ A @ ( relation_dom_restriction @ B @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[306]) ).
thf(308,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(309,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(310,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(311,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(312,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(313,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(314,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(315,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(316,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(317,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(318,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(319,plain,
$true = $true,
inference(unfold_def,[status(thm)],[74]) ).
thf(320,plain,
$true = $true,
inference(unfold_def,[status(thm)],[75]) ).
thf(321,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(322,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(323,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(324,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(325,plain,
$true = $true,
inference(unfold_def,[status(thm)],[84]) ).
thf(326,plain,
$true = $true,
inference(unfold_def,[status(thm)],[85]) ).
thf(327,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(328,plain,
$true = $true,
inference(unfold_def,[status(thm)],[87]) ).
thf(329,plain,
$true = $true,
inference(unfold_def,[status(thm)],[88]) ).
thf(330,plain,
$true = $true,
inference(unfold_def,[status(thm)],[90]) ).
thf(331,plain,
$true = $true,
inference(unfold_def,[status(thm)],[91]) ).
thf(332,plain,
$true = $true,
inference(unfold_def,[status(thm)],[92]) ).
thf(333,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(334,plain,
$true = $true,
inference(unfold_def,[status(thm)],[94]) ).
thf(335,plain,
$true = $true,
inference(unfold_def,[status(thm)],[96]) ).
thf(336,plain,
$true = $true,
inference(unfold_def,[status(thm)],[98]) ).
thf(337,plain,
$true = $true,
inference(unfold_def,[status(thm)],[99]) ).
thf(338,plain,
$true = $true,
inference(unfold_def,[status(thm)],[100]) ).
thf(339,plain,
$true = $true,
inference(unfold_def,[status(thm)],[101]) ).
thf(340,plain,
$true = $true,
inference(unfold_def,[status(thm)],[102]) ).
thf(341,plain,
$true = $true,
inference(unfold_def,[status(thm)],[103]) ).
thf(342,plain,
$true = $true,
inference(unfold_def,[status(thm)],[104]) ).
thf(343,plain,
$true = $true,
inference(unfold_def,[status(thm)],[105]) ).
thf(344,plain,
$true = $true,
inference(unfold_def,[status(thm)],[106]) ).
thf(345,plain,
$true = $true,
inference(unfold_def,[status(thm)],[107]) ).
thf(346,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(347,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(348,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_dom_restriction @ ( relation_rng_restriction @ A @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(349,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)],[275]) ).
thf(350,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(351,plain,
( ( ! [SY39: $i] :
( ( relation @ SY39 )
=> ( ( relation_restriction @ SY39 @ sK1_A )
= ( relation_rng_restriction @ sK1_A @ ( relation_dom_restriction @ SY39 @ sK1_A ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[307]) ).
thf(352,plain,
( ( ( relation @ sK2_SY39 )
=> ( ( relation_restriction @ sK2_SY39 @ sK1_A )
= ( relation_rng_restriction @ sK1_A @ ( relation_dom_restriction @ sK2_SY39 @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[351]) ).
thf(353,plain,
( ( relation @ sK2_SY39 )
= $true ),
inference(standard_cnf,[status(thm)],[352]) ).
thf(354,plain,
( ( ( relation_restriction @ sK2_SY39 @ sK1_A )
= ( relation_rng_restriction @ sK1_A @ ( relation_dom_restriction @ sK2_SY39 @ sK1_A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[352]) ).
thf(355,plain,
( ( ( relation_restriction @ sK2_SY39 @ sK1_A )
!= ( relation_rng_restriction @ sK1_A @ ( relation_dom_restriction @ sK2_SY39 @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[354]) ).
thf(356,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng_restriction @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[350]) ).
thf(357,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)],[349]) ).
thf(358,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( relation_restriction @ B @ A )
= ( relation_dom_restriction @ ( relation_rng_restriction @ A @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[348]) ).
thf(359,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[347]) ).
thf(360,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[346]) ).
