%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU219+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 : n012.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 10:43:30 AM UTC 2026
% Result : Theorem 1.38s 0.43s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 52
% Syntax : Number of formulae : 847 ( 472 unt; 0 typ; 0 def)
% Number of atoms : 5304 (1724 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 6982 (1994 ~;1324 |; 145 &;3399 @)
% ( 4 <=>; 116 =>; 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 : 56 ( 53 usr; 16 con; 0-3 aty)
% Number of variables : 805 ( 0 ^; 781 !; 24 ?; 805 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apply,type,
apply: $i > $i > $i ).
thf(tp_are_equipotent,type,
are_equipotent: $i > $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_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_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_meet_of_subsets,type,
meet_of_subsets: $i > $i > $i ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_composition,type,
relation_composition: $i > $i > $i ).
thf(tp_relation_dom,type,
relation_dom: $i > $i ).
thf(tp_relation_dom_restriction,type,
relation_dom_restriction: $i > $i > $i ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_field,type,
relation_field: $i > $i ).
thf(tp_relation_image,type,
relation_image: $i > $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_inverse_image,type,
relation_inverse_image: $i > $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK10_SX0,type,
sK10_SX0: $i ).
thf(tp_sK11_SX0,type,
sK11_SX0: $i ).
thf(tp_sK12_SX0,type,
sK12_SX0: $i ).
thf(tp_sK13_SX0,type,
sK13_SX0: $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_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(20,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(21,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(24,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(25,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(28,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(29,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(32,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(37,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(38,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(39,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(40,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(45,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) )
=> ( ( relation @ ( relation_inverse @ A ) )
& ( function @ ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_funct_1) ).
thf(48,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(49,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(53,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(54,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(59,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(60,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k9_relat_1) ).
thf(61,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(63,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(66,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(68,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(69,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(70,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(71,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(72,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(73,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(75,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(76,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(77,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(78,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(80,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(81,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(82,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(83,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(84,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(85,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(86,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(87,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_funct_1) ).
thf(88,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k10_relat_1) ).
thf(89,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_funct_1) ).
thf(126,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(127,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(128,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(145,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(149,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(150,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(153,axiom,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(178,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(188,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(203,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(231,conjecture,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
thf(232,negated_conjecture,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[231]) ).
thf(233,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( function_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( function_inverse @ A ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[232]) ).
thf(234,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(235,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(236,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(237,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(238,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(239,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(240,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(241,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(242,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(243,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(244,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(245,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) )
=> ( ( relation @ ( relation_inverse @ A ) )
& ( function @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(246,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(247,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(248,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(249,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)],[54]) ).
thf(250,plain,
$true = $true,
inference(unfold_def,[status(thm)],[59]) ).
thf(251,plain,
$true = $true,
inference(unfold_def,[status(thm)],[60]) ).
thf(252,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(253,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(254,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(255,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(256,plain,
$true = $true,
inference(unfold_def,[status(thm)],[69]) ).
thf(257,plain,
$true = $true,
inference(unfold_def,[status(thm)],[70]) ).
thf(258,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(259,plain,
$true = $true,
inference(unfold_def,[status(thm)],[72]) ).
thf(260,plain,
$true = $true,
inference(unfold_def,[status(thm)],[73]) ).
thf(261,plain,
$true = $true,
inference(unfold_def,[status(thm)],[75]) ).
thf(262,plain,
$true = $true,
inference(unfold_def,[status(thm)],[76]) ).
thf(263,plain,
$true = $true,
inference(unfold_def,[status(thm)],[77]) ).
thf(264,plain,
$true = $true,
inference(unfold_def,[status(thm)],[78]) ).
thf(265,plain,
$true = $true,
inference(unfold_def,[status(thm)],[80]) ).
thf(266,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(267,plain,
$true = $true,
inference(unfold_def,[status(thm)],[82]) ).
thf(268,plain,
$true = $true,
inference(unfold_def,[status(thm)],[83]) ).
thf(269,plain,
$true = $true,
inference(unfold_def,[status(thm)],[84]) ).
thf(270,plain,
$true = $true,
inference(unfold_def,[status(thm)],[85]) ).
thf(271,plain,
$true = $true,
inference(unfold_def,[status(thm)],[86]) ).
thf(272,plain,
$true = $true,
inference(unfold_def,[status(thm)],[87]) ).
thf(273,plain,
$true = $true,
inference(unfold_def,[status(thm)],[88]) ).
thf(274,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(275,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(276,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(277,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(278,plain,
( ( ! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(279,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(280,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(281,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(282,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)],[178]) ).
thf(283,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)],[188]) ).
thf(284,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(285,plain,
( ( ( ( relation @ sK1_A )
& ( function @ sK1_A ) )
=> ( ( one_to_one @ sK1_A )
=> ( ( ( relation_rng @ sK1_A )
= ( relation_dom @ ( function_inverse @ sK1_A ) ) )
& ( ( relation_dom @ sK1_A )
= ( relation_rng @ ( function_inverse @ sK1_A ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[233]) ).
thf(286,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[285]) ).
thf(287,plain,
( ( function @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[285]) ).
thf(288,plain,
( ( one_to_one @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[285]) ).
thf(289,plain,
( ( ( ( relation_rng @ sK1_A )
= ( relation_dom @ ( function_inverse @ sK1_A ) ) )
& ( ( relation_dom @ sK1_A )
= ( relation_rng @ ( function_inverse @ sK1_A ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[285]) ).
thf(290,plain,
( ( ( relation_rng @ sK1_A )
= ( relation_dom @ ( function_inverse @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[289]) ).
thf(291,plain,
( ( ( relation_dom @ sK1_A )
= ( relation_rng @ ( function_inverse @ sK1_A ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[289]) ).
thf(292,plain,
( ( ( relation_rng @ sK1_A )
!= ( relation_dom @ ( function_inverse @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[290]) ).
thf(293,plain,
( ( ( relation_dom @ sK1_A )
!= ( relation_rng @ ( function_inverse @ sK1_A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[291]) ).
thf(294,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(295,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)],[283]) ).
thf(296,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)],[282]) ).
thf(297,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(298,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(299,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(300,plain,
( ( ! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(301,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(302,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(303,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(304,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(305,plain,
$true = $true,
inference(copy,[status(thm)],[273]) ).
thf(306,plain,
$true = $true,
inference(copy,[status(thm)],[272]) ).
thf(307,plain,
$true = $true,
inference(copy,[status(thm)],[271]) ).
thf(308,plain,
$true = $true,
inference(copy,[status(thm)],[270]) ).
thf(309,plain,
$true = $true,
inference(copy,[status(thm)],[269]) ).
thf(310,plain,
$true = $true,
inference(copy,[status(thm)],[268]) ).
thf(311,plain,
$true = $true,
inference(copy,[status(thm)],[267]) ).
thf(312,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(313,plain,
$true = $true,
inference(copy,[status(thm)],[265]) ).
thf(314,plain,
$true = $true,
inference(copy,[status(thm)],[264]) ).
thf(315,plain,
$true = $true,
inference(copy,[status(thm)],[263]) ).
thf(316,plain,
$true = $true,
inference(copy,[status(thm)],[262]) ).
thf(317,plain,
$true = $true,
inference(copy,[status(thm)],[261]) ).
thf(318,plain,
$true = $true,
inference(copy,[status(thm)],[260]) ).
thf(319,plain,
$true = $true,
inference(copy,[status(thm)],[259]) ).
thf(320,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(321,plain,
$true = $true,
inference(copy,[status(thm)],[257]) ).
thf(322,plain,
$true = $true,
inference(copy,[status(thm)],[256]) ).
thf(323,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(324,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(325,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(326,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(327,plain,
$true = $true,
inference(copy,[status(thm)],[251]) ).
thf(328,plain,
$true = $true,
inference(copy,[status(thm)],[250]) ).
thf(329,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)],[249]) ).
thf(330,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(331,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(332,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(333,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) )
=> ( ( relation @ ( relation_inverse @ A ) )
& ( function @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(334,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(335,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(336,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(337,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(338,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(339,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(340,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(341,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(342,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(343,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(344,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(345,plain,
( ( one_to_one @ sK1_A )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(346,plain,
( ( function @ sK1_A )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(347,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(348,plain,
( ( ( relation_rng @ sK1_A )
!= ( relation_dom @ ( function_inverse @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(349,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(350,plain,
( ( ! [SX0: $i] :
~ ( ( ( relation_dom @ ( identity_relation @ SX0 ) )
!= SX0 )
| ( ( relation_rng @ ( identity_relation @ SX0 ) )
!= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(351,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 )
| ( ( function_inverse @ SX0 )
= ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(352,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( ~ ( relation @ ( function_inverse @ SX0 ) )
| ~ ( function @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(353,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)],[299]) ).
thf(354,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_rng @ SX0 ) )
| ~ ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(355,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(356,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)],[329]) ).
thf(357,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_inverse @ ( relation_inverse @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(358,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(359,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ( ( relation_dom @ SX0 )
= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(360,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(361,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)],[296]) ).
thf(362,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(363,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(364,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(365,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(366,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(367,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(368,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(369,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(370,plain,
( ( ! [SX0: $i] :
~ ( ~ ( relation @ ( identity_relation @ SX0 ) )
| ~ ( function @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(371,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(372,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) )
| ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(373,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) )
| ~ ( ~ ( relation @ ( relation_inverse @ SX0 ) )
| ~ ( function @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(374,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_image @ SX0 @ ( relation_dom @ SX0 ) )
= ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(375,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(376,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(377,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)],[295]) ).
