%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU303+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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 10:43:52 AM UTC 2026
% Result : Theorem 7.36s 1.42s
% Output : CNFRefutation 7.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 74
% Syntax : Number of formulae : 654 ( 409 unt; 0 typ; 0 def)
% Number of atoms : 3472 (1047 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 4702 (1201 ~; 746 |; 130 &;2503 @)
% ( 3 <=>; 119 =>; 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 : 88 ( 85 usr; 13 con; 0-3 aty)
% Number of variables : 750 ( 0 ^; 720 !; 30 ?; 750 :)
% 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_equipotent,type,
equipotent: $i > $i > $o ).
thf(tp_fiber,type,
fiber: $i > $i > $i ).
thf(tp_finite,type,
finite: $i > $o ).
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_inclusion_relation,type,
inclusion_relation: $i > $i ).
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_natural,type,
natural: $i > $o ).
thf(tp_omega,type,
omega: $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_pair_first,type,
pair_first: $i > $i ).
thf(tp_pair_second,type,
pair_second: $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_quasi_total,type,
quasi_total: $i > $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_as_subset,type,
relation_dom_as_subset: $i > $i > $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_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_isomorphism,type,
relation_isomorphism: $i > $i > $i > $o ).
thf(tp_relation_of2,type,
relation_of2: $i > $i > $i > $o ).
thf(tp_relation_of2_as_subset,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(tp_relation_restriction,type,
relation_restriction: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_as_subset,type,
relation_rng_as_subset: $i > $i > $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_SY78,type,
sK10_SY78: $i > $i ).
thf(tp_sK11_SY92,type,
sK11_SY92: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SX0,type,
sK7_SX0: $i ).
thf(tp_sK8_SX0,type,
sK8_SX0: $i ).
thf(tp_sK9_SX0,type,
sK9_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(39,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(40,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(42,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(46,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(47,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(49,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(53,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(58,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(59,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(63,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(69,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(70,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(71,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(72,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( relation_dom_restriction @ A @ B ) )
& ( function @ ( relation_dom_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(87,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(92,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
thf(100,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(109,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(110,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_relset_1) ).
thf(111,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(117,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(121,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_ordinal2) ).
thf(122,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(123,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(125,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(126,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(127,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(129,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(130,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(131,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(132,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(133,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(135,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(136,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_mcart_1) ).
thf(137,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(138,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(139,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(140,axiom,
! [A: $i] : ( relation @ ( inclusion_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
thf(141,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord1) ).
thf(142,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(143,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(144,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(145,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_ordinal1) ).
thf(146,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_mcart_1) ).
thf(147,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(148,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_enumset1) ).
thf(149,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(229,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(231,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(232,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(255,axiom,
! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
thf(263,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).
thf(264,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
thf(268,axiom,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(307,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
thf(324,axiom,
! [A: $i] :
? [B: $i] :
( ( relation @ B )
& ( well_orders @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_wellord2) ).
thf(327,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/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(352,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).
thf(360,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finset_1) ).
thf(363,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
thf(370,axiom,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
thf(420,conjecture,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
=> ( finite @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).
thf(421,negated_conjecture,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
=> ( finite @ ( relation_rng @ A ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[420]) ).
thf(422,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( finite @ ( relation_dom @ A ) )
=> ( finite @ ( relation_rng @ A ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[421]) ).
thf(423,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(424,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(425,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(426,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(427,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(428,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(429,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(430,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(431,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(432,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(433,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(434,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(435,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(436,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(437,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(438,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)],[73]) ).
thf(439,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)],[77]) ).
thf(440,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(441,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(442,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(443,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(444,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(445,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(446,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(447,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(448,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(449,plain,
$true = $true,
inference(unfold_def,[status(thm)],[109]) ).
thf(450,plain,
$true = $true,
inference(unfold_def,[status(thm)],[110]) ).
thf(451,plain,
$true = $true,
inference(unfold_def,[status(thm)],[111]) ).
thf(452,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(453,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(454,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(455,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(456,plain,
$true = $true,
inference(unfold_def,[status(thm)],[121]) ).
thf(457,plain,
$true = $true,
inference(unfold_def,[status(thm)],[122]) ).
thf(458,plain,
$true = $true,
inference(unfold_def,[status(thm)],[123]) ).
thf(459,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(460,plain,
$true = $true,
inference(unfold_def,[status(thm)],[126]) ).
thf(461,plain,
$true = $true,
inference(unfold_def,[status(thm)],[127]) ).
thf(462,plain,
$true = $true,
inference(unfold_def,[status(thm)],[129]) ).
thf(463,plain,
$true = $true,
inference(unfold_def,[status(thm)],[130]) ).
thf(464,plain,
$true = $true,
inference(unfold_def,[status(thm)],[131]) ).
thf(465,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(466,plain,
$true = $true,
inference(unfold_def,[status(thm)],[133]) ).
thf(467,plain,
$true = $true,
inference(unfold_def,[status(thm)],[135]) ).
thf(468,plain,
$true = $true,
inference(unfold_def,[status(thm)],[136]) ).
thf(469,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(470,plain,
$true = $true,
inference(unfold_def,[status(thm)],[138]) ).
thf(471,plain,
$true = $true,
inference(unfold_def,[status(thm)],[139]) ).
thf(472,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(473,plain,
$true = $true,
inference(unfold_def,[status(thm)],[141]) ).
thf(474,plain,
$true = $true,
inference(unfold_def,[status(thm)],[142]) ).
thf(475,plain,
$true = $true,
inference(unfold_def,[status(thm)],[143]) ).
thf(476,plain,
$true = $true,
inference(unfold_def,[status(thm)],[144]) ).
thf(477,plain,
$true = $true,
inference(unfold_def,[status(thm)],[145]) ).
thf(478,plain,
$true = $true,
inference(unfold_def,[status(thm)],[146]) ).
thf(479,plain,
$true = $true,
inference(unfold_def,[status(thm)],[147]) ).
thf(480,plain,
$true = $true,
inference(unfold_def,[status(thm)],[148]) ).
thf(481,plain,
$true = $true,
inference(unfold_def,[status(thm)],[149]) ).
thf(482,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(483,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(484,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(485,plain,
( ( ! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(486,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(487,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(488,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(489,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(490,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( relation @ B )
& ( well_orders @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(491,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)],[327]) ).
thf(492,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(493,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(494,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(496,plain,
( ( ( ( relation @ sK1_A )
& ( function @ sK1_A ) )
=> ( ( finite @ ( relation_dom @ sK1_A ) )
=> ( finite @ ( relation_rng @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[422]) ).
thf(497,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[496]) ).
thf(498,plain,
( ( function @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[496]) ).
thf(499,plain,
( ( finite @ ( relation_dom @ sK1_A ) )
= $true ),
inference(standard_cnf,[status(thm)],[496]) ).
thf(500,plain,
( ( finite @ ( relation_rng @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[496]) ).
thf(501,plain,
( ( ~ ( finite @ ( relation_rng @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[500]) ).
thf(502,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(503,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(504,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(505,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( finite @ A )
=> ( finite @ ( relation_image @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(506,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)],[491]) ).
thf(507,plain,
( ( ! [A: $i] :
? [B: $i] :
( ( relation @ B )
& ( well_orders @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(508,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(509,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(510,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(511,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(512,plain,
( ( ! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(513,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(514,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(515,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(516,plain,
$true = $true,
inference(copy,[status(thm)],[481]) ).
thf(517,plain,
$true = $true,
inference(copy,[status(thm)],[480]) ).
thf(518,plain,
$true = $true,
inference(copy,[status(thm)],[479]) ).
thf(519,plain,
$true = $true,
inference(copy,[status(thm)],[478]) ).
thf(520,plain,
$true = $true,
inference(copy,[status(thm)],[477]) ).
thf(521,plain,
$true = $true,
inference(copy,[status(thm)],[476]) ).
thf(522,plain,
$true = $true,
inference(copy,[status(thm)],[475]) ).
thf(523,plain,
$true = $true,
inference(copy,[status(thm)],[474]) ).
thf(524,plain,
$true = $true,
inference(copy,[status(thm)],[473]) ).
thf(525,plain,
( ( ! [A: $i] : ( relation @ ( inclusion_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(526,plain,
$true = $true,
inference(copy,[status(thm)],[471]) ).
thf(527,plain,
$true = $true,
inference(copy,[status(thm)],[470]) ).
thf(528,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(529,plain,
$true = $true,
inference(copy,[status(thm)],[468]) ).
thf(530,plain,
$true = $true,
inference(copy,[status(thm)],[467]) ).
thf(531,plain,
$true = $true,
inference(copy,[status(thm)],[466]) ).
thf(532,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(533,plain,
$true = $true,
inference(copy,[status(thm)],[464]) ).
thf(534,plain,
$true = $true,
inference(copy,[status(thm)],[463]) ).
thf(535,plain,
$true = $true,
inference(copy,[status(thm)],[462]) ).
thf(536,plain,
$true = $true,
inference(copy,[status(thm)],[461]) ).
thf(537,plain,
$true = $true,
inference(copy,[status(thm)],[460]) ).
thf(538,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(539,plain,
$true = $true,
inference(copy,[status(thm)],[458]) ).