thf(361,plain,
$true = $true,
inference(copy,[status(thm)],[345]) ).
thf(362,plain,
$true = $true,
inference(copy,[status(thm)],[344]) ).
thf(363,plain,
$true = $true,
inference(copy,[status(thm)],[343]) ).
thf(364,plain,
$true = $true,
inference(copy,[status(thm)],[342]) ).
thf(365,plain,
$true = $true,
inference(copy,[status(thm)],[341]) ).
thf(366,plain,
$true = $true,
inference(copy,[status(thm)],[340]) ).
thf(367,plain,
$true = $true,
inference(copy,[status(thm)],[339]) ).
thf(368,plain,
$true = $true,
inference(copy,[status(thm)],[338]) ).
thf(369,plain,
$true = $true,
inference(copy,[status(thm)],[337]) ).
thf(370,plain,
$true = $true,
inference(copy,[status(thm)],[336]) ).
thf(371,plain,
$true = $true,
inference(copy,[status(thm)],[335]) ).
thf(372,plain,
$true = $true,
inference(copy,[status(thm)],[334]) ).
thf(373,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[333]) ).
thf(374,plain,
$true = $true,
inference(copy,[status(thm)],[332]) ).
thf(375,plain,
$true = $true,
inference(copy,[status(thm)],[331]) ).
thf(376,plain,
$true = $true,
inference(copy,[status(thm)],[330]) ).
thf(377,plain,
$true = $true,
inference(copy,[status(thm)],[329]) ).
thf(378,plain,
$true = $true,
inference(copy,[status(thm)],[328]) ).
thf(379,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[327]) ).
thf(380,plain,
$true = $true,
inference(copy,[status(thm)],[326]) ).
thf(381,plain,
$true = $true,
inference(copy,[status(thm)],[325]) ).
thf(382,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[324]) ).
thf(383,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[323]) ).
thf(384,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[322]) ).
thf(385,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[321]) ).
thf(386,plain,
$true = $true,
inference(copy,[status(thm)],[320]) ).
thf(387,plain,
$true = $true,
inference(copy,[status(thm)],[319]) ).
thf(388,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation_empty_yielding @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( relation_empty_yielding @ ( relation_dom_restriction @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[318]) ).
thf(389,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[317]) ).
thf(390,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[316]) ).
thf(391,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[315]) ).
thf(392,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[314]) ).
thf(393,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)],[313]) ).
thf(394,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[312]) ).
thf(395,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[311]) ).
thf(396,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[310]) ).
thf(397,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[309]) ).
thf(398,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[308]) ).
thf(399,plain,
( ( relation @ sK2_SY39 )
= $true ),
inference(copy,[status(thm)],[353]) ).
thf(400,plain,
( ( ( relation_restriction @ sK2_SY39 @ sK1_A )
!= ( relation_rng_restriction @ sK1_A @ ( relation_dom_restriction @ sK2_SY39 @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[355]) ).
thf(401,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(402,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)],[393]) ).
thf(403,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(404,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( ( relation_restriction @ SX1 @ SX0 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(405,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(406,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_inverse @ ( relation_inverse @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(407,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(408,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(409,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(410,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(411,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(412,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(413,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng_restriction @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(414,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(415,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom_restriction @ SX1 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(416,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(417,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(418,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(419,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) )
| ~ ( function @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(420,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)],[357]) ).