thf(378,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(379,plain,
( ( ~ ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(380,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(381,plain,
! [SV1: $i] :
( ( relation @ ( identity_relation @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(382,plain,
( ( ( relation_rng @ sK1_A )
= ( relation_dom @ ( function_inverse @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(383,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ~ ( ~ ( empty @ ( relation_dom @ SV2 ) )
| ~ ( relation @ ( relation_dom @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(384,plain,
! [SV3: $i] :
( ( ~ ( ( ( relation_dom @ ( identity_relation @ SV3 ) )
!= SV3 )
| ( ( relation_rng @ ( identity_relation @ SV3 ) )
!= SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(385,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ( relation @ SV4 )
| ~ ( function @ SV4 ) )
| ~ ( one_to_one @ SV4 )
| ( ( function_inverse @ SV4 )
= ( relation_inverse @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(386,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
| ~ ( ~ ( relation @ ( function_inverse @ SV5 ) )
| ~ ( function @ ( function_inverse @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(387,plain,
! [SV6: $i] :
( ( ~ ( relation @ SV6 )
| ~ ( ~ ( ( ( relation_dom @ SV6 )
!= empty_set )
| ( ( relation_rng @ SV6 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV6 )
!= empty_set )
| ( ( relation_dom @ SV6 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(388,plain,
! [SV7: $i] :
( ( ~ ( empty @ SV7 )
| ~ ( ~ ( empty @ ( relation_rng @ SV7 ) )
| ~ ( relation @ ( relation_rng @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(389,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(390,plain,
! [SV8: $i] :
( ( ! [SY40: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( relation @ SY40 ) )
| ~ ( function @ SY40 ) )
| ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SY40 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SY40 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(391,plain,
! [SV9: $i] :
( ( ~ ( relation @ SV9 )
| ( ( relation_inverse @ ( relation_inverse @ SV9 ) )
= SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(392,plain,
! [SV10: $i] :
( ( ! [SY41: $i] :
( ~ ( relation @ SV10 )
| ( relation @ ( relation_dom_restriction @ SV10 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(393,plain,
! [SV11: $i] :
( ( ~ ( relation @ SV11 )
| ~ ( ( ( relation_dom @ SV11 )
= empty_set )
| ( ( relation_rng @ SV11 )
= empty_set ) )
| ( SV11 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(394,plain,
! [SV12: $i] :
( ( ~ ( relation @ SV12 )
| ( relation @ ( relation_inverse @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(395,plain,
! [SV13: $i] :
( ( ~ ( relation @ SV13 )
| ~ ( ( ( relation_rng @ SV13 )
!= ( relation_dom @ ( relation_inverse @ SV13 ) ) )
| ( ( relation_dom @ SV13 )
!= ( relation_rng @ ( relation_inverse @ SV13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(396,plain,
! [SV14: $i] :
( ( ! [SY42: $i] :
( ~ ~ ( ~ ( relation @ SV14 )
| ~ ( relation @ SY42 ) )
| ( relation @ ( relation_composition @ SV14 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(397,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(398,plain,
! [SV15: $i] :
( ( ! [SY43: $i] :
( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( relation @ SY43 ) )
| ( relation @ ( set_union2 @ SV15 @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(399,plain,
! [SV16: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV16 )
| ~ ( relation @ SV16 ) )
| ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(400,plain,
! [SV17: $i] :
( ( ~ ( empty @ SV17 )
| ( function @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(401,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(402,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(403,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(404,plain,
! [SV18: $i] :
( ( ~ ( ~ ( relation @ ( identity_relation @ SV18 ) )
| ~ ( function @ ( identity_relation @ SV18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(405,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(406,plain,
! [SV19: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( empty @ SV19 ) )
| ~ ( function @ SV19 ) )
| ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( one_to_one @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(407,plain,
! [SV20: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV20 )
| ~ ( function @ SV20 ) )
| ~ ( one_to_one @ SV20 ) )
| ~ ( ~ ( relation @ ( relation_inverse @ SV20 ) )
| ~ ( function @ ( relation_inverse @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(408,plain,
! [SV21: $i] :
( ( ~ ( relation @ SV21 )
| ( ( relation_image @ SV21 @ ( relation_dom @ SV21 ) )
= ( relation_rng @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(409,plain,
! [SV22: $i] :
( ( ! [SY44: $i] :
( ~ ~ ( ~ ( relation @ SV22 )
| ~ ( relation @ SY44 ) )
| ( relation @ ( set_intersection2 @ SV22 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(410,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV23 )
| ~ ( relation @ SV23 ) )
| ~ ( empty @ ( relation_dom @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(411,plain,
! [SV24: $i] :
( ( ~ ( relation @ SV24 )
| ! [SY45: $i] :
( ~ ( relation @ SY45 )
| ~ ( subset @ SV24 @ SY45 )
| ~ ( ~ ( subset @ ( relation_dom @ SV24 ) @ ( relation_dom @ SY45 ) )
| ~ ( subset @ ( relation_rng @ SV24 ) @ ( relation_rng @ SY45 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(412,plain,
! [SV25: $i] :
( ( ! [SY46: $i] :
( ~ ( relation @ SY46 )
| ( relation @ ( relation_rng_restriction @ SV25 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(413,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(414,plain,
! [SV26: $i] :
( ( ~ ( empty @ SV26 )
| ( relation @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(415,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV2 ) )
| ~ ( relation @ ( relation_dom @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(416,plain,
! [SV3: $i] :
( ( ( ( relation_dom @ ( identity_relation @ SV3 ) )
!= SV3 )
| ( ( relation_rng @ ( identity_relation @ SV3 ) )
!= SV3 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(417,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV4 )
| ~ ( function @ SV4 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV4 )
| ( ( function_inverse @ SV4 )
= ( relation_inverse @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[385]) ).
thf(418,plain,
! [SV5: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV5 ) )
| ~ ( function @ ( function_inverse @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(419,plain,
! [SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ~ ( ~ ( ( ( relation_dom @ SV6 )
!= empty_set )
| ( ( relation_rng @ SV6 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV6 )
!= empty_set )
| ( ( relation_dom @ SV6 )
= empty_set ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[387]) ).
thf(420,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV7 ) )
| ~ ( relation @ ( relation_rng @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(421,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( empty @ sK2_SX0 ) )
| ~ ( function @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[389]) ).
thf(422,plain,
! [SV27: $i,SV8: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( relation @ SV27 ) )
| ~ ( function @ SV27 ) )
| ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(423,plain,
! [SV9: $i] :
( ( ( ~ ( relation @ SV9 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV9 ) )
= SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(424,plain,
! [SV28: $i,SV10: $i] :
( ( ~ ( relation @ SV10 )
| ( relation @ ( relation_dom_restriction @ SV10 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(425,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ~ ( ( ( relation_dom @ SV11 )
= empty_set )
| ( ( relation_rng @ SV11 )
= empty_set ) )
| ( SV11 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(426,plain,
! [SV12: $i] :
( ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(427,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ~ ( ( ( relation_rng @ SV13 )
!= ( relation_dom @ ( relation_inverse @ SV13 ) ) )
| ( ( relation_dom @ SV13 )
!= ( relation_rng @ ( relation_inverse @ SV13 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(428,plain,
! [SV29: $i,SV14: $i] :
( ( ~ ~ ( ~ ( relation @ SV14 )
| ~ ( relation @ SV29 ) )
| ( relation @ ( relation_composition @ SV14 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(429,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) )
| ~ ( one_to_one @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[397]) ).
thf(430,plain,
! [SV30: $i,SV15: $i] :
( ( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( relation @ SV30 ) )
| ( relation @ ( set_union2 @ SV15 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(431,plain,
! [SV16: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV16 )
| ~ ( relation @ SV16 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(432,plain,
! [SV17: $i] :
( ( ( ~ ( empty @ SV17 ) )
= $true )
| ( ( function @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(433,plain,
( ( ~ ~ ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[401]) ).
thf(434,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[402]) ).
thf(435,plain,
( ( ~ ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[403]) ).
thf(436,plain,
! [SV18: $i] :
( ( ~ ( relation @ ( identity_relation @ SV18 ) )
| ~ ( function @ ( identity_relation @ SV18 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(437,plain,
( ( ~ ~ ( ~ ( relation @ sK7_SX0 )
| ~ ( relation_empty_yielding @ sK7_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[405]) ).
thf(438,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( empty @ SV19 ) )
| ~ ( function @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( one_to_one @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(439,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV20 )
| ~ ( function @ SV20 ) )
| ~ ( one_to_one @ SV20 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV20 ) )
| ~ ( function @ ( relation_inverse @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(440,plain,
! [SV21: $i] :
( ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( ( relation_image @ SV21 @ ( relation_dom @ SV21 ) )
= ( relation_rng @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(441,plain,
! [SV31: $i,SV22: $i] :
( ( ~ ~ ( ~ ( relation @ SV22 )
| ~ ( relation @ SV31 ) )
| ( relation @ ( set_intersection2 @ SV22 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(442,plain,
! [SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV23 )
| ~ ( relation @ SV23 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(443,plain,
! [SV24: $i] :
( ( ( ~ ( relation @ SV24 ) )
= $true )
| ( ( ! [SY45: $i] :
( ~ ( relation @ SY45 )
| ~ ( subset @ SV24 @ SY45 )
| ~ ( ~ ( subset @ ( relation_dom @ SV24 ) @ ( relation_dom @ SY45 ) )
| ~ ( subset @ ( relation_rng @ SV24 ) @ ( relation_rng @ SY45 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(444,plain,
! [SV25: $i,SV32: $i] :
( ( ~ ( relation @ SV32 )
| ( relation @ ( relation_rng_restriction @ SV25 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(445,plain,
( ( ( relation_dom @ empty_set )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(446,plain,
( ( ( relation_rng @ empty_set )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(447,plain,
! [SV26: $i] :
( ( ( ~ ( empty @ SV26 ) )
= $true )
| ( ( relation @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(448,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV2 ) )
| ~ ( relation @ ( relation_dom @ SV2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(449,plain,
! [SV3: $i] :
( ( ( relation_dom @ ( identity_relation @ SV3 ) )
!= SV3 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(450,plain,
! [SV3: $i] :
( ( ( relation_rng @ ( identity_relation @ SV3 ) )
!= SV3 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(451,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( relation @ SV4 )
| ~ ( function @ SV4 ) ) )
= $false )
| ( ( ~ ( one_to_one @ SV4 )
| ( ( function_inverse @ SV4 )
= ( relation_inverse @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(452,plain,
! [SV5: $i] :
( ( ( ~ ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV5 ) )
| ~ ( function @ ( function_inverse @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(453,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ~ ( ~ ( ( ( relation_dom @ SV6 )
!= empty_set )
| ( ( relation_rng @ SV6 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV6 )
!= empty_set )
| ( ( relation_dom @ SV6 )
= empty_set ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(454,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV7 ) )
| ~ ( relation @ ( relation_rng @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(455,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( empty @ sK2_SX0 ) )
| ~ ( function @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(456,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( relation @ SV27 ) )
| ~ ( function @ SV27 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(457,plain,
! [SV9: $i] :
( ( ( relation @ SV9 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV9 ) )
= SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(458,plain,
! [SV28: $i,SV10: $i] :
( ( ( ~ ( relation @ SV10 ) )
= $true )
| ( ( relation @ ( relation_dom_restriction @ SV10 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(459,plain,
! [SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ~ ( ( ( relation_dom @ SV11 )
= empty_set )
| ( ( relation_rng @ SV11 )
= empty_set ) )
| ( SV11 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(460,plain,
! [SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( relation @ ( relation_inverse @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(461,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( ~ ( ( ( relation_rng @ SV13 )
!= ( relation_dom @ ( relation_inverse @ SV13 ) ) )
| ( ( relation_dom @ SV13 )
!= ( relation_rng @ ( relation_inverse @ SV13 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(462,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV14 )
| ~ ( relation @ SV29 ) ) )
= $true )
| ( ( relation @ ( relation_composition @ SV14 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(463,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) )
| ~ ( one_to_one @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[429]) ).
thf(464,plain,
! [SV30: $i,SV15: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV15 )
| ~ ( relation @ SV30 ) ) )
= $true )
| ( ( relation @ ( set_union2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(465,plain,
! [SV16: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV16 )
| ~ ( relation @ SV16 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(466,plain,
! [SV17: $i] :
( ( ( empty @ SV17 )
= $false )
| ( ( function @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(467,plain,
( ( ~ ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[433]) ).
thf(468,plain,
( ( ~ ( ~ ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(469,plain,
( ( ~ ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(470,plain,
! [SV18: $i] :
( ( ~ ( relation @ ( identity_relation @ SV18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(471,plain,
! [SV18: $i] :
( ( ~ ( function @ ( identity_relation @ SV18 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[436]) ).