thf(540,plain,
$true = $true,
inference(copy,[status(thm)],[457]) ).
thf(541,plain,
$true = $true,
inference(copy,[status(thm)],[456]) ).
thf(542,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(543,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[454]) ).
thf(544,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[453]) ).
thf(545,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[452]) ).
thf(546,plain,
$true = $true,
inference(copy,[status(thm)],[451]) ).
thf(547,plain,
$true = $true,
inference(copy,[status(thm)],[450]) ).
thf(548,plain,
$true = $true,
inference(copy,[status(thm)],[449]) ).
thf(549,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[448]) ).
thf(550,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[447]) ).
thf(551,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[446]) ).
thf(552,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( finite @ B ) )
=> ( finite @ ( relation_image @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[445]) ).
thf(553,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[444]) ).
thf(554,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[443]) ).
thf(555,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[442]) ).
thf(556,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[441]) ).
thf(557,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[440]) ).
thf(558,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)],[439]) ).
thf(559,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)],[438]) ).
thf(560,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[437]) ).
thf(561,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[436]) ).
thf(562,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[435]) ).
thf(563,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[434]) ).
thf(564,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[433]) ).
thf(565,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[432]) ).
thf(566,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[431]) ).
thf(567,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[430]) ).
thf(568,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[429]) ).
thf(569,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[428]) ).
thf(570,plain,
( ( ! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ) )
= $true ),
inference(copy,[status(thm)],[427]) ).
thf(571,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[426]) ).
thf(572,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[425]) ).
thf(573,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[424]) ).
thf(574,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[423]) ).
thf(575,plain,
( ( finite @ ( relation_dom @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(576,plain,
( ( function @ sK1_A )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(577,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(578,plain,
( ( ~ ( finite @ ( relation_rng @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(579,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ( ( relation_dom @ SX0 )
= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(580,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( finite @ SX1 )
| ( finite @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(581,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(582,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(583,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(584,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(585,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)],[506]) ).
thf(586,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( finite @ SX0 )
| ( finite @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(587,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( ~ ( relation @ ( function_inverse @ SX0 ) )
| ~ ( function @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(588,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(589,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ( ( relation_rng @ SX0 )
!= ( relation_dom @ ( relation_inverse @ SX0 ) ) )
| ( ( relation_dom @ SX0 )
!= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(590,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(591,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(592,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX1 )
| ~ ( function @ SX1 ) )
| ~ ( finite @ SX0 )
| ( finite @ ( relation_image @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(593,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( finite @ SX1 ) )
| ( finite @ ( relation_image @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(594,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( relation @ SX1 )
| ~ ( well_orders @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(595,plain,
( ( ~ ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(596,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(597,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ~ ( ( ( relation_dom @ SX0 )
!= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SX0 )
!= empty_set )
| ( ( relation_dom @ SX0 )
= empty_set ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(598,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(599,plain,
( ( ! [SX0: $i] :
~ ( ~ ( relation @ ( identity_relation @ SX0 ) )
| ~ ( function @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(600,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(601,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(602,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566]) ).
thf(603,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(604,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(605,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_image @ SX0 @ ( relation_dom @ SX0 ) )
= ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503]) ).
thf(606,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(607,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(608,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(609,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( relation @ SX1 ) )
| ~ ( function @ SX1 ) )
| ~ ( ~ ( relation @ ( relation_composition @ SX0 @ SX1 ) )
| ~ ( function @ ( relation_composition @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(610,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(611,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( finite @ SX1 ) )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(612,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(613,plain,
( ( ! [SX0: $i] :
~ ( ( ( relation_dom @ ( identity_relation @ SX0 ) )
!= SX0 )
| ( ( relation_rng @ ( identity_relation @ SX0 ) )
!= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(614,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( relation_of2 @ SX2 @ SX0 @ SX1 )
| ~ ( relation @ SX2 ) )
| ~ ( function @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(615,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)],[558]) ).
thf(616,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(617,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(618,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( finite @ SX0 )
| ( finite @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(619,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_inverse @ ( relation_inverse @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(620,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( finite @ SX0 )
| ~ ( finite @ SX1 ) )
| ( finite @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(621,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(622,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( finite @ SX0 )
| ( finite @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(623,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_rng @ SX0 ) )
| ~ ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(624,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)],[559]) ).
thf(625,plain,
! [SV1: $i] :
( ( relation @ ( inclusion_relation @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(626,plain,
! [SV2: $i] :
( ( relation @ ( identity_relation @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(627,plain,
( ( finite @ ( relation_rng @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(628,plain,
! [SV3: $i] :
( ( ~ ( relation @ SV3 )
| ~ ( ( ( relation_dom @ SV3 )
= empty_set )
| ( ( relation_rng @ SV3 )
= empty_set ) )
| ( SV3 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(629,plain,
! [SV4: $i] :
( ( ! [SY70: $i] :
( ~ ( finite @ SY70 )
| ( finite @ ( set_intersection2 @ SV4 @ SY70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(630,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(631,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(632,plain,
! [SV5: $i] :
( ( ! [SY71: $i] :
( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( relation @ SY71 ) )
| ( relation @ ( relation_composition @ SV5 @ SY71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(633,plain,
! [SV6: $i] :
( ( ~ ( empty @ SV6 )
| ( relation @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(634,plain,
! [SV7: $i] :
( ( ~ ( relation @ SV7 )
| ! [SY72: $i] :
( ~ ( relation @ SY72 )
| ~ ( subset @ SV7 @ SY72 )
| ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SY72 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SY72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(635,plain,
! [SV8: $i] :
( ( ! [SY73: $i] :
( ~ ( finite @ SV8 )
| ( finite @ ( set_intersection2 @ SV8 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(636,plain,
! [SV9: $i] :
( ( ~ ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) )
| ~ ( ~ ( relation @ ( function_inverse @ SV9 ) )
| ~ ( function @ ( function_inverse @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(637,plain,
! [SV10: $i] :
( ( ! [SY74: $i] :
( ~ ( relation @ SV10 )
| ( relation @ ( relation_dom_restriction @ SV10 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(638,plain,
! [SV11: $i] :
( ( ~ ( relation @ SV11 )
| ~ ( ( ( relation_rng @ SV11 )
!= ( relation_dom @ ( relation_inverse @ SV11 ) ) )
| ( ( relation_dom @ SV11 )
!= ( relation_rng @ ( relation_inverse @ SV11 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(639,plain,
! [SV12: $i] :
( ( ! [SY75: $i] :
( ~ ( relation @ SV12 )
| ( relation @ ( relation_restriction @ SV12 @ SY75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(640,plain,
! [SV13: $i] :
( ( ~ ( relation @ SV13 )
| ( relation @ ( relation_inverse @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(641,plain,
! [SV14: $i] :
( ( ! [SY76: $i] :
( ~ ~ ( ~ ( relation @ SY76 )
| ~ ( function @ SY76 ) )
| ~ ( finite @ SV14 )
| ( finite @ ( relation_image @ SY76 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(642,plain,
! [SV15: $i] :
( ( ! [SY77: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( function @ SV15 ) )
| ~ ( finite @ SY77 ) )
| ( finite @ ( relation_image @ SV15 @ SY77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(643,plain,
! [SV16: $i] :
( ( ~ ! [SY78: $i] :
~ ~ ( ~ ( relation @ SY78 )
| ~ ( well_orders @ SY78 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(644,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(645,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(646,plain,
! [SV17: $i] :
( ( ~ ( relation @ SV17 )
| ~ ( ~ ( ( ( relation_dom @ SV17 )
!= empty_set )
| ( ( relation_rng @ SV17 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV17 )
!= empty_set )
| ( ( relation_dom @ SV17 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(647,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(648,plain,
! [SV18: $i] :
( ( ~ ( ~ ( relation @ ( identity_relation @ SV18 ) )