thf(421,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(422,plain,
! [SV1: $i] :
( ( relation @ ( identity_relation @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(423,plain,
( ( ( relation_restriction @ sK2_SY39 @ sK1_A )
= ( relation_rng_restriction @ sK1_A @ ( relation_dom_restriction @ sK2_SY39 @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(424,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( relation @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(425,plain,
! [SV3: $i] :
( ( ! [SY40: $i] :
( ~ ~ ( ~ ( relation @ SY40 )
| ~ ( function @ SY40 ) )
| ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SY40 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SY40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(426,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(427,plain,
! [SV4: $i] :
( ( ! [SY41: $i] :
( ~ ( relation @ SY41 )
| ( ( relation_restriction @ SY41 @ SV4 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SV4 @ SY41 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(428,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(429,plain,
! [SV5: $i] :
( ( ~ ( relation @ SV5 )
| ( ( relation_inverse @ ( relation_inverse @ SV5 ) )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(430,plain,
! [SV6: $i] :
( ( ~ ( relation @ SV6 )
| ( relation @ ( relation_inverse @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(431,plain,
! [SV7: $i] :
( ( ! [SY42: $i] :
( ~ ~ ( ~ ( relation @ SV7 )
| ~ ( relation @ SY42 ) )
| ( relation @ ( relation_composition @ SV7 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(432,plain,
! [SV8: $i] :
( ( ! [SY43: $i] :
( ~ ( relation @ SV8 )
| ( relation @ ( relation_restriction @ SV8 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(433,plain,
! [SV9: $i] :
( ( ! [SY44: $i] :
( ~ ( relation @ SV9 )
| ( relation @ ( relation_dom_restriction @ SV9 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(434,plain,
! [SV10: $i] :
( ( ! [SY45: $i] :
( ~ ~ ( ~ ( relation @ SV10 )
| ~ ( relation_empty_yielding @ SV10 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV10 @ SY45 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV10 @ SY45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(435,plain,
! [SV11: $i] :
( ( ! [SY46: $i] :
( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( relation @ SY46 ) )
| ( relation @ ( set_union2 @ SV11 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(436,plain,
! [SV12: $i] :
( ( ! [SY47: $i] :
( ~ ( relation @ SY47 )
| ( subset @ ( relation_rng_restriction @ SV12 @ SY47 ) @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(437,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(438,plain,
! [SV13: $i] :
( ( ! [SY48: $i] :
( ~ ( relation @ SY48 )
| ( subset @ ( relation_dom_restriction @ SY48 @ SV13 ) @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(439,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(440,plain,
! [SV14: $i] :
( ( ! [SY49: $i] :
( ~ ~ ( ~ ( relation @ SV14 )
| ~ ( relation @ SY49 ) )
| ( relation @ ( set_intersection2 @ SV14 @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(441,plain,
! [SV15: $i] :
( ( ! [SY50: $i] :
( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( relation @ SY50 ) )
| ( relation @ ( set_difference @ SV15 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(442,plain,
! [SV16: $i] :
( ( ! [SY51: $i] :
( ~ ~ ( ~ ( relation @ SV16 )
| ~ ( function @ SV16 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV16 @ SY51 ) )
| ~ ( function @ ( relation_dom_restriction @ SV16 @ SY51 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(443,plain,
! [SV17: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( relation @ SY53 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV17 @ SY53 ) @ SY52 )
= ( relation_rng_restriction @ SV17 @ ( relation_dom_restriction @ SY53 @ SY52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(444,plain,
! [SV18: $i] :
( ( ! [SY54: $i] :
( ~ ( relation @ SY54 )
| ( relation @ ( relation_rng_restriction @ SV18 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(445,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( relation @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(446,plain,
! [SV3: $i,SV19: $i] :
( ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV19 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(447,plain,
( ( ~ ~ ( ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[426]) ).
thf(448,plain,
! [SV4: $i,SV20: $i] :
( ( ~ ( relation @ SV20 )
| ( ( relation_restriction @ SV20 @ SV4 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SV4 @ SV20 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(449,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[428]) ).