thf(472,plain,
( ( ~ ( ~ ( relation @ sK7_SX0 )
| ~ ( relation_empty_yielding @ sK7_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(473,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( empty @ SV19 ) )
| ~ ( function @ SV19 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( one_to_one @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(474,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV20 )
| ~ ( function @ SV20 ) )
| ~ ( one_to_one @ SV20 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV20 ) )
| ~ ( function @ ( relation_inverse @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(475,plain,
! [SV21: $i] :
( ( ( relation @ SV21 )
= $false )
| ( ( ( relation_image @ SV21 @ ( relation_dom @ SV21 ) )
= ( relation_rng @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(476,plain,
! [SV31: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV22 )
| ~ ( relation @ SV31 ) ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV22 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(477,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV23 )
| ~ ( relation @ SV23 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(478,plain,
! [SV24: $i] :
( ( ( relation @ SV24 )
= $false )
| ( ( ! [SY45: $i] :
( ~ ( relation @ SY45 )
| ~ ( subset @ SV24 @ SY45 )
| ~ ( ~ ( subset @ ( relation_dom @ SV24 ) @ ( relation_dom @ SY45 ) )
| ~ ( subset @ ( relation_rng @ SV24 ) @ ( relation_rng @ SY45 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(479,plain,
! [SV25: $i,SV32: $i] :
( ( ( ~ ( relation @ SV32 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV25 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(480,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(481,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(482,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
= $false )
| ( ( relation @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(483,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV2 ) )
| ~ ( relation @ ( relation_dom @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(484,plain,
! [SV3: $i] :
( ( ( relation_dom @ ( identity_relation @ SV3 ) )
= SV3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(485,plain,
! [SV3: $i] :
( ( ( relation_rng @ ( identity_relation @ SV3 ) )
= SV3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(486,plain,
! [SV4: $i] :
( ( ( ~ ( relation @ SV4 )
| ~ ( function @ SV4 ) )
= $true )
| ( ( ~ ( one_to_one @ SV4 )
| ( ( function_inverse @ SV4 )
= ( relation_inverse @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(487,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 )
| ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV5 ) )
| ~ ( function @ ( function_inverse @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(488,plain,
! [SV6: $i] :
( ( ( ~ ( ( ( relation_dom @ SV6 )
!= empty_set )
| ( ( relation_rng @ SV6 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV6 )
!= empty_set )
| ( ( relation_dom @ SV6 )
= empty_set ) ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(489,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV7 ) )
| ~ ( relation @ ( relation_rng @ SV7 ) ) )
= $false )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(490,plain,
( ( ~ ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( empty @ sK2_SX0 ) )
| ~ ( function @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(491,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( relation @ SV27 ) )
| ~ ( function @ SV27 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(492,plain,
! [SV28: $i,SV10: $i] :
( ( ( relation @ SV10 )
= $false )
| ( ( relation @ ( relation_dom_restriction @ SV10 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(493,plain,
! [SV11: $i] :
( ( ( ~ ( ( ( relation_dom @ SV11 )
= empty_set )
| ( ( relation_rng @ SV11 )
= empty_set ) ) )
= $true )
| ( ( SV11 = empty_set )
= $true )
| ( ( relation @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(494,plain,
! [SV13: $i] :
( ( ( ( ( relation_rng @ SV13 )
!= ( relation_dom @ ( relation_inverse @ SV13 ) ) )
| ( ( relation_dom @ SV13 )
!= ( relation_rng @ ( relation_inverse @ SV13 ) ) ) )
= $false )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(495,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( ~ ( relation @ SV14 )
| ~ ( relation @ SV29 ) ) )
= $false )
| ( ( relation @ ( relation_composition @ SV14 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(496,plain,
( ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) )
| ~ ( one_to_one @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(497,plain,
! [SV30: $i,SV15: $i] :
( ( ( ~ ( ~ ( relation @ SV15 )
| ~ ( relation @ SV30 ) ) )
= $false )
| ( ( relation @ ( set_union2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(498,plain,
! [SV16: $i] :
( ( ( ~ ~ ( empty @ SV16 )
| ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(499,plain,
( ( ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(500,plain,
( ( ~ ~ ( empty @ sK5_SX0 )
| ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(501,plain,
( ( ~ ( relation @ sK6_SX0 )
| ~ ( function @ sK6_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(502,plain,
! [SV18: $i] :
( ( relation @ ( identity_relation @ SV18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(503,plain,
! [SV18: $i] :
( ( function @ ( identity_relation @ SV18 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(504,plain,
( ( ~ ( relation @ sK7_SX0 )
| ~ ( relation_empty_yielding @ sK7_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(505,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( empty @ SV19 ) )
| ~ ( function @ SV19 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( one_to_one @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(506,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV20 )
| ~ ( function @ SV20 ) )
| ~ ( one_to_one @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV20 ) )
| ~ ( function @ ( relation_inverse @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(507,plain,
! [SV31: $i,SV22: $i] :
( ( ( ~ ( ~ ( relation @ SV22 )
| ~ ( relation @ SV31 ) ) )
= $false )
| ( ( relation @ ( set_intersection2 @ SV22 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(508,plain,
! [SV23: $i] :
( ( ( ~ ~ ( empty @ SV23 )
| ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(509,plain,
! [SV24: $i,SV33: $i] :
( ( ( ~ ( relation @ SV33 )
| ~ ( subset @ SV24 @ SV33 )
| ~ ( ~ ( subset @ ( relation_dom @ SV24 ) @ ( relation_dom @ SV33 ) )
| ~ ( subset @ ( relation_rng @ SV24 ) @ ( relation_rng @ SV33 ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(510,plain,
! [SV25: $i,SV32: $i] :
( ( ( relation @ SV32 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV25 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(511,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(512,plain,
! [SV2: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(513,plain,
! [SV4: $i] :
( ( ( ~ ( relation @ SV4 ) )
= $true )
| ( ( ~ ( function @ SV4 ) )
= $true )
| ( ( ~ ( one_to_one @ SV4 )
| ( ( function_inverse @ SV4 )
= ( relation_inverse @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(514,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ SV5 ) )
= $true )
| ( ( ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV5 ) )
| ~ ( function @ ( function_inverse @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(515,plain,
! [SV6: $i] :
( ( ( ~ ( ( ( relation_dom @ SV6 )
!= empty_set )
| ( ( relation_rng @ SV6 )
= empty_set ) ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(516,plain,
! [SV6: $i] :
( ( ( ~ ( ( ( relation_rng @ SV6 )
!= empty_set )
| ( ( relation_dom @ SV6 )
= empty_set ) ) )
= $false )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[488]) ).
thf(517,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV7 ) ) )
= $false )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(518,plain,
! [SV7: $i] :
( ( ( ~ ( relation @ ( relation_rng @ SV7 ) ) )
= $false )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[489]) ).
thf(519,plain,
( ( ~ ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( empty @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(520,plain,
( ( ~ ( function @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[490]) ).
thf(521,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( relation @ SV27 ) )
| ~ ( function @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(522,plain,
! [SV11: $i] :
( ( ( ( ( relation_dom @ SV11 )
= empty_set )
| ( ( relation_rng @ SV11 )
= empty_set ) )
= $false )
| ( ( SV11 = empty_set )
= $true )
| ( ( relation @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(523,plain,
! [SV13: $i] :
( ( ( ( relation_rng @ SV13 )
!= ( relation_dom @ ( relation_inverse @ SV13 ) ) )
= $false )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(524,plain,
! [SV13: $i] :
( ( ( ( relation_dom @ SV13 )
!= ( relation_rng @ ( relation_inverse @ SV13 ) ) )
= $false )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(525,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( relation @ SV14 )
| ~ ( relation @ SV29 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV14 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(526,plain,
( ( ~ ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(527,plain,
( ( ~ ( one_to_one @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(528,plain,
! [SV30: $i,SV15: $i] :
( ( ( ~ ( relation @ SV15 )
| ~ ( relation @ SV30 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(529,plain,
! [SV16: $i] :
( ( ( ~ ~ ( empty @ SV16 ) )
= $true )
| ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(530,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(531,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[499]) ).
thf(532,plain,
( ( ~ ~ ( empty @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(533,plain,
( ( ~ ( relation @ sK5_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[500]) ).
thf(534,plain,
( ( ~ ( relation @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(535,plain,
( ( ~ ( function @ sK6_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[501]) ).
thf(536,plain,
( ( ~ ( relation @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(537,plain,
( ( ~ ( relation_empty_yielding @ sK7_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[504]) ).
thf(538,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( empty @ SV19 ) ) )
= $true )
| ( ( ~ ( function @ SV19 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( one_to_one @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(539,plain,
! [SV20: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV20 )
| ~ ( function @ SV20 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV20 ) )
| ~ ( function @ ( relation_inverse @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(540,plain,
! [SV31: $i,SV22: $i] :
( ( ( ~ ( relation @ SV22 )
| ~ ( relation @ SV31 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV22 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(541,plain,
! [SV23: $i] :
( ( ( ~ ~ ( empty @ SV23 ) )
= $true )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(542,plain,
! [SV24: $i,SV33: $i] :
( ( ( ~ ( relation @ SV33 ) )
= $true )
| ( ( ~ ( subset @ SV24 @ SV33 )
| ~ ( ~ ( subset @ ( relation_dom @ SV24 ) @ ( relation_dom @ SV33 ) )
| ~ ( subset @ ( relation_rng @ SV24 ) @ ( relation_rng @ SV33 ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(543,plain,
! [SV2: $i] :
( ( ( empty @ ( relation_dom @ SV2 ) )
= $true )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(544,plain,
! [SV2: $i] :
( ( ( relation @ ( relation_dom @ SV2 ) )
= $true )
| ( ( empty @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(545,plain,
! [SV4: $i] :
( ( ( relation @ SV4 )
= $false )
| ( ( ~ ( function @ SV4 ) )
= $true )
| ( ( ~ ( one_to_one @ SV4 )
| ( ( function_inverse @ SV4 )
= ( relation_inverse @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[513]) ).
thf(546,plain,
! [SV5: $i] :
( ( ( relation @ SV5 )
= $false )
| ( ( ~ ( function @ SV5 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV5 ) )
| ~ ( function @ ( function_inverse @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(547,plain,
! [SV6: $i] :
( ( ( ( ( relation_dom @ SV6 )
!= empty_set )
| ( ( relation_rng @ SV6 )
= empty_set ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(548,plain,
! [SV6: $i] :
( ( ( ( ( relation_rng @ SV6 )
!= empty_set )
| ( ( relation_dom @ SV6 )
= empty_set ) )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(549,plain,
! [SV7: $i] :
( ( ( empty @ ( relation_rng @ SV7 ) )
= $true )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(550,plain,
! [SV7: $i] :
( ( ( relation @ ( relation_rng @ SV7 ) )
= $true )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(551,plain,
( ( ~ ( ~ ( relation @ sK2_SX0 )
| ~ ( empty @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(552,plain,
( ( function @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(553,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( relation @ SV27 ) ) )
= $true )
| ( ( ~ ( function @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(554,plain,
! [SV11: $i] :
( ( ( ( relation_dom @ SV11 )
= empty_set )
= $false )
| ( ( SV11 = empty_set )
= $true )
| ( ( relation @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(555,plain,
! [SV11: $i] :
( ( ( ( relation_rng @ SV11 )
= empty_set )
= $false )
| ( ( SV11 = empty_set )
= $true )
| ( ( relation @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(556,plain,
! [SV13: $i] :
( ( ( ( relation_rng @ SV13 )
= ( relation_dom @ ( relation_inverse @ SV13 ) ) )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(557,plain,
! [SV13: $i] :
( ( ( ( relation_dom @ SV13 )
= ( relation_rng @ ( relation_inverse @ SV13 ) ) )
= $true )
| ( ( relation @ SV13 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(558,plain,
! [SV29: $i,SV14: $i] :
( ( ( ~ ( relation @ SV14 ) )
= $true )
| ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV14 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(559,plain,
( ( ~ ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(560,plain,
( ( one_to_one @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(561,plain,
! [SV30: $i,SV15: $i] :
( ( ( ~ ( relation @ SV15 ) )
= $true )
| ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(562,plain,
! [SV16: $i] :
( ( ( ~ ( empty @ SV16 ) )
= $false )
| ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(563,plain,
( ( empty @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(564,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(565,plain,
( ( ~ ( empty @ sK5_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(566,plain,
( ( relation @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(567,plain,
( ( relation @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(568,plain,
( ( function @ sK6_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(569,plain,
( ( relation @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(570,plain,
( ( relation_empty_yielding @ sK7_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(571,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( relation @ SV19 )
| ~ ( empty @ SV19 ) ) )
= $false )
| ( ( ~ ( function @ SV19 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( one_to_one @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(572,plain,
! [SV20: $i] :
( ( ( ~ ( ~ ( relation @ SV20 )
| ~ ( function @ SV20 ) ) )
= $false )
| ( ( ~ ( one_to_one @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV20 ) )
| ~ ( function @ ( relation_inverse @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(573,plain,
! [SV31: $i,SV22: $i] :
( ( ( ~ ( relation @ SV22 ) )
= $true )
| ( ( ~ ( relation @ SV31 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV22 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(574,plain,
! [SV23: $i] :
( ( ( ~ ( empty @ SV23 ) )
= $false )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(575,plain,
! [SV24: $i,SV33: $i] :
( ( ( relation @ SV33 )
= $false )
| ( ( ~ ( subset @ SV24 @ SV33 )
| ~ ( ~ ( subset @ ( relation_dom @ SV24 ) @ ( relation_dom @ SV33 ) )
| ~ ( subset @ ( relation_rng @ SV24 ) @ ( relation_rng @ SV33 ) ) ) )
= $true )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(576,plain,
! [SV4: $i] :
( ( ( function @ SV4 )
= $false )
| ( ( relation @ SV4 )
= $false )
| ( ( ~ ( one_to_one @ SV4 )
| ( ( function_inverse @ SV4 )
= ( relation_inverse @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(577,plain,
! [SV5: $i] :
( ( ( function @ SV5 )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV5 ) )
| ~ ( function @ ( function_inverse @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(578,plain,
! [SV6: $i] :
( ( ( ( relation_dom @ SV6 )
!= empty_set )
= $true )
| ( ( ( relation_rng @ SV6 )
= empty_set )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(579,plain,
! [SV6: $i] :
( ( ( ( relation_rng @ SV6 )
!= empty_set )
= $true )
| ( ( ( relation_dom @ SV6 )
= empty_set )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(580,plain,
( ( ~ ( relation @ sK2_SX0 )
| ~ ( empty @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(581,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( relation @ SV27 ) ) )
= $false )
| ( ( ~ ( function @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(582,plain,
! [SV29: $i,SV14: $i] :
( ( ( relation @ SV14 )
= $false )
| ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV14 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(583,plain,
( ( ~ ( relation @ sK3_SX0 )
| ~ ( function @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(584,plain,
! [SV30: $i,SV15: $i] :
( ( ( relation @ SV15 )
= $false )
| ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(585,plain,
! [SV16: $i] :
( ( ( empty @ SV16 )
= $true )
| ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[562]) ).