| ~ ( function @ ( identity_relation @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(649,plain,
! [SV19: $i] :
( ( ! [SY79: $i] :
( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( relation @ SY79 ) )
| ( relation @ ( set_difference @ SV19 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(650,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(651,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(652,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(653,plain,
! [SV20: $i] :
( ( ~ ( empty @ SV20 )
| ( function @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(654,plain,
! [SV21: $i] :
( ( ~ ( relation @ SV21 )
| ( ( relation_image @ SV21 @ ( relation_dom @ SV21 ) )
= ( relation_rng @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(655,plain,
! [SV22: $i] :
( ( ! [SY80: $i] :
( ~ ( relation @ SY80 )
| ( relation @ ( relation_rng_restriction @ SV22 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(656,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV23 )
| ~ ( relation @ SV23 ) )
| ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(657,plain,
! [SV24: $i] :
( ( ~ ( empty @ SV24 )
| ( finite @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(658,plain,
! [SV25: $i] :
( ( ! [SY81: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV25 )
| ~ ( function @ SV25 ) )
| ~ ( relation @ SY81 ) )
| ~ ( function @ SY81 ) )
| ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SY81 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SY81 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(659,plain,
! [SV26: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV26 )
| ~ ( relation @ SV26 ) )
| ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(660,plain,
! [SV27: $i] :
( ( ! [SY82: $i] :
( ~ ~ ( ~ ( subset @ SV27 @ SY82 )
| ~ ( finite @ SY82 ) )
| ( finite @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(661,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(662,plain,
! [SV28: $i] :
( ( ~ ( ( ( relation_dom @ ( identity_relation @ SV28 ) )
!= SV28 )
| ( ( relation_rng @ ( identity_relation @ SV28 ) )
!= SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(663,plain,
! [SV29: $i] :
( ( ! [SY83: $i] :
~ ! [SY84: $i] :
~ ~ ( ~ ~ ( ~ ( relation_of2 @ SY84 @ SV29 @ SY83 )
| ~ ( relation @ SY84 ) )
| ~ ( function @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(664,plain,
! [SV30: $i] :
( ( ! [SY85: $i] :
( ~ ~ ( ~ ( relation @ SV30 )
| ~ ( function @ SV30 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV30 @ SY85 ) )
| ~ ( function @ ( relation_dom_restriction @ SV30 @ SY85 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(665,plain,
! [SV31: $i] :
( ( ! [SY86: $i] :
( ~ ~ ( ~ ( relation @ SV31 )
| ~ ( relation @ SY86 ) )
| ( relation @ ( set_union2 @ SV31 @ SY86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(666,plain,
! [SV32: $i] :
( ( ! [SY87: $i] :
( ~ ~ ( ~ ( relation @ SV32 )
| ~ ( relation @ SY87 ) )
| ( relation @ ( set_intersection2 @ SV32 @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(667,plain,
! [SV33: $i] :
( ( ! [SY88: $i] :
( ~ ( finite @ SV33 )
| ( finite @ ( set_difference @ SV33 @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(668,plain,
! [SV34: $i] :
( ( ~ ( relation @ SV34 )
| ( ( relation_inverse @ ( relation_inverse @ SV34 ) )
= SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(669,plain,
! [SV35: $i] :
( ( ! [SY89: $i] :
( ~ ~ ( ~ ( finite @ SV35 )
| ~ ( finite @ SY89 ) )
| ( finite @ ( set_union2 @ SV35 @ SY89 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(670,plain,
! [SV36: $i] :
( ( ~ ( empty @ SV36 )
| ~ ( ~ ( empty @ ( relation_dom @ SV36 ) )
| ~ ( relation @ ( relation_dom @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(671,plain,
! [SV37: $i] :
( ( ! [SY90: $i] :
( ~ ( finite @ SV37 )
| ( finite @ ( set_intersection2 @ SV37 @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(672,plain,
! [SV38: $i] :
( ( ~ ( empty @ SV38 )
| ~ ( ~ ( empty @ ( relation_rng @ SV38 ) )
| ~ ( relation @ ( relation_rng @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(673,plain,
! [SV39: $i] :
( ( ! [SY91: $i] :
( ~ ~ ( ~ ( relation @ SY91 )
| ~ ( function @ SY91 ) )
| ~ ( ~ ( relation @ ( relation_rng_restriction @ SV39 @ SY91 ) )
| ~ ( function @ ( relation_rng_restriction @ SV39 @ SY91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(674,plain,
! [SV3: $i] :
( ( ( ~ ( relation @ SV3 ) )
= $true )
| ( ( ~ ( ( ( relation_dom @ SV3 )
= empty_set )
| ( ( relation_rng @ SV3 )
= empty_set ) )
| ( SV3 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(675,plain,
! [SV4: $i,SV40: $i] :
( ( ~ ( finite @ SV40 )
| ( finite @ ( set_intersection2 @ SV4 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(676,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( function @ sK2_SX0 ) )
| ~ ( one_to_one @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[630]) ).
thf(677,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[631]) ).
thf(678,plain,
! [SV41: $i,SV5: $i] :
( ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( relation @ SV41 ) )
| ( relation @ ( relation_composition @ SV5 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(679,plain,
! [SV6: $i] :
( ( ( ~ ( empty @ SV6 ) )
= $true )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(680,plain,
! [SV7: $i] :
( ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ! [SY72: $i] :
( ~ ( relation @ SY72 )
| ~ ( subset @ SV7 @ SY72 )
| ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SY72 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SY72 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(681,plain,
! [SV42: $i,SV8: $i] :
( ( ~ ( finite @ SV8 )
| ( finite @ ( set_intersection2 @ SV8 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(682,plain,
! [SV9: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV9 ) )
| ~ ( function @ ( function_inverse @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(683,plain,
! [SV43: $i,SV10: $i] :
( ( ~ ( relation @ SV10 )
| ( relation @ ( relation_dom_restriction @ SV10 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(684,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ~ ( ( ( relation_rng @ SV11 )
!= ( relation_dom @ ( relation_inverse @ SV11 ) ) )
| ( ( relation_dom @ SV11 )
!= ( relation_rng @ ( relation_inverse @ SV11 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(685,plain,
! [SV44: $i,SV12: $i] :
( ( ~ ( relation @ SV12 )
| ( relation @ ( relation_restriction @ SV12 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(686,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(687,plain,
! [SV14: $i,SV45: $i] :
( ( ~ ~ ( ~ ( relation @ SV45 )
| ~ ( function @ SV45 ) )
| ~ ( finite @ SV14 )
| ( finite @ ( relation_image @ SV45 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(688,plain,
! [SV46: $i,SV15: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( function @ SV15 ) )
| ~ ( finite @ SV46 ) )
| ( finite @ ( relation_image @ SV15 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(689,plain,
! [SV16: $i] :
( ( ! [SY78: $i] :
~ ~ ( ~ ( relation @ SY78 )
| ~ ( well_orders @ SY78 @ SV16 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(690,plain,
( ( ( relation_dom @ empty_set )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(691,plain,
( ( ( relation_rng @ empty_set )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[644]) ).
thf(692,plain,
( ( ~ ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( relation_empty_yielding @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[645]) ).
thf(693,plain,
! [SV17: $i] :
( ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ( ~ ( ( ( relation_dom @ SV17 )
!= empty_set )
| ( ( relation_rng @ SV17 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV17 )
!= empty_set )
| ( ( relation_dom @ SV17 )
= empty_set ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(694,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( empty @ sK5_SX0 ) )
| ~ ( function @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[647]) ).
thf(695,plain,
! [SV18: $i] :
( ( ~ ( relation @ ( identity_relation @ SV18 ) )
| ~ ( function @ ( identity_relation @ SV18 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(696,plain,
! [SV47: $i,SV19: $i] :
( ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( relation @ SV47 ) )
| ( relation @ ( set_difference @ SV19 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(697,plain,
( ( ~ ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[650]) ).
thf(698,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK7_SX0 )
| ~ ( finite @ sK7_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[651]) ).
thf(699,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( relation_empty_yielding @ sK8_SX0 ) )
| ~ ( function @ sK8_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[652]) ).
thf(700,plain,
! [SV20: $i] :
( ( ( ~ ( empty @ SV20 ) )
= $true )
| ( ( function @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(701,plain,
! [SV21: $i] :
( ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( ( relation_image @ SV21 @ ( relation_dom @ SV21 ) )
= ( relation_rng @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(702,plain,
! [SV22: $i,SV48: $i] :
( ( ~ ( relation @ SV48 )
| ( relation @ ( relation_rng_restriction @ SV22 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(703,plain,
! [SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV23 )
| ~ ( relation @ SV23 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(704,plain,
! [SV24: $i] :
( ( ( ~ ( empty @ SV24 ) )
= $true )
| ( ( finite @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[657]) ).
thf(705,plain,
! [SV49: $i,SV25: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV25 )
| ~ ( function @ SV25 ) )
| ~ ( relation @ SV49 ) )
| ~ ( function @ SV49 ) )
| ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(706,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV26 )
| ~ ( relation @ SV26 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(707,plain,
! [SV50: $i,SV27: $i] :
( ( ~ ~ ( ~ ( subset @ SV27 @ SV50 )
| ~ ( finite @ SV50 ) )
| ( finite @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(708,plain,
( ( ~ ~ ( ~ ( empty @ sK9_SX0 )
| ~ ( relation @ sK9_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[661]) ).
thf(709,plain,
! [SV28: $i] :
( ( ( ( relation_dom @ ( identity_relation @ SV28 ) )
!= SV28 )
| ( ( relation_rng @ ( identity_relation @ SV28 ) )
!= SV28 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(710,plain,
! [SV51: $i,SV29: $i] :
( ( ~ ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ( relation_of2 @ SY92 @ SV29 @ SV51 )
| ~ ( relation @ SY92 ) )
| ~ ( function @ SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(711,plain,
! [SV52: $i,SV30: $i] :
( ( ~ ~ ( ~ ( relation @ SV30 )
| ~ ( function @ SV30 ) )
| ~ ( ~ ( relation @ ( relation_dom_restriction @ SV30 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV30 @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(712,plain,
! [SV53: $i,SV31: $i] :
( ( ~ ~ ( ~ ( relation @ SV31 )
| ~ ( relation @ SV53 ) )
| ( relation @ ( set_union2 @ SV31 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(713,plain,
! [SV54: $i,SV32: $i] :
( ( ~ ~ ( ~ ( relation @ SV32 )
| ~ ( relation @ SV54 ) )
| ( relation @ ( set_intersection2 @ SV32 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(714,plain,
! [SV55: $i,SV33: $i] :
( ( ~ ( finite @ SV33 )
| ( finite @ ( set_difference @ SV33 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(715,plain,
! [SV34: $i] :
( ( ( ~ ( relation @ SV34 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV34 ) )
= SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[668]) ).