thf(450,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV5 ) )
= SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(451,plain,
! [SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(452,plain,
! [SV21: $i,SV7: $i] :
( ( ~ ~ ( ~ ( relation @ SV7 )
| ~ ( relation @ SV21 ) )
| ( relation @ ( relation_composition @ SV7 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(453,plain,
! [SV22: $i,SV8: $i] :
( ( ~ ( relation @ SV8 )
| ( relation @ ( relation_restriction @ SV8 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(454,plain,
! [SV23: $i,SV9: $i] :
( ( ~ ( relation @ SV9 )
| ( relation @ ( relation_dom_restriction @ SV9 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(455,plain,
! [SV24: $i,SV10: $i] :
( ( ~ ~ ( ~ ( relation @ SV10 )
| ~ ( relation_empty_yielding @ SV10 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV10 @ SV24 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV10 @ SV24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(456,plain,
! [SV25: $i,SV11: $i] :
( ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( relation @ SV25 ) )
| ( relation @ ( set_union2 @ SV11 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(457,plain,
! [SV12: $i,SV26: $i] :
( ( ~ ( relation @ SV26 )
| ( subset @ ( relation_rng_restriction @ SV12 @ SV26 ) @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(458,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_empty_yielding @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[437]) ).
thf(459,plain,
! [SV13: $i,SV27: $i] :
( ( ~ ( relation @ SV27 )
| ( subset @ ( relation_dom_restriction @ SV27 @ SV13 ) @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(460,plain,
( ( ~ ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[439]) ).
thf(461,plain,
! [SV28: $i,SV14: $i] :
( ( ~ ~ ( ~ ( relation @ SV14 )
| ~ ( relation @ SV28 ) )
| ( relation @ ( set_intersection2 @ SV14 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(462,plain,
! [SV29: $i,SV15: $i] :
( ( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( relation @ SV29 ) )
| ( relation @ ( set_difference @ SV15 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(463,plain,
! [SV30: $i,SV16: $i] :
( ( ~ ~ ( ~ ( relation @ SV16 )
| ~ ( function @ SV16 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV16 @ SV30 ) )
| ~ ( function @ ( relation_dom_restriction @ SV16 @ SV30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(464,plain,
! [SV31: $i,SV17: $i] :
( ( ! [SY55: $i] :
( ~ ( relation @ SY55 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV17 @ SY55 ) @ SV31 )
= ( relation_rng_restriction @ SV17 @ ( relation_dom_restriction @ SY55 @ SV31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(465,plain,
! [SV18: $i,SV32: $i] :
( ( ~ ( relation @ SV32 )
| ( relation @ ( relation_rng_restriction @ SV18 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(466,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( relation @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(467,plain,
! [SV3: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV19 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(468,plain,
( ( ~ ( ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(469,plain,
! [SV4: $i,SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ( relation_restriction @ SV20 @ SV4 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SV4 @ SV20 ) @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(470,plain,
( ( ~ ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(471,plain,
! [SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV5 ) )
= SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(472,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( relation @ ( relation_inverse @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(473,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV7 )
| ~ ( relation @ SV21 ) ) )
= $true )
| ( ( relation @ ( relation_composition @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(474,plain,
! [SV22: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( relation @ ( relation_restriction @ SV8 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(475,plain,
! [SV23: $i,SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( relation @ ( relation_dom_restriction @ SV9 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(476,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV10 )
| ~ ( relation_empty_yielding @ SV10 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV10 @ SV24 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV10 @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(477,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( relation @ SV25 ) ) )
= $true )
| ( ( relation @ ( set_union2 @ SV11 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(478,plain,
! [SV12: $i,SV26: $i] :
( ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( subset @ ( relation_rng_restriction @ SV12 @ SV26 ) @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(479,plain,
( ( ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_empty_yielding @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(480,plain,
! [SV13: $i,SV27: $i] :
( ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV27 @ SV13 ) @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(481,plain,
( ( ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(482,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV14 )
| ~ ( relation @ SV28 ) ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV14 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(483,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( relation @ SV29 ) ) )
= $true )
| ( ( relation @ ( set_difference @ SV15 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(484,plain,
! [SV30: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV16 )
| ~ ( function @ SV16 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV16 @ SV30 ) )
| ~ ( function @ ( relation_dom_restriction @ SV16 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(485,plain,
! [SV31: $i,SV17: $i,SV33: $i] :
( ( ~ ( relation @ SV33 )
| ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV17 @ SV33 ) @ SV31 )
= ( relation_rng_restriction @ SV17 @ ( relation_dom_restriction @ SV33 @ SV31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(486,plain,
! [SV18: $i,SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV18 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(487,plain,
! [SV3: $i,SV19: $i] :
( ( ( ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV19 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(488,plain,
( ( ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(489,plain,
! [SV4: $i,SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( ( relation_restriction @ SV20 @ SV4 )
= ( relation_dom_restriction @ ( relation_rng_restriction @ SV4 @ SV20 ) @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(490,plain,
( ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[470]) ).