thf(586,plain,
( ( empty @ sK5_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(587,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 )
| ~ ( empty @ SV19 ) )
= $true )
| ( ( ~ ( function @ SV19 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( one_to_one @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[571]) ).
thf(588,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 )
| ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( one_to_one @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV20 ) )
| ~ ( function @ ( relation_inverse @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[572]) ).
thf(589,plain,
! [SV31: $i,SV22: $i] :
( ( ( relation @ SV22 )
= $false )
| ( ( ~ ( relation @ SV31 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV22 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(590,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
= $true )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(591,plain,
! [SV33: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV33 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV24 ) @ ( relation_dom @ SV33 ) )
| ~ ( subset @ ( relation_rng @ SV24 ) @ ( relation_rng @ SV33 ) ) ) )
= $true )
| ( ( relation @ SV33 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(592,plain,
! [SV4: $i] :
( ( ( ~ ( one_to_one @ SV4 ) )
= $true )
| ( ( ( function_inverse @ SV4 )
= ( relation_inverse @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(593,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ ( function_inverse @ SV5 ) )
| ~ ( function @ ( function_inverse @ SV5 ) ) )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(594,plain,
! [SV6: $i] :
( ( ( ( relation_dom @ SV6 )
= empty_set )
= $false )
| ( ( ( relation_rng @ SV6 )
= empty_set )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(595,plain,
! [SV6: $i] :
( ( ( ( relation_rng @ SV6 )
= empty_set )
= $false )
| ( ( ( relation_dom @ SV6 )
= empty_set )
= $true )
| ( ( relation @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(596,plain,
( ( ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[580]) ).
thf(597,plain,
( ( ~ ( empty @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[580]) ).
thf(598,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
| ~ ( relation @ SV27 ) )
= $true )
| ( ( ~ ( function @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[581]) ).
thf(599,plain,
! [SV14: $i,SV29: $i] :
( ( ( relation @ SV29 )
= $false )
| ( ( relation @ SV14 )
= $false )
| ( ( relation @ ( relation_composition @ SV14 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(600,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(601,plain,
( ( ~ ( function @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[583]) ).
thf(602,plain,
! [SV15: $i,SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( relation @ SV15 )
= $false )
| ( ( relation @ ( set_union2 @ SV15 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(603,plain,
! [SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( empty @ SV16 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(604,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ~ ( empty @ SV19 ) )
= $true )
| ( ( ~ ( function @ SV19 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( one_to_one @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(605,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( one_to_one @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV20 ) )
| ~ ( function @ ( relation_inverse @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(606,plain,
! [SV22: $i,SV31: $i] :
( ( ( relation @ SV31 )
= $false )
| ( ( relation @ SV22 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV22 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(607,plain,
! [SV23: $i] :
( ( ( relation @ SV23 )
= $false )
| ( ( empty @ SV23 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(608,plain,
! [SV33: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV33 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV24 ) @ ( relation_dom @ SV33 ) )
| ~ ( subset @ ( relation_rng @ SV24 ) @ ( relation_rng @ SV33 ) ) ) )
= $true )
| ( ( relation @ SV33 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(609,plain,
! [SV4: $i] :
( ( ( one_to_one @ SV4 )
= $false )
| ( ( ( function_inverse @ SV4 )
= ( relation_inverse @ SV4 ) )
= $true )
| ( ( relation @ SV4 )
= $false )
| ( ( function @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(610,plain,
! [SV5: $i] :
( ( ( ~ ( relation @ ( function_inverse @ SV5 ) ) )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[593]) ).
thf(611,plain,
! [SV5: $i] :
( ( ( ~ ( function @ ( function_inverse @ SV5 ) ) )
= $false )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[593]) ).
thf(612,plain,
( ( relation @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(613,plain,
( ( empty @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[597]) ).
thf(614,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) ) )
= $true )
| ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ~ ( function @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(615,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[600]) ).
thf(616,plain,
( ( function @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[601]) ).
thf(617,plain,
! [SV16: $i] :
( ( ( empty @ ( relation_rng @ SV16 ) )
= $false )
| ( ( empty @ SV16 )
= $true )
| ( ( relation @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(618,plain,
! [SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( ~ ( empty @ SV19 ) )
= $true )
| ( ( ~ ( function @ SV19 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( one_to_one @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(619,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( ~ ( function @ SV20 ) )
= $true )
| ( ( ~ ( one_to_one @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV20 ) )
| ~ ( function @ ( relation_inverse @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(620,plain,
! [SV23: $i] :
( ( ( empty @ ( relation_dom @ SV23 ) )
= $false )
| ( ( empty @ SV23 )
= $true )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(621,plain,
! [SV33: $i,SV24: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV24 ) @ ( relation_dom @ SV33 ) )
| ~ ( subset @ ( relation_rng @ SV24 ) @ ( relation_rng @ SV33 ) ) )
= $false )
| ( ( subset @ SV24 @ SV33 )
= $false )
| ( ( relation @ SV33 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(622,plain,
! [SV5: $i] :
( ( ( relation @ ( function_inverse @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[610]) ).
thf(623,plain,
! [SV5: $i] :
( ( ( function @ ( function_inverse @ SV5 ) )
= $true )
| ( ( relation @ SV5 )
= $false )
| ( ( function @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[611]) ).
thf(624,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) ) )
= $false )
| ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ~ ( function @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(625,plain,
! [SV19: $i] :
( ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( ~ ( function @ SV19 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( one_to_one @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[618]) ).
thf(626,plain,
! [SV20: $i] :
( ( ( function @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false )
| ( ( ~ ( one_to_one @ SV20 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV20 ) )
| ~ ( function @ ( relation_inverse @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(627,plain,
! [SV33: $i,SV24: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV24 ) @ ( relation_dom @ SV33 ) ) )
= $false )
| ( ( subset @ SV24 @ SV33 )
= $false )
| ( ( relation @ SV33 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[621]) ).
thf(628,plain,
! [SV33: $i,SV24: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV24 ) @ ( relation_rng @ SV33 ) ) )
= $false )
| ( ( subset @ SV24 @ SV33 )
= $false )
| ( ( relation @ SV33 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[621]) ).
thf(629,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 )
| ~ ( function @ SV8 ) )
= $true )
| ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ~ ( function @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[624]) ).
thf(630,plain,
! [SV19: $i] :
( ( ( function @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( empty @ SV19 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( one_to_one @ SV19 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[625]) ).
thf(631,plain,
! [SV20: $i] :
( ( ( one_to_one @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false )
| ( ( function @ SV20 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV20 ) )
| ~ ( function @ ( relation_inverse @ SV20 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[626]) ).
thf(632,plain,
! [SV33: $i,SV24: $i] :
( ( ( subset @ ( relation_dom @ SV24 ) @ ( relation_dom @ SV33 ) )
= $true )
| ( ( subset @ SV24 @ SV33 )
= $false )
| ( ( relation @ SV33 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[627]) ).
thf(633,plain,
! [SV33: $i,SV24: $i] :
( ( ( subset @ ( relation_rng @ SV24 ) @ ( relation_rng @ SV33 ) )
= $true )
| ( ( subset @ SV24 @ SV33 )
= $false )
| ( ( relation @ SV33 )
= $false )
| ( ( relation @ SV24 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[628]) ).
thf(634,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ~ ( function @ SV8 ) )
= $true )
| ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ~ ( function @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(635,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
| ~ ( one_to_one @ SV19 ) )
= $false )
| ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(636,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ ( relation_inverse @ SV20 ) )
| ~ ( function @ ( relation_inverse @ SV20 ) ) )
= $false )
| ( ( function @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false )
| ( ( one_to_one @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[631]) ).
thf(637,plain,
! [SV27: $i,SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ~ ( function @ SV8 ) )
= $true )
| ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ~ ( function @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(638,plain,
! [SV19: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) ) )
= $false )
| ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(639,plain,
! [SV19: $i] :
( ( ( ~ ( one_to_one @ SV19 ) )
= $false )
| ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(640,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ ( relation_inverse @ SV20 ) ) )
= $false )
| ( ( function @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false )
| ( ( one_to_one @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(641,plain,
! [SV20: $i] :
( ( ( ~ ( function @ ( relation_inverse @ SV20 ) ) )
= $false )
| ( ( function @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false )
| ( ( one_to_one @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[636]) ).
thf(642,plain,
! [SV27: $i,SV8: $i] :
( ( ( function @ SV8 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ~ ( function @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(643,plain,
! [SV19: $i] :
( ( ( ~ ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) ) )
= $true )
| ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[638]) ).
thf(644,plain,
! [SV19: $i] :
( ( ( one_to_one @ SV19 )
= $true )
| ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[639]) ).
thf(645,plain,
! [SV20: $i] :
( ( ( relation @ ( relation_inverse @ SV20 ) )
= $true )
| ( ( function @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false )
| ( ( one_to_one @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[640]) ).
thf(646,plain,
! [SV20: $i] :
( ( ( function @ ( relation_inverse @ SV20 ) )
= $true )
| ( ( function @ SV20 )
= $false )
| ( ( relation @ SV20 )
= $false )
| ( ( one_to_one @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(647,plain,
! [SV8: $i,SV27: $i] :
( ( ( relation @ SV27 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false )
| ( ( ~ ( function @ SV27 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[642]) ).
thf(648,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 )
| ~ ( function @ SV19 ) )
= $false )
| ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[643]) ).
thf(649,plain,
! [SV8: $i,SV27: $i] :
( ( ( function @ SV27 )
= $false )
| ( ( function @ SV8 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( relation @ SV27 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(650,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $false )
| ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[648]) ).