thf(716,plain,
! [SV56: $i,SV35: $i] :
( ( ~ ~ ( ~ ( finite @ SV35 )
| ~ ( finite @ SV56 ) )
| ( finite @ ( set_union2 @ SV35 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(717,plain,
! [SV36: $i] :
( ( ( ~ ( empty @ SV36 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV36 ) )
| ~ ( relation @ ( relation_dom @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(718,plain,
! [SV57: $i,SV37: $i] :
( ( ~ ( finite @ SV37 )
| ( finite @ ( set_intersection2 @ SV37 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(719,plain,
! [SV38: $i] :
( ( ( ~ ( empty @ SV38 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV38 ) )
| ~ ( relation @ ( relation_rng @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(720,plain,
! [SV39: $i,SV58: $i] :
( ( ~ ~ ( ~ ( relation @ SV58 )
| ~ ( function @ SV58 ) )
| ~ ( ~ ( relation @ ( relation_rng_restriction @ SV39 @ SV58 ) )
| ~ ( function @ ( relation_rng_restriction @ SV39 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(721,plain,
! [SV3: $i] :
( ( ( relation @ SV3 )
= $false )
| ( ( ~ ( ( ( relation_dom @ SV3 )
= empty_set )
| ( ( relation_rng @ SV3 )
= empty_set ) )
| ( SV3 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(722,plain,
! [SV4: $i,SV40: $i] :
( ( ( ~ ( finite @ SV40 ) )
= $true )
| ( ( finite @ ( set_intersection2 @ SV4 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(723,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( function @ sK2_SX0 ) )
| ~ ( one_to_one @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[676]) ).
thf(724,plain,
( ( ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[677]) ).
thf(725,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( relation @ SV41 ) ) )
= $true )
| ( ( relation @ ( relation_composition @ SV5 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(726,plain,
! [SV6: $i] :
( ( ( empty @ SV6 )
= $false )
| ( ( relation @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(727,plain,
! [SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( ! [SY72: $i] :
( ~ ( relation @ SY72 )
| ~ ( subset @ SV7 @ SY72 )
| ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SY72 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SY72 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(728,plain,
! [SV42: $i,SV8: $i] :
( ( ( ~ ( finite @ SV8 ) )
= $true )
| ( ( finite @ ( set_intersection2 @ SV8 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(729,plain,
! [SV9: $i] :
( ( ( ~ ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV9 ) )
| ~ ( function @ ( function_inverse @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(730,plain,
! [SV43: $i,SV10: $i] :
( ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( relation @ ( relation_dom_restriction @ SV10 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(731,plain,
! [SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ~ ( ( ( relation_rng @ SV11 )
!= ( relation_dom @ ( relation_inverse @ SV11 ) ) )
| ( ( relation_dom @ SV11 )
!= ( relation_rng @ ( relation_inverse @ SV11 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(732,plain,
! [SV44: $i,SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( relation @ ( relation_restriction @ SV12 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(733,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( relation @ ( relation_inverse @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(734,plain,
! [SV14: $i,SV45: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV45 )
| ~ ( function @ SV45 ) ) )
= $true )
| ( ( ~ ( finite @ SV14 )
| ( finite @ ( relation_image @ SV45 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(735,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( function @ SV15 ) )
| ~ ( finite @ SV46 ) ) )
= $true )
| ( ( finite @ ( relation_image @ SV15 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(736,plain,
! [SV16: $i] :
( ( ~ ~ ( ~ ( relation @ ( sK10_SY78 @ SV16 ) )
| ~ ( well_orders @ ( sK10_SY78 @ SV16 ) @ SV16 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[689]) ).
thf(737,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[690]) ).
thf(738,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[691]) ).
thf(739,plain,
( ( ~ ( ~ ( relation @ sK4_SX0 )
| ~ ( relation_empty_yielding @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(740,plain,
! [SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( ~ ( ~ ( ( ( relation_dom @ SV17 )
!= empty_set )
| ( ( relation_rng @ SV17 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV17 )
!= empty_set )
| ( ( relation_dom @ SV17 )
= empty_set ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(741,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( empty @ sK5_SX0 ) )
| ~ ( function @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[694]) ).
thf(742,plain,
! [SV18: $i] :
( ( ~ ( relation @ ( identity_relation @ SV18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(743,plain,
! [SV18: $i] :
( ( ~ ( function @ ( identity_relation @ SV18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[695]) ).
thf(744,plain,
! [SV47: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( relation @ SV47 ) ) )
= $true )
| ( ( relation @ ( set_difference @ SV19 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(745,plain,
( ( ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[697]) ).
thf(746,plain,
( ( ~ ( ~ ~ ( empty @ sK7_SX0 )
| ~ ( finite @ sK7_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(747,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( relation_empty_yielding @ sK8_SX0 ) )
| ~ ( function @ sK8_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[699]) ).
thf(748,plain,
! [SV20: $i] :
( ( ( empty @ SV20 )
= $false )
| ( ( function @ SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(749,plain,
! [SV21: $i] :
( ( ( relation @ SV21 )
= $false )
| ( ( ( relation_image @ SV21 @ ( relation_dom @ SV21 ) )
= ( relation_rng @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(750,plain,
! [SV22: $i,SV48: $i] :
( ( ( ~ ( relation @ SV48 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV22 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(751,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV23 )
| ~ ( relation @ SV23 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(752,plain,
! [SV24: $i] :
( ( ( empty @ SV24 )
= $false )
| ( ( finite @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(753,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV25 )
| ~ ( function @ SV25 ) )
| ~ ( relation @ SV49 ) )
| ~ ( function @ SV49 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[705]) ).
thf(754,plain,
! [SV26: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV26 )
| ~ ( relation @ SV26 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(755,plain,
! [SV50: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV27 @ SV50 )
| ~ ( finite @ SV50 ) ) )
= $true )
| ( ( finite @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[707]) ).
thf(756,plain,
( ( ~ ( ~ ( empty @ sK9_SX0 )
| ~ ( relation @ sK9_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(757,plain,
! [SV28: $i] :
( ( ( relation_dom @ ( identity_relation @ SV28 ) )
!= SV28 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(758,plain,
! [SV28: $i] :
( ( ( relation_rng @ ( identity_relation @ SV28 ) )
!= SV28 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[709]) ).
thf(759,plain,
! [SV51: $i,SV29: $i] :
( ( ! [SY92: $i] :
~ ~ ( ~ ~ ( ~ ( relation_of2 @ SY92 @ SV29 @ SV51 )
| ~ ( relation @ SY92 ) )
| ~ ( function @ SY92 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(760,plain,
! [SV52: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV30 )
| ~ ( function @ SV30 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV30 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV30 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(761,plain,
! [SV53: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV31 )
| ~ ( relation @ SV53 ) ) )
= $true )
| ( ( relation @ ( set_union2 @ SV31 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(762,plain,
! [SV54: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV32 )
| ~ ( relation @ SV54 ) ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV32 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(763,plain,
! [SV55: $i,SV33: $i] :
( ( ( ~ ( finite @ SV33 ) )
= $true )
| ( ( finite @ ( set_difference @ SV33 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(764,plain,
! [SV34: $i] :
( ( ( relation @ SV34 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV34 ) )
= SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(765,plain,
! [SV56: $i,SV35: $i] :
( ( ( ~ ~ ( ~ ( finite @ SV35 )
| ~ ( finite @ SV56 ) ) )
= $true )
| ( ( finite @ ( set_union2 @ SV35 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(766,plain,
! [SV36: $i] :
( ( ( empty @ SV36 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV36 ) )
| ~ ( relation @ ( relation_dom @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(767,plain,
! [SV57: $i,SV37: $i] :
( ( ( ~ ( finite @ SV37 ) )
= $true )
| ( ( finite @ ( set_intersection2 @ SV37 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(768,plain,
! [SV38: $i] :
( ( ( empty @ SV38 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV38 ) )
| ~ ( relation @ ( relation_rng @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(769,plain,
! [SV39: $i,SV58: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV58 )
| ~ ( function @ SV58 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV39 @ SV58 ) )
| ~ ( function @ ( relation_rng_restriction @ SV39 @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(770,plain,
! [SV3: $i] :
( ( ( ~ ( ( ( relation_dom @ SV3 )
= empty_set )
| ( ( relation_rng @ SV3 )
= empty_set ) ) )
= $true )
| ( ( SV3 = empty_set )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(771,plain,
! [SV4: $i,SV40: $i] :
( ( ( finite @ SV40 )
= $false )
| ( ( finite @ ( set_intersection2 @ SV4 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(772,plain,
( ( ~ ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( function @ sK2_SX0 ) )
| ~ ( one_to_one @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(773,plain,
( ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(774,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ( ~ ( relation @ SV5 )
| ~ ( relation @ SV41 ) ) )
= $false )
| ( ( relation @ ( relation_composition @ SV5 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(775,plain,
! [SV7: $i,SV59: $i] :
( ( ( ~ ( relation @ SV59 )
| ~ ( subset @ SV7 @ SV59 )
| ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV59 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV59 ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(776,plain,
! [SV42: $i,SV8: $i] :
( ( ( finite @ SV8 )
= $false )
| ( ( finite @ ( set_intersection2 @ SV8 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(777,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ SV9 )
| ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV9 ) )
| ~ ( function @ ( function_inverse @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[729]) ).