thf(491,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ( ~ ( relation @ SV7 )
| ~ ( relation @ SV21 ) ) )
= $false )
| ( ( relation @ ( relation_composition @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(492,plain,
! [SV22: $i,SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( relation @ ( relation_restriction @ SV8 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(493,plain,
! [SV23: $i,SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( relation @ ( relation_dom_restriction @ SV9 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[475]) ).
thf(494,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( ~ ( relation @ SV10 )
| ~ ( relation_empty_yielding @ SV10 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV10 @ SV24 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV10 @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(495,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( ~ ( relation @ SV11 )
| ~ ( relation @ SV25 ) ) )
= $false )
| ( ( relation @ ( set_union2 @ SV11 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(496,plain,
! [SV12: $i,SV26: $i] :
( ( ( relation @ SV26 )
= $false )
| ( ( subset @ ( relation_rng_restriction @ SV12 @ SV26 ) @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(497,plain,
( ( ~ ( relation @ sK5_SX0 )
| ~ ( relation_empty_yielding @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(498,plain,
! [SV13: $i,SV27: $i] :
( ( ( relation @ SV27 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV27 @ SV13 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(499,plain,
( ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(500,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( ~ ( relation @ SV14 )
| ~ ( relation @ SV28 ) ) )
= $false )
| ( ( relation @ ( set_intersection2 @ SV14 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(501,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ( ~ ( relation @ SV15 )
| ~ ( relation @ SV29 ) ) )
= $false )
| ( ( relation @ ( set_difference @ SV15 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(502,plain,
! [SV30: $i,SV16: $i] :
( ( ( ~ ( ~ ( relation @ SV16 )
| ~ ( function @ SV16 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV16 @ SV30 ) )
| ~ ( function @ ( relation_dom_restriction @ SV16 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(503,plain,
! [SV31: $i,SV17: $i,SV33: $i] :
( ( ( ~ ( relation @ SV33 ) )
= $true )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV17 @ SV33 ) @ SV31 )
= ( relation_rng_restriction @ SV17 @ ( relation_dom_restriction @ SV33 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(504,plain,
! [SV18: $i,SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV18 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(505,plain,
! [SV3: $i,SV19: $i] :
( ( ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV19 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(506,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(507,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(508,plain,
( ( ~ ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(509,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(510,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ( relation @ SV7 )
| ~ ( relation @ SV21 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(511,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( relation @ SV10 )
| ~ ( relation_empty_yielding @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV10 @ SV24 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV10 @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(512,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( relation @ SV11 )
| ~ ( relation @ SV25 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV11 @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(513,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[497]) ).
thf(514,plain,
( ( ~ ( relation_empty_yielding @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[497]) ).