thf(651,plain,
! [SV19: $i] :
( ( ( ~ ( function @ SV19 ) )
= $false )
| ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[648]) ).
thf(652,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) )
| ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) )
= $false )
| ( ( relation @ SV27 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false )
| ( ( function @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(653,plain,
! [SV19: $i] :
( ( ( relation @ SV19 )
= $true )
| ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[650]) ).
thf(654,plain,
! [SV19: $i] :
( ( ( function @ SV19 )
= $true )
| ( ( empty @ SV19 )
= $false )
| ( ( relation @ SV19 )
= $false )
| ( ( function @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[651]) ).
thf(655,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ( relation @ ( relation_composition @ SV8 @ SV27 ) ) )
= $false )
| ( ( relation @ SV27 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false )
| ( ( function @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(656,plain,
! [SV27: $i,SV8: $i] :
( ( ( ~ ( function @ ( relation_composition @ SV8 @ SV27 ) ) )
= $false )
| ( ( relation @ SV27 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false )
| ( ( function @ SV27 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[652]) ).
thf(657,plain,
! [SV27: $i,SV8: $i] :
( ( ( relation @ ( relation_composition @ SV8 @ SV27 ) )
= $true )
| ( ( relation @ SV27 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false )
| ( ( function @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[655]) ).
thf(658,plain,
! [SV27: $i,SV8: $i] :
( ( ( function @ ( relation_composition @ SV8 @ SV27 ) )
= $true )
| ( ( relation @ SV27 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( function @ SV8 )
= $false )
| ( ( function @ SV27 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[656]) ).
thf(659,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[305,658,657,654,653,646,645,644,633,632,623,622,620,617,616,615,613,612,609,606,602,599,595,594,586,570,569,568,567,566,564,563,560,557,556,555,554,552,550,549,544,543,510,503,502,492,485,484,482,481,480,475,466,460,457,382,381,347,346,345,328,327,322,321,319,318,317,316,315,314,313,311,310,309,308,307,306]) ).
thf(660,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_image @ A @ ( relation_dom @ A ) )
= ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(661,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)],[283]) ).
thf(662,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)],[282]) ).
thf(663,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(664,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(665,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_dom @ A )
= empty_set )
<=> ( ( relation_rng @ A )
= empty_set ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(666,plain,
( ( ! [A: $i] :
( ( ( relation_dom @ ( identity_relation @ A ) )
= A )
& ( ( relation_rng @ ( identity_relation @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(667,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(668,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(669,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(670,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
=> ( ( function_inverse @ A )
= ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(671,plain,
$true = $true,
inference(copy,[status(thm)],[273]) ).
thf(672,plain,
$true = $true,
inference(copy,[status(thm)],[272]) ).
thf(673,plain,
$true = $true,
inference(copy,[status(thm)],[271]) ).
thf(674,plain,
$true = $true,
inference(copy,[status(thm)],[270]) ).
thf(675,plain,
$true = $true,
inference(copy,[status(thm)],[269]) ).
thf(676,plain,
$true = $true,
inference(copy,[status(thm)],[268]) ).
thf(677,plain,
$true = $true,
inference(copy,[status(thm)],[267]) ).
thf(678,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( relation @ ( function_inverse @ A ) )
& ( function @ ( function_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(679,plain,
$true = $true,
inference(copy,[status(thm)],[265]) ).
thf(680,plain,
$true = $true,
inference(copy,[status(thm)],[264]) ).
thf(681,plain,
$true = $true,
inference(copy,[status(thm)],[263]) ).
thf(682,plain,
$true = $true,
inference(copy,[status(thm)],[262]) ).
thf(683,plain,
$true = $true,
inference(copy,[status(thm)],[261]) ).
thf(684,plain,
$true = $true,
inference(copy,[status(thm)],[260]) ).
thf(685,plain,
$true = $true,
inference(copy,[status(thm)],[259]) ).
thf(686,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(687,plain,
$true = $true,
inference(copy,[status(thm)],[257]) ).
thf(688,plain,
$true = $true,
inference(copy,[status(thm)],[256]) ).
thf(689,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(690,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(691,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(692,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(693,plain,
$true = $true,
inference(copy,[status(thm)],[251]) ).
thf(694,plain,
$true = $true,
inference(copy,[status(thm)],[250]) ).
thf(695,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)],[249]) ).
thf(696,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(697,plain,
( ( ! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(698,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(699,plain,
( ( ! [A: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) )
=> ( ( relation @ ( relation_inverse @ A ) )
& ( function @ ( relation_inverse @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(700,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(701,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(702,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(703,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(704,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(705,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(706,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(707,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(708,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(709,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(710,plain,
( ( ? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(711,plain,
( ( one_to_one @ sK1_A )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(712,plain,
( ( function @ sK1_A )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(713,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(714,plain,
( ( ( relation_dom @ sK1_A )
!= ( relation_rng @ ( function_inverse @ sK1_A ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(715,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[709]) ).
thf(716,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 )
| ( ( function_inverse @ SX0 )
= ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[670]) ).
thf(717,plain,
( ( ~ ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663]) ).
thf(718,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_inverse @ ( relation_inverse @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[704]) ).
thf(719,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[692]) ).
thf(720,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)],[661]) ).
thf(721,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[700]) ).
thf(722,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[708]) ).
thf(723,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[705]) ).
thf(724,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( ~ ( relation @ ( function_inverse @ SX0 ) )
| ~ ( function @ ( function_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[678]) ).
thf(725,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_image @ SX0 @ ( relation_dom @ SX0 ) )
= ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(726,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) )
| ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(727,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)],[665]) ).
thf(728,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) )
| ~ ( ~ ( relation @ ( relation_inverse @ SX0 ) )
| ~ ( function @ ( relation_inverse @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(729,plain,
( ( ! [SX0: $i] :
~ ( ( ( relation_dom @ ( identity_relation @ SX0 ) )
!= SX0 )
| ( ( relation_rng @ ( identity_relation @ SX0 ) )
!= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(730,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)],[695]) ).
thf(731,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_rng @ SX0 ) )
| ~ ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[703]) ).
thf(732,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[710]) ).
thf(733,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ( ( relation_dom @ SX0 )
= empty_set )
| ( ( relation_rng @ SX0 )
= empty_set ) )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(734,plain,
( ( ! [SX0: $i] :
~ ( ~ ( relation @ ( identity_relation @ SX0 ) )
| ~ ( function @ ( identity_relation @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(735,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(736,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(737,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[701]) ).
thf(738,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[702]) ).
thf(739,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[706]) ).
thf(740,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)],[662]) ).
thf(741,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[667]) ).
thf(742,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[707]) ).
thf(743,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[689]) ).
thf(744,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(745,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[668]) ).
thf(746,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(747,plain,
! [SV34: $i] :
( ( relation @ ( identity_relation @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(748,plain,
( ( ( relation_dom @ sK1_A )
= ( relation_rng @ ( function_inverse @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(749,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) )
| ~ ( one_to_one @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(750,plain,
! [SV35: $i] :
( ( ~ ~ ( ~ ( relation @ SV35 )
| ~ ( function @ SV35 ) )
| ~ ( one_to_one @ SV35 )
| ( ( function_inverse @ SV35 )
= ( relation_inverse @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(751,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(752,plain,
! [SV36: $i] :
( ( ~ ( relation @ SV36 )
| ( ( relation_inverse @ ( relation_inverse @ SV36 ) )
= SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(753,plain,
! [SV37: $i] :
( ( ! [SY47: $i] :
( ~ ( relation @ SY47 )
| ( relation @ ( relation_rng_restriction @ SV37 @ SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(754,plain,
! [SV38: $i] :
( ( ~ ( relation @ SV38 )
| ! [SY48: $i] :
( ~ ( relation @ SY48 )
| ~ ( subset @ SV38 @ SY48 )
| ~ ( ~ ( subset @ ( relation_dom @ SV38 ) @ ( relation_dom @ SY48 ) )
| ~ ( subset @ ( relation_rng @ SV38 ) @ ( relation_rng @ SY48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(755,plain,
! [SV39: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV39 )
| ~ ( relation @ SV39 ) )
| ~ ( empty @ ( relation_dom @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(756,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(757,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(758,plain,
! [SV40: $i] :
( ( ~ ~ ( ~ ( relation @ SV40 )
| ~ ( function @ SV40 ) )
| ~ ( ~ ( relation @ ( function_inverse @ SV40 ) )
| ~ ( function @ ( function_inverse @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(759,plain,
! [SV41: $i] :
( ( ~ ( relation @ SV41 )
| ( ( relation_image @ SV41 @ ( relation_dom @ SV41 ) )
= ( relation_rng @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(760,plain,
! [SV42: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( empty @ SV42 ) )
| ~ ( function @ SV42 ) )
| ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
| ~ ( one_to_one @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(761,plain,
! [SV43: $i] :
( ( ~ ( relation @ SV43 )
| ~ ( ~ ( ( ( relation_dom @ SV43 )
!= empty_set )
| ( ( relation_rng @ SV43 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV43 )
!= empty_set )
| ( ( relation_dom @ SV43 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(762,plain,
! [SV44: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV44 )
| ~ ( function @ SV44 ) )
| ~ ( one_to_one @ SV44 ) )
| ~ ( ~ ( relation @ ( relation_inverse @ SV44 ) )
| ~ ( function @ ( relation_inverse @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(763,plain,
! [SV45: $i] :
( ( ~ ( ( ( relation_dom @ ( identity_relation @ SV45 ) )
!= SV45 )
| ( ( relation_rng @ ( identity_relation @ SV45 ) )
!= SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(764,plain,
! [SV46: $i] :
( ( ! [SY49: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV46 )
| ~ ( function @ SV46 ) )
| ~ ( relation @ SY49 ) )
| ~ ( function @ SY49 ) )
| ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SY49 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SY49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(765,plain,
! [SV47: $i] :
( ( ~ ( empty @ SV47 )
| ~ ( ~ ( empty @ ( relation_rng @ SV47 ) )
| ~ ( relation @ ( relation_rng @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(766,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation_empty_yielding @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(767,plain,
! [SV48: $i] :
( ( ~ ( relation @ SV48 )
| ~ ( ( ( relation_dom @ SV48 )
= empty_set )
| ( ( relation_rng @ SV48 )
= empty_set ) )
| ( SV48 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(768,plain,
! [SV49: $i] :
( ( ~ ( ~ ( relation @ ( identity_relation @ SV49 ) )
| ~ ( function @ ( identity_relation @ SV49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(769,plain,
! [SV50: $i] :
( ( ! [SY50: $i] :
( ~ ~ ( ~ ( relation @ SV50 )
| ~ ( relation @ SY50 ) )
| ( relation @ ( set_union2 @ SV50 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(770,plain,
! [SV51: $i] :
( ( ! [SY51: $i] :
( ~ ~ ( ~ ( relation @ SV51 )
| ~ ( relation @ SY51 ) )
| ( relation @ ( set_intersection2 @ SV51 @ SY51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(771,plain,
! [SV52: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV52 )
| ~ ( relation @ SV52 ) )
| ~ ( empty @ ( relation_rng @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(772,plain,
! [SV53: $i] :
( ( ~ ( empty @ SV53 )
| ~ ( ~ ( empty @ ( relation_dom @ SV53 ) )
| ~ ( relation @ ( relation_dom @ SV53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(773,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(774,plain,
! [SV54: $i] :
( ( ~ ( relation @ SV54 )
| ~ ( ( ( relation_rng @ SV54 )
!= ( relation_dom @ ( relation_inverse @ SV54 ) ) )
| ( ( relation_dom @ SV54 )
!= ( relation_rng @ ( relation_inverse @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(775,plain,
! [SV55: $i] :
( ( ~ ( empty @ SV55 )
| ( function @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(776,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( empty @ SX0 ) )
| ~ ( function @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(777,plain,
! [SV56: $i] :
( ( ! [SY52: $i] :
( ~ ~ ( ~ ( relation @ SV56 )
| ~ ( relation @ SY52 ) )
| ( relation @ ( relation_composition @ SV56 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(778,plain,
! [SV57: $i] :
( ( ~ ( relation @ SV57 )
| ( relation @ ( relation_inverse @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(779,plain,
! [SV58: $i] :
( ( ~ ( empty @ SV58 )
| ( relation @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(780,plain,
! [SV59: $i] :
( ( ! [SY53: $i] :
( ~ ( relation @ SV59 )
| ( relation @ ( relation_dom_restriction @ SV59 @ SY53 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(781,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
| ~ ( one_to_one @ sK8_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[749]) ).