thf(778,plain,
! [SV43: $i,SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( relation @ ( relation_dom_restriction @ SV10 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(779,plain,
! [SV11: $i] :
( ( ( ( ( relation_rng @ SV11 )
!= ( relation_dom @ ( relation_inverse @ SV11 ) ) )
| ( ( relation_dom @ SV11 )
!= ( relation_rng @ ( relation_inverse @ SV11 ) ) ) )
= $false )
| ( ( relation @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(780,plain,
! [SV44: $i,SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( relation @ ( relation_restriction @ SV12 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(781,plain,
! [SV14: $i,SV45: $i] :
( ( ( ~ ( ~ ( relation @ SV45 )
| ~ ( function @ SV45 ) ) )
= $false )
| ( ( ~ ( finite @ SV14 )
| ( finite @ ( relation_image @ SV45 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(782,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( function @ SV15 ) )
| ~ ( finite @ SV46 ) ) )
= $false )
| ( ( finite @ ( relation_image @ SV15 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(783,plain,
! [SV16: $i] :
( ( ~ ( ~ ( relation @ ( sK10_SY78 @ SV16 ) )
| ~ ( well_orders @ ( sK10_SY78 @ SV16 ) @ SV16 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[736]) ).
thf(784,plain,
( ( ~ ( relation @ sK4_SX0 )
| ~ ( relation_empty_yielding @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(785,plain,
! [SV17: $i] :
( ( ( ~ ( ( ( relation_dom @ SV17 )
!= empty_set )
| ( ( relation_rng @ SV17 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV17 )
!= empty_set )
| ( ( relation_dom @ SV17 )
= empty_set ) ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(786,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( empty @ sK5_SX0 ) )
| ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(787,plain,
! [SV18: $i] :
( ( relation @ ( identity_relation @ SV18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[742]) ).
thf(788,plain,
! [SV18: $i] :
( ( function @ ( identity_relation @ SV18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[743]) ).
thf(789,plain,
! [SV47: $i,SV19: $i] :
( ( ( ~ ( ~ ( relation @ SV19 )
| ~ ( relation @ SV47 ) ) )
= $false )
| ( ( relation @ ( set_difference @ SV19 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(790,plain,
( ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(791,plain,
( ( ~ ~ ( empty @ sK7_SX0 )
| ~ ( finite @ sK7_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(792,plain,
( ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( relation_empty_yielding @ sK8_SX0 ) )
| ~ ( function @ sK8_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(793,plain,
! [SV22: $i,SV48: $i] :
( ( ( relation @ SV48 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV22 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(794,plain,
! [SV23: $i] :
( ( ( ~ ~ ( empty @ SV23 )
| ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[751]) ).
thf(795,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV25 )
| ~ ( function @ SV25 ) )
| ~ ( relation @ SV49 ) )
| ~ ( function @ SV49 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(796,plain,
! [SV26: $i] :
( ( ( ~ ~ ( empty @ SV26 )
| ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[754]) ).
thf(797,plain,
! [SV50: $i,SV27: $i] :
( ( ( ~ ( ~ ( subset @ SV27 @ SV50 )
| ~ ( finite @ SV50 ) ) )
= $false )
| ( ( finite @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(798,plain,
( ( ~ ( empty @ sK9_SX0 )
| ~ ( relation @ sK9_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(799,plain,
! [SV28: $i] :
( ( ( relation_dom @ ( identity_relation @ SV28 ) )
= SV28 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[757]) ).
thf(800,plain,
! [SV28: $i] :
( ( ( relation_rng @ ( identity_relation @ SV28 ) )
= SV28 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[758]) ).
thf(801,plain,
! [SV29: $i,SV51: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation_of2 @ ( sK11_SY92 @ SV51 @ SV29 ) @ SV29 @ SV51 )
| ~ ( relation @ ( sK11_SY92 @ SV51 @ SV29 ) ) )
| ~ ( function @ ( sK11_SY92 @ SV51 @ SV29 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[759]) ).
thf(802,plain,
! [SV52: $i,SV30: $i] :
( ( ( ~ ( ~ ( relation @ SV30 )
| ~ ( function @ SV30 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV30 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV30 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(803,plain,
! [SV53: $i,SV31: $i] :
( ( ( ~ ( ~ ( relation @ SV31 )
| ~ ( relation @ SV53 ) ) )
= $false )
| ( ( relation @ ( set_union2 @ SV31 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(804,plain,
! [SV54: $i,SV32: $i] :
( ( ( ~ ( ~ ( relation @ SV32 )
| ~ ( relation @ SV54 ) ) )
= $false )
| ( ( relation @ ( set_intersection2 @ SV32 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(805,plain,
! [SV55: $i,SV33: $i] :
( ( ( finite @ SV33 )
= $false )
| ( ( finite @ ( set_difference @ SV33 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(806,plain,
! [SV56: $i,SV35: $i] :
( ( ( ~ ( ~ ( finite @ SV35 )
| ~ ( finite @ SV56 ) ) )
= $false )
| ( ( finite @ ( set_union2 @ SV35 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(807,plain,
! [SV36: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV36 ) )
| ~ ( relation @ ( relation_dom @ SV36 ) ) )
= $false )
| ( ( empty @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(808,plain,
! [SV57: $i,SV37: $i] :
( ( ( finite @ SV37 )
= $false )
| ( ( finite @ ( set_intersection2 @ SV37 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[767]) ).
thf(809,plain,
! [SV38: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV38 ) )
| ~ ( relation @ ( relation_rng @ SV38 ) ) )
= $false )
| ( ( empty @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(810,plain,
! [SV39: $i,SV58: $i] :
( ( ( ~ ( ~ ( relation @ SV58 )
| ~ ( function @ SV58 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV39 @ SV58 ) )
| ~ ( function @ ( relation_rng_restriction @ SV39 @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[769]) ).
thf(811,plain,
! [SV3: $i] :
( ( ( ( ( relation_dom @ SV3 )
= empty_set )
| ( ( relation_rng @ SV3 )
= empty_set ) )
= $false )
| ( ( SV3 = empty_set )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[770]) ).
thf(812,plain,
( ( ~ ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( function @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(813,plain,
( ( ~ ( one_to_one @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[772]) ).
thf(814,plain,
( ( ~ ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(815,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[773]) ).
thf(816,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ( relation @ SV5 )
| ~ ( relation @ SV41 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV5 @ SV41 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[774]) ).
thf(817,plain,
! [SV7: $i,SV59: $i] :
( ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( ~ ( subset @ SV7 @ SV59 )
| ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV59 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV59 ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(818,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV9 ) )
| ~ ( function @ ( function_inverse @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(819,plain,
! [SV11: $i] :
( ( ( ( relation_rng @ SV11 )
!= ( relation_dom @ ( relation_inverse @ SV11 ) ) )
= $false )
| ( ( relation @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[779]) ).
thf(820,plain,
! [SV11: $i] :
( ( ( ( relation_dom @ SV11 )
!= ( relation_rng @ ( relation_inverse @ SV11 ) ) )
= $false )
| ( ( relation @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[779]) ).
thf(821,plain,
! [SV14: $i,SV45: $i] :
( ( ( ~ ( relation @ SV45 )
| ~ ( function @ SV45 ) )
= $true )
| ( ( ~ ( finite @ SV14 )
| ( finite @ ( relation_image @ SV45 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(822,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( function @ SV15 ) )
| ~ ( finite @ SV46 ) )
= $true )
| ( ( finite @ ( relation_image @ SV15 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(823,plain,
! [SV16: $i] :
( ( ~ ( relation @ ( sK10_SY78 @ SV16 ) )
| ~ ( well_orders @ ( sK10_SY78 @ SV16 ) @ SV16 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[783]) ).
thf(824,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(825,plain,
( ( ~ ( relation_empty_yielding @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[784]) ).
thf(826,plain,
! [SV17: $i] :
( ( ( ~ ( ( ( relation_dom @ SV17 )
!= empty_set )
| ( ( relation_rng @ SV17 )
= empty_set ) ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(827,plain,
! [SV17: $i] :
( ( ( ~ ( ( ( relation_rng @ SV17 )
!= empty_set )
| ( ( relation_dom @ SV17 )
= empty_set ) ) )
= $false )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[785]) ).
thf(828,plain,
( ( ~ ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( empty @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(829,plain,
( ( ~ ( function @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(830,plain,
! [SV47: $i,SV19: $i] :
( ( ( ~ ( relation @ SV19 )
| ~ ( relation @ SV47 ) )
= $true )
| ( ( relation @ ( set_difference @ SV19 @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(831,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[790]) ).
thf(832,plain,
( ( ~ ( function @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[790]) ).
thf(833,plain,
( ( ~ ~ ( empty @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(834,plain,
( ( ~ ( finite @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(835,plain,
( ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( relation_empty_yielding @ sK8_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[792]) ).
thf(836,plain,
( ( ~ ( function @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[792]) ).