thf(515,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(516,plain,
( ( ~ ( function @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(517,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( relation @ SV14 )
| ~ ( relation @ SV28 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV14 @ SV28 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(518,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ( relation @ SV15 )
| ~ ( relation @ SV29 ) )
= $true )
| ( ( relation @ ( set_difference @ SV15 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(519,plain,
! [SV30: $i,SV16: $i] :
( ( ( ~ ( relation @ SV16 )
| ~ ( function @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV16 @ SV30 ) )
| ~ ( function @ ( relation_dom_restriction @ SV16 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(520,plain,
! [SV31: $i,SV17: $i,SV33: $i] :
( ( ( relation @ SV33 )
= $false )
| ( ( ( relation_dom_restriction @ ( relation_rng_restriction @ SV17 @ SV33 ) @ SV31 )
= ( relation_rng_restriction @ SV17 @ ( relation_dom_restriction @ SV33 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(521,plain,
! [SV3: $i,SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ~ ( function @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV19 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(522,plain,
( ( empty @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(523,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(524,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(525,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(526,plain,
! [SV21: $i,SV7: $i] :
( ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(527,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( ~ ( relation_empty_yielding @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV10 @ SV24 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV10 @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[511]) ).
thf(528,plain,
! [SV25: $i,SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ~ ( relation @ SV25 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV11 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(529,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(530,plain,
( ( relation_empty_yielding @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(531,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(532,plain,
( ( function @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(533,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ~ ( relation @ SV28 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV14 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(534,plain,
! [SV29: $i,SV15: $i] :
( ( ( ~ ( relation @ SV15 ) )
= $true )
| ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( relation @ ( set_difference @ SV15 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(535,plain,
! [SV30: $i,SV16: $i] :
( ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( function @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV16 @ SV30 ) )
| ~ ( function @ ( relation_dom_restriction @ SV16 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(536,plain,
! [SV3: $i,SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( ~ ( function @ SV19 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV19 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(537,plain,
( ( empty @ sK4_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(538,plain,
! [SV21: $i,SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(539,plain,
! [SV24: $i,SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( ~ ( relation_empty_yielding @ SV10 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV10 @ SV24 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV10 @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(540,plain,
! [SV25: $i,SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ~ ( relation @ SV25 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV11 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(541,plain,
! [SV28: $i,SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ~ ( relation @ SV28 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV14 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(542,plain,
! [SV29: $i,SV15: $i] :
( ( ( relation @ SV15 )
= $false )
| ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( relation @ ( set_difference @ SV15 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(543,plain,
! [SV30: $i,SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( ~ ( function @ SV16 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV16 @ SV30 ) )
| ~ ( function @ ( relation_dom_restriction @ SV16 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(544,plain,
! [SV3: $i,SV19: $i] :
( ( ( function @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV19 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV19 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(545,plain,
! [SV7: $i,SV21: $i] :
( ( ( relation @ SV21 )
= $false )
| ( ( relation @ SV7 )
= $false )
| ( ( relation @ ( relation_composition @ SV7 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(546,plain,
! [SV24: $i,SV10: $i] :
( ( ( relation_empty_yielding @ SV10 )
= $false )
| ( ( relation @ SV10 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV10 @ SV24 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV10 @ SV24 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(547,plain,
! [SV11: $i,SV25: $i] :
( ( ( relation @ SV25 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( relation @ ( set_union2 @ SV11 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(548,plain,
! [SV14: $i,SV28: $i] :
( ( ( relation @ SV28 )
= $false )
| ( ( relation @ SV14 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV14 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(549,plain,
! [SV15: $i,SV29: $i] :
( ( ( relation @ SV29 )
= $false )
| ( ( relation @ SV15 )
= $false )
| ( ( relation @ ( set_difference @ SV15 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(550,plain,
! [SV30: $i,SV16: $i] :
( ( ( function @ SV16 )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV16 @ SV30 ) )
| ~ ( function @ ( relation_dom_restriction @ SV16 @ SV30 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(551,plain,
! [SV19: $i,SV3: $i] :
( ( ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV19 ) )
| ~ ( function @ ( relation_rng_restriction @ SV3 @ SV19 ) ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(552,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV10 @ SV24 ) )
| ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV10 @ SV24 ) ) )
= $false )
| ( ( relation @ SV10 )
= $false )
| ( ( relation_empty_yielding @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(553,plain,
! [SV30: $i,SV16: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV16 @ SV30 ) )
| ~ ( function @ ( relation_dom_restriction @ SV16 @ SV30 ) ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(554,plain,
! [SV19: $i,SV3: $i] :
( ( ( ~ ( relation @ ( relation_rng_restriction @ SV3 @ SV19 ) ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(555,plain,
! [SV19: $i,SV3: $i] :
( ( ( ~ ( function @ ( relation_rng_restriction @ SV3 @ SV19 ) ) )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[551]) ).