thf(782,plain,
! [SV35: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV35 )
| ~ ( function @ SV35 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV35 )
| ( ( function_inverse @ SV35 )
= ( relation_inverse @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(783,plain,
( ( ( relation_dom @ empty_set )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[751]) ).
thf(784,plain,
( ( ( relation_rng @ empty_set )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[751]) ).
thf(785,plain,
! [SV36: $i] :
( ( ( ~ ( relation @ SV36 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV36 ) )
= SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[752]) ).
thf(786,plain,
! [SV37: $i,SV60: $i] :
( ( ~ ( relation @ SV60 )
| ( relation @ ( relation_rng_restriction @ SV37 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(787,plain,
! [SV38: $i] :
( ( ( ~ ( relation @ SV38 ) )
= $true )
| ( ( ! [SY48: $i] :
( ~ ( relation @ SY48 )
| ~ ( subset @ SV38 @ SY48 )
| ~ ( ~ ( subset @ ( relation_dom @ SV38 ) @ ( relation_dom @ SY48 ) )
| ~ ( subset @ ( relation_rng @ SV38 ) @ ( relation_rng @ SY48 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(788,plain,
! [SV39: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV39 )
| ~ ( relation @ SV39 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(789,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK9_SX0 )
| ~ ( relation @ sK9_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[756]) ).
thf(790,plain,
( ( ~ ~ ( ~ ( relation @ sK10_SX0 )
| ~ ( function @ sK10_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[757]) ).
thf(791,plain,
! [SV40: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV40 )
| ~ ( function @ SV40 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV40 ) )
| ~ ( function @ ( function_inverse @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(792,plain,
! [SV41: $i] :
( ( ( ~ ( relation @ SV41 ) )
= $true )
| ( ( ( relation_image @ SV41 @ ( relation_dom @ SV41 ) )
= ( relation_rng @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(793,plain,
! [SV42: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( empty @ SV42 ) )
| ~ ( function @ SV42 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
| ~ ( one_to_one @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(794,plain,
! [SV43: $i] :
( ( ( ~ ( relation @ SV43 ) )
= $true )
| ( ( ~ ( ~ ( ( ( relation_dom @ SV43 )
!= empty_set )
| ( ( relation_rng @ SV43 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV43 )
!= empty_set )
| ( ( relation_dom @ SV43 )
= empty_set ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(795,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV44 )
| ~ ( function @ SV44 ) )
| ~ ( one_to_one @ SV44 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV44 ) )
| ~ ( function @ ( relation_inverse @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(796,plain,
! [SV45: $i] :
( ( ( ( relation_dom @ ( identity_relation @ SV45 ) )
!= SV45 )
| ( ( relation_rng @ ( identity_relation @ SV45 ) )
!= SV45 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(797,plain,
! [SV61: $i,SV46: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV46 )
| ~ ( function @ SV46 ) )
| ~ ( relation @ SV61 ) )
| ~ ( function @ SV61 ) )
| ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(798,plain,
! [SV47: $i] :
( ( ( ~ ( empty @ SV47 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV47 ) )
| ~ ( relation @ ( relation_rng @ SV47 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(799,plain,
( ( ~ ~ ( ~ ( relation @ sK11_SX0 )
| ~ ( relation_empty_yielding @ sK11_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[766]) ).
thf(800,plain,
! [SV48: $i] :
( ( ( ~ ( relation @ SV48 ) )
= $true )
| ( ( ~ ( ( ( relation_dom @ SV48 )
= empty_set )
| ( ( relation_rng @ SV48 )
= empty_set ) )
| ( SV48 = empty_set ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(801,plain,
! [SV49: $i] :
( ( ~ ( relation @ ( identity_relation @ SV49 ) )
| ~ ( function @ ( identity_relation @ SV49 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[768]) ).
thf(802,plain,
! [SV62: $i,SV50: $i] :
( ( ~ ~ ( ~ ( relation @ SV50 )
| ~ ( relation @ SV62 ) )
| ( relation @ ( set_union2 @ SV50 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(803,plain,
! [SV63: $i,SV51: $i] :
( ( ~ ~ ( ~ ( relation @ SV51 )
| ~ ( relation @ SV63 ) )
| ( relation @ ( set_intersection2 @ SV51 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(804,plain,
! [SV52: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV52 )
| ~ ( relation @ SV52 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(805,plain,
! [SV53: $i] :
( ( ( ~ ( empty @ SV53 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV53 ) )
| ~ ( relation @ ( relation_dom @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(806,plain,
( ( ~ ~ ( ~ ( empty @ sK12_SX0 )
| ~ ( relation @ sK12_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[773]) ).
thf(807,plain,
! [SV54: $i] :
( ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( ~ ( ( ( relation_rng @ SV54 )
!= ( relation_dom @ ( relation_inverse @ SV54 ) ) )
| ( ( relation_dom @ SV54 )
!= ( relation_rng @ ( relation_inverse @ SV54 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[774]) ).
thf(808,plain,
! [SV55: $i] :
( ( ( ~ ( empty @ SV55 ) )
= $true )
| ( ( function @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[775]) ).
thf(809,plain,
( ( ~ ~ ( ~ ~ ( ~ ( relation @ sK13_SX0 )
| ~ ( empty @ sK13_SX0 ) )
| ~ ( function @ sK13_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[776]) ).
thf(810,plain,
! [SV64: $i,SV56: $i] :
( ( ~ ~ ( ~ ( relation @ SV56 )
| ~ ( relation @ SV64 ) )
| ( relation @ ( relation_composition @ SV56 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(811,plain,
! [SV57: $i] :
( ( ( ~ ( relation @ SV57 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[778]) ).
thf(812,plain,
! [SV58: $i] :
( ( ( ~ ( empty @ SV58 ) )
= $true )
| ( ( relation @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(813,plain,
! [SV65: $i,SV59: $i] :
( ( ~ ( relation @ SV59 )
| ( relation @ ( relation_dom_restriction @ SV59 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(814,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
| ~ ( one_to_one @ sK8_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(815,plain,
! [SV35: $i] :
( ( ( ~ ( ~ ( relation @ SV35 )
| ~ ( function @ SV35 ) ) )
= $false )
| ( ( ~ ( one_to_one @ SV35 )
| ( ( function_inverse @ SV35 )
= ( relation_inverse @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(816,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[783]) ).
thf(817,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[784]) ).
thf(818,plain,
! [SV36: $i] :
( ( ( relation @ SV36 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV36 ) )
= SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(819,plain,
! [SV37: $i,SV60: $i] :
( ( ( ~ ( relation @ SV60 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV37 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(820,plain,
! [SV38: $i] :
( ( ( relation @ SV38 )
= $false )
| ( ( ! [SY48: $i] :
( ~ ( relation @ SY48 )
| ~ ( subset @ SV38 @ SY48 )
| ~ ( ~ ( subset @ ( relation_dom @ SV38 ) @ ( relation_dom @ SY48 ) )
| ~ ( subset @ ( relation_rng @ SV38 ) @ ( relation_rng @ SY48 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(821,plain,
! [SV39: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV39 )
| ~ ( relation @ SV39 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(822,plain,
( ( ~ ( ~ ~ ( empty @ sK9_SX0 )
| ~ ( relation @ sK9_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[789]) ).
thf(823,plain,
( ( ~ ( ~ ( relation @ sK10_SX0 )
| ~ ( function @ sK10_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[790]) ).
thf(824,plain,
! [SV40: $i] :
( ( ( ~ ( ~ ( relation @ SV40 )
| ~ ( function @ SV40 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV40 ) )
| ~ ( function @ ( function_inverse @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[791]) ).
thf(825,plain,
! [SV41: $i] :
( ( ( relation @ SV41 )
= $false )
| ( ( ( relation_image @ SV41 @ ( relation_dom @ SV41 ) )
= ( relation_rng @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(826,plain,
! [SV42: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( empty @ SV42 ) )
| ~ ( function @ SV42 ) ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
| ~ ( one_to_one @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(827,plain,
! [SV43: $i] :
( ( ( relation @ SV43 )
= $false )
| ( ( ~ ( ~ ( ( ( relation_dom @ SV43 )
!= empty_set )
| ( ( relation_rng @ SV43 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV43 )
!= empty_set )
| ( ( relation_dom @ SV43 )
= empty_set ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(828,plain,
! [SV44: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV44 )
| ~ ( function @ SV44 ) )
| ~ ( one_to_one @ SV44 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV44 ) )
| ~ ( function @ ( relation_inverse @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(829,plain,
! [SV45: $i] :
( ( ( relation_dom @ ( identity_relation @ SV45 ) )
!= SV45 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(830,plain,
! [SV45: $i] :
( ( ( relation_rng @ ( identity_relation @ SV45 ) )
!= SV45 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[796]) ).
thf(831,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV46 )
| ~ ( function @ SV46 ) )
| ~ ( relation @ SV61 ) )
| ~ ( function @ SV61 ) ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[797]) ).
thf(832,plain,
! [SV47: $i] :
( ( ( empty @ SV47 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV47 ) )
| ~ ( relation @ ( relation_rng @ SV47 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[798]) ).
thf(833,plain,
( ( ~ ( ~ ( relation @ sK11_SX0 )
| ~ ( relation_empty_yielding @ sK11_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(834,plain,
! [SV48: $i] :
( ( ( relation @ SV48 )
= $false )
| ( ( ~ ( ( ( relation_dom @ SV48 )
= empty_set )
| ( ( relation_rng @ SV48 )
= empty_set ) )
| ( SV48 = empty_set ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(835,plain,
! [SV49: $i] :
( ( ~ ( relation @ ( identity_relation @ SV49 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[801]) ).
thf(836,plain,
! [SV49: $i] :
( ( ~ ( function @ ( identity_relation @ SV49 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[801]) ).
thf(837,plain,
! [SV62: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV50 )
| ~ ( relation @ SV62 ) ) )
= $true )
| ( ( relation @ ( set_union2 @ SV50 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(838,plain,
! [SV63: $i,SV51: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV51 )
| ~ ( relation @ SV63 ) ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV51 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[803]) ).
thf(839,plain,
! [SV52: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV52 )
| ~ ( relation @ SV52 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[804]) ).
thf(840,plain,
! [SV53: $i] :
( ( ( empty @ SV53 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV53 ) )
| ~ ( relation @ ( relation_dom @ SV53 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(841,plain,
( ( ~ ( ~ ( empty @ sK12_SX0 )
| ~ ( relation @ sK12_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(842,plain,
! [SV54: $i] :
( ( ( relation @ SV54 )
= $false )
| ( ( ~ ( ( ( relation_rng @ SV54 )
!= ( relation_dom @ ( relation_inverse @ SV54 ) ) )
| ( ( relation_dom @ SV54 )
!= ( relation_rng @ ( relation_inverse @ SV54 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[807]) ).
thf(843,plain,
! [SV55: $i] :
( ( ( empty @ SV55 )
= $false )
| ( ( function @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(844,plain,
( ( ~ ( ~ ~ ( ~ ( relation @ sK13_SX0 )
| ~ ( empty @ sK13_SX0 ) )
| ~ ( function @ sK13_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[809]) ).