thf(837,plain,
! [SV23: $i] :
( ( ( ~ ~ ( empty @ SV23 ) )
= $true )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(838,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV25 )
| ~ ( function @ SV25 ) )
| ~ ( relation @ SV49 ) )
| ~ ( function @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(839,plain,
! [SV26: $i] :
( ( ( ~ ~ ( empty @ SV26 ) )
= $true )
| ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(840,plain,
! [SV50: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ SV50 )
| ~ ( finite @ SV50 ) )
= $true )
| ( ( finite @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(841,plain,
( ( ~ ( empty @ sK9_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(842,plain,
( ( ~ ( relation @ sK9_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(843,plain,
! [SV29: $i,SV51: $i] :
( ( ~ ( ~ ~ ( ~ ( relation_of2 @ ( sK11_SY92 @ SV51 @ SV29 ) @ SV29 @ SV51 )
| ~ ( relation @ ( sK11_SY92 @ SV51 @ SV29 ) ) )
| ~ ( function @ ( sK11_SY92 @ SV51 @ SV29 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[801]) ).
thf(844,plain,
! [SV52: $i,SV30: $i] :
( ( ( ~ ( relation @ SV30 )
| ~ ( function @ SV30 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV30 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV30 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[802]) ).
thf(845,plain,
! [SV53: $i,SV31: $i] :
( ( ( ~ ( relation @ SV31 )
| ~ ( relation @ SV53 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV31 @ SV53 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[803]) ).
thf(846,plain,
! [SV54: $i,SV32: $i] :
( ( ( ~ ( relation @ SV32 )
| ~ ( relation @ SV54 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV32 @ SV54 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[804]) ).
thf(847,plain,
! [SV56: $i,SV35: $i] :
( ( ( ~ ( finite @ SV35 )
| ~ ( finite @ SV56 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV35 @ SV56 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(848,plain,
! [SV36: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV36 ) ) )
= $false )
| ( ( empty @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[807]) ).
thf(849,plain,
! [SV36: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV36 ) ) )
= $false )
| ( ( empty @ SV36 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[807]) ).
thf(850,plain,
! [SV38: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV38 ) ) )
= $false )
| ( ( empty @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(851,plain,
! [SV38: $i] :
( ( ( ~ ( relation @ ( relation_rng @ SV38 ) ) )
= $false )
| ( ( empty @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[809]) ).
thf(852,plain,
! [SV39: $i,SV58: $i] :
( ( ( ~ ( relation @ SV58 )
| ~ ( function @ SV58 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV39 @ SV58 ) )
| ~ ( function @ ( relation_rng_restriction @ SV39 @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(853,plain,
! [SV3: $i] :
( ( ( ( relation_dom @ SV3 )
= empty_set )
= $false )
| ( ( SV3 = empty_set )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[811]) ).
thf(854,plain,
! [SV3: $i] :
( ( ( ( relation_rng @ SV3 )
= empty_set )
= $false )
| ( ( SV3 = empty_set )
= $true )
| ( ( relation @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[811]) ).
thf(855,plain,
( ( ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( function @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[812]) ).
thf(856,plain,
( ( one_to_one @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[813]) ).
thf(857,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[814]) ).
thf(858,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(859,plain,
! [SV41: $i,SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ~ ( relation @ SV41 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV5 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(860,plain,
! [SV7: $i,SV59: $i] :
( ( ( relation @ SV59 )
= $false )
| ( ( ~ ( subset @ SV7 @ SV59 )
| ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV59 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV59 ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(861,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( ~ ( function @ SV9 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV9 ) )
| ~ ( function @ ( function_inverse @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[818]) ).
thf(862,plain,
! [SV11: $i] :
( ( ( ( relation_rng @ SV11 )
= ( relation_dom @ ( relation_inverse @ SV11 ) ) )
= $true )
| ( ( relation @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[819]) ).
thf(863,plain,
! [SV11: $i] :
( ( ( ( relation_dom @ SV11 )
= ( relation_rng @ ( relation_inverse @ SV11 ) ) )
= $true )
| ( ( relation @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[820]) ).
thf(864,plain,
! [SV14: $i,SV45: $i] :
( ( ( ~ ( relation @ SV45 ) )
= $true )
| ( ( ~ ( function @ SV45 ) )
= $true )
| ( ( ~ ( finite @ SV14 )
| ( finite @ ( relation_image @ SV45 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(865,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( function @ SV15 ) ) )
= $true )
| ( ( ~ ( finite @ SV46 ) )
= $true )
| ( ( finite @ ( relation_image @ SV15 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[822]) ).
thf(866,plain,
! [SV16: $i] :
( ( ~ ( relation @ ( sK10_SY78 @ SV16 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[823]) ).
thf(867,plain,
! [SV16: $i] :
( ( ~ ( well_orders @ ( sK10_SY78 @ SV16 ) @ SV16 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[823]) ).
thf(868,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(869,plain,
( ( relation_empty_yielding @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[825]) ).
thf(870,plain,
! [SV17: $i] :
( ( ( ( ( relation_dom @ SV17 )
!= empty_set )
| ( ( relation_rng @ SV17 )
= empty_set ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(871,plain,
! [SV17: $i] :
( ( ( ( ( relation_rng @ SV17 )
!= empty_set )
| ( ( relation_dom @ SV17 )
= empty_set ) )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(872,plain,
( ( ~ ( ~ ( relation @ sK5_SX0 )
| ~ ( empty @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(873,plain,
( ( function @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(874,plain,
! [SV47: $i,SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ~ ( relation @ SV47 ) )
= $true )
| ( ( relation @ ( set_difference @ SV19 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[830]) ).
thf(875,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[831]) ).
thf(876,plain,
( ( function @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[832]) ).
thf(877,plain,
( ( ~ ( empty @ sK7_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[833]) ).
thf(878,plain,
( ( finite @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[834]) ).
thf(879,plain,
( ( ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( relation_empty_yielding @ sK8_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(880,plain,
( ( function @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(881,plain,
! [SV23: $i] :
( ( ( ~ ( empty @ SV23 ) )
= $false )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(882,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV25 )
| ~ ( function @ SV25 ) )
| ~ ( relation @ SV49 ) ) )
= $true )
| ( ( ~ ( function @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(883,plain,
! [SV26: $i] :
( ( ( ~ ( empty @ SV26 ) )
= $false )
| ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(884,plain,
! [SV50: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ SV50 ) )
= $true )
| ( ( ~ ( finite @ SV50 ) )
= $true )
| ( ( finite @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(885,plain,
( ( empty @ sK9_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[841]) ).
thf(886,plain,
( ( relation @ sK9_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[842]) ).
thf(887,plain,
! [SV29: $i,SV51: $i] :
( ( ~ ~ ( ~ ( relation_of2 @ ( sK11_SY92 @ SV51 @ SV29 ) @ SV29 @ SV51 )
| ~ ( relation @ ( sK11_SY92 @ SV51 @ SV29 ) ) )
| ~ ( function @ ( sK11_SY92 @ SV51 @ SV29 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[843]) ).
thf(888,plain,
! [SV52: $i,SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ~ ( function @ SV30 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV30 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV30 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(889,plain,
! [SV53: $i,SV31: $i] :
( ( ( ~ ( relation @ SV31 ) )
= $true )
| ( ( ~ ( relation @ SV53 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV31 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(890,plain,
! [SV54: $i,SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV32 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(891,plain,
! [SV56: $i,SV35: $i] :
( ( ( ~ ( finite @ SV35 ) )
= $true )
| ( ( ~ ( finite @ SV56 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV35 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(892,plain,
! [SV36: $i] :
( ( ( empty @ ( relation_dom @ SV36 ) )
= $true )
| ( ( empty @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[848]) ).
thf(893,plain,
! [SV36: $i] :
( ( ( relation @ ( relation_dom @ SV36 ) )
= $true )
| ( ( empty @ SV36 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[849]) ).
thf(894,plain,
! [SV38: $i] :
( ( ( empty @ ( relation_rng @ SV38 ) )
= $true )
| ( ( empty @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(895,plain,
! [SV38: $i] :
( ( ( relation @ ( relation_rng @ SV38 ) )
= $true )
| ( ( empty @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(896,plain,
! [SV39: $i,SV58: $i] :
( ( ( ~ ( relation @ SV58 ) )
= $true )
| ( ( ~ ( function @ SV58 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV39 @ SV58 ) )
| ~ ( function @ ( relation_rng_restriction @ SV39 @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(897,plain,
( ( ~ ( relation @ sK2_SX0 )
| ~ ( function @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(898,plain,
( ( empty @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(899,plain,
! [SV41: $i,SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( ~ ( relation @ SV41 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV5 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(900,plain,
! [SV59: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV59 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV59 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV59 ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(901,plain,
! [SV9: $i] :
( ( ( function @ SV9 )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV9 ) )
| ~ ( function @ ( function_inverse @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[861]) ).