thf(556,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV10 @ SV24 ) ) )
= $false )
| ( ( relation @ SV10 )
= $false )
| ( ( relation_empty_yielding @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(557,plain,
! [SV24: $i,SV10: $i] :
( ( ( ~ ( relation_empty_yielding @ ( relation_dom_restriction @ SV10 @ SV24 ) ) )
= $false )
| ( ( relation @ SV10 )
= $false )
| ( ( relation_empty_yielding @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[552]) ).
thf(558,plain,
! [SV30: $i,SV16: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV16 @ SV30 ) ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[553]) ).
thf(559,plain,
! [SV30: $i,SV16: $i] :
( ( ( ~ ( function @ ( relation_dom_restriction @ SV16 @ SV30 ) ) )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[553]) ).
thf(560,plain,
! [SV19: $i,SV3: $i] :
( ( ( relation @ ( relation_rng_restriction @ SV3 @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(561,plain,
! [SV19: $i,SV3: $i] :
( ( ( function @ ( relation_rng_restriction @ SV3 @ SV19 ) )
= $true )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(562,plain,
! [SV24: $i,SV10: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV10 @ SV24 ) )
= $true )
| ( ( relation @ SV10 )
= $false )
| ( ( relation_empty_yielding @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(563,plain,
! [SV24: $i,SV10: $i] :
( ( ( relation_empty_yielding @ ( relation_dom_restriction @ SV10 @ SV24 ) )
= $true )
| ( ( relation @ SV10 )
= $false )
| ( ( relation_empty_yielding @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(564,plain,
! [SV30: $i,SV16: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV16 @ SV30 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(565,plain,
! [SV30: $i,SV16: $i] :
( ( ( function @ ( relation_dom_restriction @ SV16 @ SV30 ) )
= $true )
| ( ( relation @ SV16 )
= $false )
| ( ( function @ SV16 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[559]) ).
thf(566,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[361,565,564,563,562,561,560,549,548,547,545,537,532,531,530,529,525,523,522,520,504,498,496,493,492,489,472,471,466,423,422,399,387,386,381,380,378,377,376,375,374,372,371,370,369,368,367,366,365,364,363,362]) ).
thf(567,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU247+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
% 0.08/0.15 % Computer : n001.cluster.edu
% 0.08/0.15 % Model : x86_64 x86_64
% 0.08/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.15 % Memory : 8046.5625MB
% 0.08/0.15 % OS : Linux 6.8.0-71-generic
% 0.08/0.15 % CPULimit : 300
% 0.08/0.15 % WCLimit : 300
% 0.08/0.15 % DateTime : Tue Oct 6 15:15:09 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
% 2.53/0.69 ..
% 2.53/0.69
% 2.53/0.69 No.of.Axioms: 43
% 2.53/0.69
% 2.53/0.69 Length.of.Defs: 0
% 2.53/0.69
% 2.53/0.69 Contains.Choice.Funs: false
% 2.53/0.69 ........
% 2.53/0.69
% 2.53/0.69 ********************************
% 2.53/0.69 * All subproblems solved! *
% 2.53/0.69 ********************************
% 2.53/0.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:44,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:566,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.53/0.69
% 2.53/0.69 %**** Beginning of derivation protocol ****
% 2.53/0.69 % SZS output start CNFRefutation
% See solution above
% 2.53/0.69
% 2.53/0.69 %**** End of derivation protocol ****
% 2.53/0.69 %**** no. of clauses in derivation: 306 ****
% 2.53/0.69 %**** clause counter: 566 ****
% 2.53/0.69
% 2.53/0.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:44,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:566,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------