thf(845,plain,
! [SV64: $i,SV56: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV56 )
| ~ ( relation @ SV64 ) ) )
= $true )
| ( ( relation @ ( relation_composition @ SV56 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(846,plain,
! [SV57: $i] :
( ( ( relation @ SV57 )
= $false )
| ( ( relation @ ( relation_inverse @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[811]) ).
thf(847,plain,
! [SV58: $i] :
( ( ( empty @ SV58 )
= $false )
| ( ( relation @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(848,plain,
! [SV65: $i,SV59: $i] :
( ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( relation @ ( relation_dom_restriction @ SV59 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(849,plain,
( ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
| ~ ( one_to_one @ sK8_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[814]) ).
thf(850,plain,
! [SV35: $i] :
( ( ( ~ ( relation @ SV35 )
| ~ ( function @ SV35 ) )
= $true )
| ( ( ~ ( one_to_one @ SV35 )
| ( ( function_inverse @ SV35 )
= ( relation_inverse @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[815]) ).
thf(851,plain,
! [SV37: $i,SV60: $i] :
( ( ( relation @ SV60 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV37 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[819]) ).
thf(852,plain,
! [SV38: $i,SV66: $i] :
( ( ( ~ ( relation @ SV66 )
| ~ ( subset @ SV38 @ SV66 )
| ~ ( ~ ( subset @ ( relation_dom @ SV38 ) @ ( relation_dom @ SV66 ) )
| ~ ( subset @ ( relation_rng @ SV38 ) @ ( relation_rng @ SV66 ) ) ) )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(853,plain,
! [SV39: $i] :
( ( ( ~ ~ ( empty @ SV39 )
| ~ ( relation @ SV39 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(854,plain,
( ( ~ ~ ( empty @ sK9_SX0 )
| ~ ( relation @ sK9_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[822]) ).
thf(855,plain,
( ( ~ ( relation @ sK10_SX0 )
| ~ ( function @ sK10_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[823]) ).
thf(856,plain,
! [SV40: $i] :
( ( ( ~ ( relation @ SV40 )
| ~ ( function @ SV40 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV40 ) )
| ~ ( function @ ( function_inverse @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(857,plain,
! [SV42: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( empty @ SV42 ) )
| ~ ( function @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
| ~ ( one_to_one @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(858,plain,
! [SV43: $i] :
( ( ( ~ ( ( ( relation_dom @ SV43 )
!= empty_set )
| ( ( relation_rng @ SV43 )
= empty_set ) )
| ~ ( ( ( relation_rng @ SV43 )
!= empty_set )
| ( ( relation_dom @ SV43 )
= empty_set ) ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(859,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV44 )
| ~ ( function @ SV44 ) )
| ~ ( one_to_one @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV44 ) )
| ~ ( function @ ( relation_inverse @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[828]) ).
thf(860,plain,
! [SV45: $i] :
( ( ( relation_dom @ ( identity_relation @ SV45 ) )
= SV45 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[829]) ).
thf(861,plain,
! [SV45: $i] :
( ( ( relation_rng @ ( identity_relation @ SV45 ) )
= SV45 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[830]) ).
thf(862,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( relation @ SV46 )
| ~ ( function @ SV46 ) )
| ~ ( relation @ SV61 ) )
| ~ ( function @ SV61 ) ) )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[831]) ).
thf(863,plain,
! [SV47: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV47 ) )
| ~ ( relation @ ( relation_rng @ SV47 ) ) )
= $false )
| ( ( empty @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(864,plain,
( ( ~ ( relation @ sK11_SX0 )
| ~ ( relation_empty_yielding @ sK11_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(865,plain,
! [SV48: $i] :
( ( ( ~ ( ( ( relation_dom @ SV48 )
= empty_set )
| ( ( relation_rng @ SV48 )
= empty_set ) ) )
= $true )
| ( ( SV48 = empty_set )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[834]) ).
thf(866,plain,
! [SV49: $i] :
( ( relation @ ( identity_relation @ SV49 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[835]) ).
thf(867,plain,
! [SV49: $i] :
( ( function @ ( identity_relation @ SV49 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(868,plain,
! [SV62: $i,SV50: $i] :
( ( ( ~ ( ~ ( relation @ SV50 )
| ~ ( relation @ SV62 ) ) )
= $false )
| ( ( relation @ ( set_union2 @ SV50 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(869,plain,
! [SV63: $i,SV51: $i] :
( ( ( ~ ( ~ ( relation @ SV51 )
| ~ ( relation @ SV63 ) ) )
= $false )
| ( ( relation @ ( set_intersection2 @ SV51 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(870,plain,
! [SV52: $i] :
( ( ( ~ ~ ( empty @ SV52 )
| ~ ( relation @ SV52 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(871,plain,
! [SV53: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV53 ) )
| ~ ( relation @ ( relation_dom @ SV53 ) ) )
= $false )
| ( ( empty @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[840]) ).
thf(872,plain,
( ( ~ ( empty @ sK12_SX0 )
| ~ ( relation @ sK12_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[841]) ).
thf(873,plain,
! [SV54: $i] :
( ( ( ( ( relation_rng @ SV54 )
!= ( relation_dom @ ( relation_inverse @ SV54 ) ) )
| ( ( relation_dom @ SV54 )
!= ( relation_rng @ ( relation_inverse @ SV54 ) ) ) )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[842]) ).
thf(874,plain,
( ( ~ ~ ( ~ ( relation @ sK13_SX0 )
| ~ ( empty @ sK13_SX0 ) )
| ~ ( function @ sK13_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[844]) ).
thf(875,plain,
! [SV64: $i,SV56: $i] :
( ( ( ~ ( ~ ( relation @ SV56 )
| ~ ( relation @ SV64 ) ) )
= $false )
| ( ( relation @ ( relation_composition @ SV56 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(876,plain,
! [SV65: $i,SV59: $i] :
( ( ( relation @ SV59 )
= $false )
| ( ( relation @ ( relation_dom_restriction @ SV59 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(877,plain,
( ( ~ ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(878,plain,
( ( ~ ( one_to_one @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[849]) ).
thf(879,plain,
! [SV35: $i] :
( ( ( ~ ( relation @ SV35 ) )
= $true )
| ( ( ~ ( function @ SV35 ) )
= $true )
| ( ( ~ ( one_to_one @ SV35 )
| ( ( function_inverse @ SV35 )
= ( relation_inverse @ SV35 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(880,plain,
! [SV38: $i,SV66: $i] :
( ( ( ~ ( relation @ SV66 ) )
= $true )
| ( ( ~ ( subset @ SV38 @ SV66 )
| ~ ( ~ ( subset @ ( relation_dom @ SV38 ) @ ( relation_dom @ SV66 ) )
| ~ ( subset @ ( relation_rng @ SV38 ) @ ( relation_rng @ SV66 ) ) ) )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(881,plain,
! [SV39: $i] :
( ( ( ~ ~ ( empty @ SV39 ) )
= $true )
| ( ( ~ ( relation @ SV39 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(882,plain,
( ( ~ ~ ( empty @ sK9_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[854]) ).
thf(883,plain,
( ( ~ ( relation @ sK9_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[854]) ).
thf(884,plain,
( ( ~ ( relation @ sK10_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(885,plain,
( ( ~ ( function @ sK10_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[855]) ).
thf(886,plain,
! [SV40: $i] :
( ( ( ~ ( relation @ SV40 ) )
= $true )
| ( ( ~ ( function @ SV40 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV40 ) )
| ~ ( function @ ( function_inverse @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[856]) ).
thf(887,plain,
! [SV42: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( empty @ SV42 ) ) )
= $true )
| ( ( ~ ( function @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
| ~ ( one_to_one @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(888,plain,
! [SV43: $i] :
( ( ( ~ ( ( ( relation_dom @ SV43 )
!= empty_set )
| ( ( relation_rng @ SV43 )
= empty_set ) ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(889,plain,
! [SV43: $i] :
( ( ( ~ ( ( ( relation_rng @ SV43 )
!= empty_set )
| ( ( relation_dom @ SV43 )
= empty_set ) ) )
= $false )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[858]) ).
thf(890,plain,
! [SV44: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV44 )
| ~ ( function @ SV44 ) ) )
= $true )
| ( ( ~ ( one_to_one @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV44 ) )
| ~ ( function @ ( relation_inverse @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(891,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV46 )
| ~ ( function @ SV46 ) )
| ~ ( relation @ SV61 ) )
| ~ ( function @ SV61 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[862]) ).
thf(892,plain,
! [SV47: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV47 ) ) )
= $false )
| ( ( empty @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(893,plain,
! [SV47: $i] :
( ( ( ~ ( relation @ ( relation_rng @ SV47 ) ) )
= $false )
| ( ( empty @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[863]) ).
thf(894,plain,
( ( ~ ( relation @ sK11_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(895,plain,
( ( ~ ( relation_empty_yielding @ sK11_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[864]) ).
thf(896,plain,
! [SV48: $i] :
( ( ( ( ( relation_dom @ SV48 )
= empty_set )
| ( ( relation_rng @ SV48 )
= empty_set ) )
= $false )
| ( ( SV48 = empty_set )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(897,plain,
! [SV62: $i,SV50: $i] :
( ( ( ~ ( relation @ SV50 )
| ~ ( relation @ SV62 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV50 @ SV62 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[868]) ).
thf(898,plain,
! [SV63: $i,SV51: $i] :
( ( ( ~ ( relation @ SV51 )
| ~ ( relation @ SV63 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV51 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[869]) ).
thf(899,plain,
! [SV52: $i] :
( ( ( ~ ~ ( empty @ SV52 ) )
= $true )
| ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(900,plain,
! [SV53: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV53 ) ) )
= $false )
| ( ( empty @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[871]) ).
thf(901,plain,
! [SV53: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV53 ) ) )
= $false )
| ( ( empty @ SV53 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[871]) ).
thf(902,plain,
( ( ~ ( empty @ sK12_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[872]) ).
thf(903,plain,
( ( ~ ( relation @ sK12_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[872]) ).
thf(904,plain,
! [SV54: $i] :
( ( ( ( relation_rng @ SV54 )
!= ( relation_dom @ ( relation_inverse @ SV54 ) ) )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(905,plain,
! [SV54: $i] :
( ( ( ( relation_dom @ SV54 )
!= ( relation_rng @ ( relation_inverse @ SV54 ) ) )
= $false )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[873]) ).
thf(906,plain,
( ( ~ ~ ( ~ ( relation @ sK13_SX0 )
| ~ ( empty @ sK13_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(907,plain,
( ( ~ ( function @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[874]) ).
thf(908,plain,
! [SV64: $i,SV56: $i] :
( ( ( ~ ( relation @ SV56 )
| ~ ( relation @ SV64 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV56 @ SV64 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[875]) ).
thf(909,plain,
( ( ~ ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[877]) ).
thf(910,plain,
( ( one_to_one @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[878]) ).
thf(911,plain,
! [SV35: $i] :
( ( ( relation @ SV35 )
= $false )
| ( ( ~ ( function @ SV35 ) )
= $true )
| ( ( ~ ( one_to_one @ SV35 )
| ( ( function_inverse @ SV35 )
= ( relation_inverse @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(912,plain,
! [SV38: $i,SV66: $i] :
( ( ( relation @ SV66 )
= $false )
| ( ( ~ ( subset @ SV38 @ SV66 )
| ~ ( ~ ( subset @ ( relation_dom @ SV38 ) @ ( relation_dom @ SV66 ) )
| ~ ( subset @ ( relation_rng @ SV38 ) @ ( relation_rng @ SV66 ) ) ) )
= $true )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[880]) ).