thf(902,plain,
! [SV14: $i,SV45: $i] :
( ( ( relation @ SV45 )
= $false )
| ( ( ~ ( function @ SV45 ) )
= $true )
| ( ( ~ ( finite @ SV14 )
| ( finite @ ( relation_image @ SV45 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(903,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ( ~ ( relation @ SV15 )
| ~ ( function @ SV15 ) ) )
= $false )
| ( ( ~ ( finite @ SV46 ) )
= $true )
| ( ( finite @ ( relation_image @ SV15 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(904,plain,
! [SV16: $i] :
( ( relation @ ( sK10_SY78 @ SV16 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[866]) ).
thf(905,plain,
! [SV16: $i] :
( ( well_orders @ ( sK10_SY78 @ SV16 ) @ SV16 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[867]) ).
thf(906,plain,
! [SV17: $i] :
( ( ( ( relation_dom @ SV17 )
!= empty_set )
= $true )
| ( ( ( relation_rng @ SV17 )
= empty_set )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(907,plain,
! [SV17: $i] :
( ( ( ( relation_rng @ SV17 )
!= empty_set )
= $true )
| ( ( ( relation_dom @ SV17 )
= empty_set )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(908,plain,
( ( ~ ( relation @ sK5_SX0 )
| ~ ( empty @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(909,plain,
! [SV47: $i,SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( ~ ( relation @ SV47 ) )
= $true )
| ( ( relation @ ( set_difference @ SV19 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(910,plain,
( ( empty @ sK7_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(911,plain,
( ( ~ ( relation @ sK8_SX0 )
| ~ ( relation_empty_yielding @ sK8_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(912,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
= $true )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[881]) ).
thf(913,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV25 )
| ~ ( function @ SV25 ) )
| ~ ( relation @ SV49 ) ) )
= $false )
| ( ( ~ ( function @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(914,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
= $true )
| ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[883]) ).
thf(915,plain,
! [SV50: $i,SV27: $i] :
( ( ( subset @ SV27 @ SV50 )
= $false )
| ( ( ~ ( finite @ SV50 ) )
= $true )
| ( ( finite @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(916,plain,
! [SV29: $i,SV51: $i] :
( ( ~ ~ ( ~ ( relation_of2 @ ( sK11_SY92 @ SV51 @ SV29 ) @ SV29 @ SV51 )
| ~ ( relation @ ( sK11_SY92 @ SV51 @ SV29 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[887]) ).
thf(917,plain,
! [SV29: $i,SV51: $i] :
( ( ~ ( function @ ( sK11_SY92 @ SV51 @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[887]) ).
thf(918,plain,
! [SV52: $i,SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ~ ( function @ SV30 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV30 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV30 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(919,plain,
! [SV53: $i,SV31: $i] :
( ( ( relation @ SV31 )
= $false )
| ( ( ~ ( relation @ SV53 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV31 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(920,plain,
! [SV54: $i,SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV32 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(921,plain,
! [SV56: $i,SV35: $i] :
( ( ( finite @ SV35 )
= $false )
| ( ( ~ ( finite @ SV56 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV35 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[891]) ).
thf(922,plain,
! [SV39: $i,SV58: $i] :
( ( ( relation @ SV58 )
= $false )
| ( ( ~ ( function @ SV58 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV39 @ SV58 ) )
| ~ ( function @ ( relation_rng_restriction @ SV39 @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(923,plain,
( ( ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(924,plain,
( ( ~ ( function @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[897]) ).
thf(925,plain,
! [SV5: $i,SV41: $i] :
( ( ( relation @ SV41 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( relation @ ( relation_composition @ SV5 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(926,plain,
! [SV59: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV59 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV59 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV59 ) ) ) )
= $true )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(927,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ ( function_inverse @ SV9 ) )
| ~ ( function @ ( function_inverse @ SV9 ) ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(928,plain,
! [SV14: $i,SV45: $i] :
( ( ( function @ SV45 )
= $false )
| ( ( relation @ SV45 )
= $false )
| ( ( ~ ( finite @ SV14 )
| ( finite @ ( relation_image @ SV45 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(929,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ( relation @ SV15 )
| ~ ( function @ SV15 ) )
= $true )
| ( ( ~ ( finite @ SV46 ) )
= $true )
| ( ( finite @ ( relation_image @ SV15 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(930,plain,
! [SV17: $i] :
( ( ( ( relation_dom @ SV17 )
= empty_set )
= $false )
| ( ( ( relation_rng @ SV17 )
= empty_set )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(931,plain,
! [SV17: $i] :
( ( ( ( relation_rng @ SV17 )
= empty_set )
= $false )
| ( ( ( relation_dom @ SV17 )
= empty_set )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[907]) ).
thf(932,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(933,plain,
( ( ~ ( empty @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[908]) ).
thf(934,plain,
! [SV19: $i,SV47: $i] :
( ( ( relation @ SV47 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( relation @ ( set_difference @ SV19 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(935,plain,
( ( ~ ( relation @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(936,plain,
( ( ~ ( relation_empty_yielding @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[911]) ).
thf(937,plain,
! [SV23: $i] :
( ( ( relation @ SV23 )
= $false )
| ( ( empty @ SV23 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(938,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV25 )
| ~ ( function @ SV25 ) )
| ~ ( relation @ SV49 ) )
= $true )
| ( ( ~ ( function @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(939,plain,
! [SV26: $i] :
( ( ( relation @ SV26 )
= $false )
| ( ( empty @ SV26 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(940,plain,
! [SV27: $i,SV50: $i] :
( ( ( finite @ SV50 )
= $false )
| ( ( subset @ SV27 @ SV50 )
= $false )
| ( ( finite @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(941,plain,
! [SV29: $i,SV51: $i] :
( ( ~ ( ~ ( relation_of2 @ ( sK11_SY92 @ SV51 @ SV29 ) @ SV29 @ SV51 )
| ~ ( relation @ ( sK11_SY92 @ SV51 @ SV29 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[916]) ).
thf(942,plain,
! [SV29: $i,SV51: $i] :
( ( function @ ( sK11_SY92 @ SV51 @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[917]) ).
thf(943,plain,
! [SV52: $i,SV30: $i] :
( ( ( function @ SV30 )
= $false )
| ( ( relation @ SV30 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_dom_restriction @ SV30 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV30 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(944,plain,
! [SV31: $i,SV53: $i] :
( ( ( relation @ SV53 )
= $false )
| ( ( relation @ SV31 )
= $false )
| ( ( relation @ ( set_union2 @ SV31 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(945,plain,
! [SV32: $i,SV54: $i] :
( ( ( relation @ SV54 )
= $false )
| ( ( relation @ SV32 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV32 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(946,plain,
! [SV35: $i,SV56: $i] :
( ( ( finite @ SV56 )
= $false )
| ( ( finite @ SV35 )
= $false )
| ( ( finite @ ( set_union2 @ SV35 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(947,plain,
! [SV39: $i,SV58: $i] :
( ( ( function @ SV58 )
= $false )
| ( ( relation @ SV58 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_rng_restriction @ SV39 @ SV58 ) )
| ~ ( function @ ( relation_rng_restriction @ SV39 @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(948,plain,
( ( relation @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[923]) ).
thf(949,plain,
( ( function @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[924]) ).
thf(950,plain,
! [SV59: $i,SV7: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV59 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV59 ) ) )
= $false )
| ( ( subset @ SV7 @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[926]) ).
thf(951,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ ( function_inverse @ SV9 ) ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(952,plain,
! [SV9: $i] :
( ( ( ~ ( function @ ( function_inverse @ SV9 ) ) )
= $false )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[927]) ).
thf(953,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( finite @ SV14 ) )
= $true )
| ( ( finite @ ( relation_image @ SV45 @ SV14 ) )
= $true )
| ( ( relation @ SV45 )
= $false )
| ( ( function @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(954,plain,
! [SV46: $i,SV15: $i] :
( ( ( ~ ( relation @ SV15 ) )
= $true )
| ( ( ~ ( function @ SV15 ) )
= $true )
| ( ( ~ ( finite @ SV46 ) )
= $true )
| ( ( finite @ ( relation_image @ SV15 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[929]) ).
thf(955,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(956,plain,
( ( empty @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[933]) ).
thf(957,plain,
( ( relation @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[935]) ).
thf(958,plain,
( ( relation_empty_yielding @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[936]) ).
thf(959,plain,
! [SV23: $i] :
( ( ( empty @ ( relation_rng @ SV23 ) )
= $false )
| ( ( empty @ SV23 )
= $true )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(960,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV25 )
| ~ ( function @ SV25 ) ) )
= $true )
| ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( ~ ( function @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(961,plain,
! [SV26: $i] :
( ( ( empty @ ( relation_dom @ SV26 ) )
= $false )
| ( ( empty @ SV26 )
= $true )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(962,plain,
! [SV29: $i,SV51: $i] :
( ( ~ ( relation_of2 @ ( sK11_SY92 @ SV51 @ SV29 ) @ SV29 @ SV51 )
| ~ ( relation @ ( sK11_SY92 @ SV51 @ SV29 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(963,plain,
! [SV52: $i,SV30: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV30 @ SV52 ) )
| ~ ( function @ ( relation_dom_restriction @ SV30 @ SV52 ) ) )
= $false )
| ( ( relation @ SV30 )
= $false )
| ( ( function @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(964,plain,
! [SV58: $i,SV39: $i] :
( ( ( ~ ( relation @ ( relation_rng_restriction @ SV39 @ SV58 ) )
| ~ ( function @ ( relation_rng_restriction @ SV39 @ SV58 ) ) )
= $false )
| ( ( relation @ SV58 )
= $false )
| ( ( function @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(965,plain,
! [SV59: $i,SV7: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV59 ) ) )
= $false )
| ( ( subset @ SV7 @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(966,plain,
! [SV59: $i,SV7: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV59 ) ) )
= $false )
| ( ( subset @ SV7 @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[950]) ).
thf(967,plain,
! [SV9: $i] :
( ( ( relation @ ( function_inverse @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[951]) ).
thf(968,plain,
! [SV9: $i] :
( ( ( function @ ( function_inverse @ SV9 ) )
= $true )
| ( ( relation @ SV9 )
= $false )
| ( ( function @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[952]) ).
thf(969,plain,
! [SV45: $i,SV14: $i] :
( ( ( finite @ SV14 )
= $false )
| ( ( finite @ ( relation_image @ SV45 @ SV14 ) )
= $true )
| ( ( relation @ SV45 )
= $false )
| ( ( function @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(970,plain,
! [SV46: $i,SV15: $i] :
( ( ( relation @ SV15 )
= $false )
| ( ( ~ ( function @ SV15 ) )
= $true )
| ( ( ~ ( finite @ SV46 ) )
= $true )
| ( ( finite @ ( relation_image @ SV15 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(971,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ( ~ ( relation @ SV25 )
| ~ ( function @ SV25 ) ) )
= $false )
| ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( ~ ( function @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(972,plain,
! [SV29: $i,SV51: $i] :
( ( ~ ( relation_of2 @ ( sK11_SY92 @ SV51 @ SV29 ) @ SV29 @ SV51 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(973,plain,
! [SV29: $i,SV51: $i] :
( ( ~ ( relation @ ( sK11_SY92 @ SV51 @ SV29 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[962]) ).
thf(974,plain,
! [SV52: $i,SV30: $i] :
( ( ( ~ ( relation @ ( relation_dom_restriction @ SV30 @ SV52 ) ) )
= $false )
| ( ( relation @ SV30 )
= $false )
| ( ( function @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(975,plain,
! [SV52: $i,SV30: $i] :
( ( ( ~ ( function @ ( relation_dom_restriction @ SV30 @ SV52 ) ) )
= $false )
| ( ( relation @ SV30 )
= $false )
| ( ( function @ SV30 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(976,plain,
! [SV58: $i,SV39: $i] :
( ( ( ~ ( relation @ ( relation_rng_restriction @ SV39 @ SV58 ) ) )
= $false )
| ( ( relation @ SV58 )
= $false )
| ( ( function @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(977,plain,
! [SV58: $i,SV39: $i] :
( ( ( ~ ( function @ ( relation_rng_restriction @ SV39 @ SV58 ) ) )
= $false )
| ( ( relation @ SV58 )
= $false )
| ( ( function @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[964]) ).
thf(978,plain,
! [SV59: $i,SV7: $i] :
( ( ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV59 ) )
= $true )
| ( ( subset @ SV7 @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[965]) ).
thf(979,plain,
! [SV59: $i,SV7: $i] :
( ( ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV59 ) )
= $true )
| ( ( subset @ SV7 @ SV59 )
= $false )
| ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[966]) ).
thf(980,plain,
! [SV46: $i,SV15: $i] :
( ( ( function @ SV15 )
= $false )
| ( ( relation @ SV15 )
= $false )
| ( ( ~ ( finite @ SV46 ) )
= $true )
| ( ( finite @ ( relation_image @ SV15 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(981,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ( relation @ SV25 )
| ~ ( function @ SV25 ) )
= $true )
| ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( ~ ( function @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[971]) ).
thf(982,plain,
! [SV29: $i,SV51: $i] :
( ( relation_of2 @ ( sK11_SY92 @ SV51 @ SV29 ) @ SV29 @ SV51 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(983,plain,
! [SV29: $i,SV51: $i] :
( ( relation @ ( sK11_SY92 @ SV51 @ SV29 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(984,plain,
! [SV52: $i,SV30: $i] :
( ( ( relation @ ( relation_dom_restriction @ SV30 @ SV52 ) )
= $true )
| ( ( relation @ SV30 )
= $false )
| ( ( function @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[974]) ).
thf(985,plain,
! [SV52: $i,SV30: $i] :
( ( ( function @ ( relation_dom_restriction @ SV30 @ SV52 ) )
= $true )
| ( ( relation @ SV30 )
= $false )
| ( ( function @ SV30 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[975]) ).
thf(986,plain,
! [SV58: $i,SV39: $i] :
( ( ( relation @ ( relation_rng_restriction @ SV39 @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false )
| ( ( function @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[976]) ).
thf(987,plain,
! [SV58: $i,SV39: $i] :
( ( ( function @ ( relation_rng_restriction @ SV39 @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $false )
| ( ( function @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[977]) ).
thf(988,plain,
! [SV15: $i,SV46: $i] :
( ( ( finite @ SV46 )
= $false )
| ( ( relation @ SV15 )
= $false )
| ( ( function @ SV15 )
= $false )
| ( ( finite @ ( relation_image @ SV15 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(989,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ( relation @ SV25 ) )
= $true )
| ( ( ~ ( function @ SV25 ) )
= $true )
| ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( ~ ( function @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(990,plain,
! [SV49: $i,SV25: $i] :
( ( ( relation @ SV25 )
= $false )
| ( ( ~ ( function @ SV25 ) )
= $true )
| ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( ~ ( function @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(991,plain,
! [SV49: $i,SV25: $i] :
( ( ( function @ SV25 )
= $false )
| ( ( relation @ SV25 )
= $false )
| ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( ~ ( function @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(992,plain,
! [SV25: $i,SV49: $i] :
( ( ( relation @ SV49 )
= $false )
| ( ( relation @ SV25 )
= $false )
| ( ( function @ SV25 )
= $false )
| ( ( ~ ( function @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(993,plain,
! [SV25: $i,SV49: $i] :
( ( ( function @ SV49 )
= $false )
| ( ( function @ SV25 )
= $false )
| ( ( relation @ SV25 )
= $false )
| ( ( relation @ SV49 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(994,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) )
| ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) )
= $false )
| ( ( relation @ SV49 )
= $false )
| ( ( relation @ SV25 )
= $false )
| ( ( function @ SV25 )
= $false )
| ( ( function @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(995,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ( relation @ ( relation_composition @ SV25 @ SV49 ) ) )
= $false )
| ( ( relation @ SV49 )
= $false )
| ( ( relation @ SV25 )
= $false )
| ( ( function @ SV25 )
= $false )
| ( ( function @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(996,plain,
! [SV49: $i,SV25: $i] :
( ( ( ~ ( function @ ( relation_composition @ SV25 @ SV49 ) ) )
= $false )
| ( ( relation @ SV49 )
= $false )
| ( ( relation @ SV25 )
= $false )
| ( ( function @ SV25 )
= $false )
| ( ( function @ SV49 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[994]) ).
thf(997,plain,
! [SV49: $i,SV25: $i] :
( ( ( relation @ ( relation_composition @ SV25 @ SV49 ) )
= $true )
| ( ( relation @ SV49 )
= $false )
| ( ( relation @ SV25 )
= $false )
| ( ( function @ SV25 )
= $false )
| ( ( function @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[995]) ).
thf(998,plain,
! [SV49: $i,SV25: $i] :
( ( ( function @ ( relation_composition @ SV25 @ SV49 ) )
= $true )
| ( ( relation @ SV49 )
= $false )
| ( ( relation @ SV25 )
= $false )
| ( ( function @ SV25 )
= $false )
| ( ( function @ SV49 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[996]) ).
thf(999,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[516,998,997,988,987,986,985,984,983,982,979,978,969,968,967,961,959,958,957,956,955,949,948,946,945,944,942,940,934,931,930,925,910,905,904,898,895,894,893,892,886,885,880,878,876,875,873,869,868,863,862,858,856,854,853,808,805,800,799,793,788,787,780,778,776,771,764,752,749,748,738,737,733,726,627,626,625,577,576,575,548,547,546,541,540,539,537,536,535,534,533,531,530,529,527,526,524,523,522,521,520,519,518,517]) ).
thf(1000,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[999]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU303+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n006.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 15:12:37 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.36/1.42 ...
% 7.36/1.42
% 7.36/1.42 No.of.Axioms: 73
% 7.36/1.42
% 7.36/1.42 Length.of.Defs: 0
% 7.36/1.42
% 7.36/1.42 Contains.Choice.Funs: false
% 7.36/1.42 .................
% 7.36/1.42
% 7.36/1.42 ********************************
% 7.36/1.42 * All subproblems solved! *
% 7.36/1.42 ********************************
% 7.36/1.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:76,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:999,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.36/1.42
% 7.36/1.42 %**** Beginning of derivation protocol ****
% 7.36/1.42 % SZS output start CNFRefutation
% See solution above
% 7.36/1.42
% 7.36/1.42 %**** End of derivation protocol ****
% 7.36/1.42 %**** no. of clauses in derivation: 654 ****
% 7.36/1.42 %**** clause counter: 999 ****
% 7.36/1.42
% 7.36/1.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:76,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:999,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------