thf(913,plain,
! [SV39: $i] :
( ( ( ~ ( empty @ SV39 ) )
= $false )
| ( ( ~ ( relation @ SV39 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(914,plain,
( ( ~ ( empty @ sK9_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[882]) ).
thf(915,plain,
( ( relation @ sK9_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[883]) ).
thf(916,plain,
( ( relation @ sK10_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[884]) ).
thf(917,plain,
( ( function @ sK10_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[885]) ).
thf(918,plain,
! [SV40: $i] :
( ( ( relation @ SV40 )
= $false )
| ( ( ~ ( function @ SV40 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV40 ) )
| ~ ( function @ ( function_inverse @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(919,plain,
! [SV42: $i] :
( ( ( ~ ( ~ ( relation @ SV42 )
| ~ ( empty @ SV42 ) ) )
= $false )
| ( ( ~ ( function @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
| ~ ( one_to_one @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(920,plain,
! [SV43: $i] :
( ( ( ( ( relation_dom @ SV43 )
!= empty_set )
| ( ( relation_rng @ SV43 )
= empty_set ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[888]) ).
thf(921,plain,
! [SV43: $i] :
( ( ( ( ( relation_rng @ SV43 )
!= empty_set )
| ( ( relation_dom @ SV43 )
= empty_set ) )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[889]) ).
thf(922,plain,
! [SV44: $i] :
( ( ( ~ ( ~ ( relation @ SV44 )
| ~ ( function @ SV44 ) ) )
= $false )
| ( ( ~ ( one_to_one @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV44 ) )
| ~ ( function @ ( relation_inverse @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(923,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( relation @ SV46 )
| ~ ( function @ SV46 ) )
| ~ ( relation @ SV61 ) ) )
= $true )
| ( ( ~ ( function @ SV61 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(924,plain,
! [SV47: $i] :
( ( ( empty @ ( relation_rng @ SV47 ) )
= $true )
| ( ( empty @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[892]) ).
thf(925,plain,
! [SV47: $i] :
( ( ( relation @ ( relation_rng @ SV47 ) )
= $true )
| ( ( empty @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[893]) ).
thf(926,plain,
( ( relation @ sK11_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[894]) ).
thf(927,plain,
( ( relation_empty_yielding @ sK11_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[895]) ).
thf(928,plain,
! [SV48: $i] :
( ( ( ( relation_dom @ SV48 )
= empty_set )
= $false )
| ( ( SV48 = empty_set )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(929,plain,
! [SV48: $i] :
( ( ( ( relation_rng @ SV48 )
= empty_set )
= $false )
| ( ( SV48 = empty_set )
= $true )
| ( ( relation @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[896]) ).
thf(930,plain,
! [SV62: $i,SV50: $i] :
( ( ( ~ ( relation @ SV50 ) )
= $true )
| ( ( ~ ( relation @ SV62 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV50 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(931,plain,
! [SV63: $i,SV51: $i] :
( ( ( ~ ( relation @ SV51 ) )
= $true )
| ( ( ~ ( relation @ SV63 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV51 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(932,plain,
! [SV52: $i] :
( ( ( ~ ( empty @ SV52 ) )
= $false )
| ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(933,plain,
! [SV53: $i] :
( ( ( empty @ ( relation_dom @ SV53 ) )
= $true )
| ( ( empty @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[900]) ).
thf(934,plain,
! [SV53: $i] :
( ( ( relation @ ( relation_dom @ SV53 ) )
= $true )
| ( ( empty @ SV53 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[901]) ).
thf(935,plain,
( ( empty @ sK12_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[902]) ).
thf(936,plain,
( ( relation @ sK12_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[903]) ).
thf(937,plain,
! [SV54: $i] :
( ( ( ( relation_rng @ SV54 )
= ( relation_dom @ ( relation_inverse @ SV54 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(938,plain,
! [SV54: $i] :
( ( ( ( relation_dom @ SV54 )
= ( relation_rng @ ( relation_inverse @ SV54 ) ) )
= $true )
| ( ( relation @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(939,plain,
( ( ~ ( ~ ( relation @ sK13_SX0 )
| ~ ( empty @ sK13_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[906]) ).
thf(940,plain,
( ( function @ sK13_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[907]) ).
thf(941,plain,
! [SV64: $i,SV56: $i] :
( ( ( ~ ( relation @ SV56 ) )
= $true )
| ( ( ~ ( relation @ SV64 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV56 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(942,plain,
( ( ~ ( relation @ sK8_SX0 )
| ~ ( function @ sK8_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(943,plain,
! [SV35: $i] :
( ( ( function @ SV35 )
= $false )
| ( ( relation @ SV35 )
= $false )
| ( ( ~ ( one_to_one @ SV35 )
| ( ( function_inverse @ SV35 )
= ( relation_inverse @ SV35 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(944,plain,
! [SV66: $i,SV38: $i] :
( ( ( ~ ( subset @ SV38 @ SV66 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV38 ) @ ( relation_dom @ SV66 ) )
| ~ ( subset @ ( relation_rng @ SV38 ) @ ( relation_rng @ SV66 ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(945,plain,
! [SV39: $i] :
( ( ( empty @ SV39 )
= $true )
| ( ( ~ ( relation @ SV39 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[913]) ).
thf(946,plain,
( ( empty @ sK9_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(947,plain,
! [SV40: $i] :
( ( ( function @ SV40 )
= $false )
| ( ( relation @ SV40 )
= $false )
| ( ( ~ ( ~ ( relation @ ( function_inverse @ SV40 ) )
| ~ ( function @ ( function_inverse @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(948,plain,
! [SV42: $i] :
( ( ( ~ ( relation @ SV42 )
| ~ ( empty @ SV42 ) )
= $true )
| ( ( ~ ( function @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
| ~ ( one_to_one @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[919]) ).
thf(949,plain,
! [SV43: $i] :
( ( ( ( relation_dom @ SV43 )
!= empty_set )
= $true )
| ( ( ( relation_rng @ SV43 )
= empty_set )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(950,plain,
! [SV43: $i] :
( ( ( ( relation_rng @ SV43 )
!= empty_set )
= $true )
| ( ( ( relation_dom @ SV43 )
= empty_set )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(951,plain,
! [SV44: $i] :
( ( ( ~ ( relation @ SV44 )
| ~ ( function @ SV44 ) )
= $true )
| ( ( ~ ( one_to_one @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV44 ) )
| ~ ( function @ ( relation_inverse @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[922]) ).
thf(952,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ( ~ ~ ( ~ ( relation @ SV46 )
| ~ ( function @ SV46 ) )
| ~ ( relation @ SV61 ) ) )
= $false )
| ( ( ~ ( function @ SV61 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(953,plain,
! [SV62: $i,SV50: $i] :
( ( ( relation @ SV50 )
= $false )
| ( ( ~ ( relation @ SV62 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV50 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(954,plain,
! [SV63: $i,SV51: $i] :
( ( ( relation @ SV51 )
= $false )
| ( ( ~ ( relation @ SV63 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV51 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[931]) ).
thf(955,plain,
! [SV52: $i] :
( ( ( empty @ SV52 )
= $true )
| ( ( ~ ( relation @ SV52 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[932]) ).
thf(956,plain,
( ( ~ ( relation @ sK13_SX0 )
| ~ ( empty @ sK13_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(957,plain,
! [SV64: $i,SV56: $i] :
( ( ( relation @ SV56 )
= $false )
| ( ( ~ ( relation @ SV64 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV56 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(958,plain,
( ( ~ ( relation @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(959,plain,
( ( ~ ( function @ sK8_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[942]) ).
thf(960,plain,
! [SV35: $i] :
( ( ( ~ ( one_to_one @ SV35 ) )
= $true )
| ( ( ( function_inverse @ SV35 )
= ( relation_inverse @ SV35 ) )
= $true )
| ( ( relation @ SV35 )
= $false )
| ( ( function @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(961,plain,
! [SV66: $i,SV38: $i] :
( ( ( subset @ SV38 @ SV66 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV38 ) @ ( relation_dom @ SV66 ) )
| ~ ( subset @ ( relation_rng @ SV38 ) @ ( relation_rng @ SV66 ) ) ) )
= $true )
| ( ( relation @ SV66 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[944]) ).
thf(962,plain,
! [SV39: $i] :
( ( ( relation @ SV39 )
= $false )
| ( ( empty @ SV39 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV39 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(963,plain,
! [SV40: $i] :
( ( ( ~ ( relation @ ( function_inverse @ SV40 ) )
| ~ ( function @ ( function_inverse @ SV40 ) ) )
= $false )
| ( ( relation @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[947]) ).
thf(964,plain,
! [SV42: $i] :
( ( ( ~ ( relation @ SV42 ) )
= $true )
| ( ( ~ ( empty @ SV42 ) )
= $true )
| ( ( ~ ( function @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
| ~ ( one_to_one @ SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(965,plain,
! [SV43: $i] :
( ( ( ( relation_dom @ SV43 )
= empty_set )
= $false )
| ( ( ( relation_rng @ SV43 )
= empty_set )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(966,plain,
! [SV43: $i] :
( ( ( ( relation_rng @ SV43 )
= empty_set )
= $false )
| ( ( ( relation_dom @ SV43 )
= empty_set )
= $true )
| ( ( relation @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(967,plain,
! [SV44: $i] :
( ( ( ~ ( relation @ SV44 ) )
= $true )
| ( ( ~ ( function @ SV44 ) )
= $true )
| ( ( ~ ( one_to_one @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV44 ) )
| ~ ( function @ ( relation_inverse @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(968,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV46 )
| ~ ( function @ SV46 ) )
| ~ ( relation @ SV61 ) )
= $true )
| ( ( ~ ( function @ SV61 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[952]) ).
thf(969,plain,
! [SV50: $i,SV62: $i] :
( ( ( relation @ SV62 )
= $false )
| ( ( relation @ SV50 )
= $false )
| ( ( relation @ ( set_union2 @ SV50 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(970,plain,
! [SV51: $i,SV63: $i] :
( ( ( relation @ SV63 )
= $false )
| ( ( relation @ SV51 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV51 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(971,plain,
! [SV52: $i] :
( ( ( relation @ SV52 )
= $false )
| ( ( empty @ SV52 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[955]) ).
thf(972,plain,
( ( ~ ( relation @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[956]) ).
thf(973,plain,
( ( ~ ( empty @ sK13_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[956]) ).
thf(974,plain,
! [SV56: $i,SV64: $i] :
( ( ( relation @ SV64 )
= $false )
| ( ( relation @ SV56 )
= $false )
| ( ( relation @ ( relation_composition @ SV56 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(975,plain,
( ( relation @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[958]) ).
thf(976,plain,
( ( function @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[959]) ).
thf(977,plain,
! [SV35: $i] :
( ( ( one_to_one @ SV35 )
= $false )
| ( ( ( function_inverse @ SV35 )
= ( relation_inverse @ SV35 ) )
= $true )
| ( ( relation @ SV35 )
= $false )
| ( ( function @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(978,plain,
! [SV66: $i,SV38: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV38 ) @ ( relation_dom @ SV66 ) )
| ~ ( subset @ ( relation_rng @ SV38 ) @ ( relation_rng @ SV66 ) ) )
= $false )
| ( ( subset @ SV38 @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[961]) ).
thf(979,plain,
! [SV39: $i] :
( ( ( empty @ ( relation_dom @ SV39 ) )
= $false )
| ( ( empty @ SV39 )
= $true )
| ( ( relation @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[962]) ).
thf(980,plain,
! [SV40: $i] :
( ( ( ~ ( relation @ ( function_inverse @ SV40 ) ) )
= $false )
| ( ( relation @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(981,plain,
! [SV40: $i] :
( ( ( ~ ( function @ ( function_inverse @ SV40 ) ) )
= $false )
| ( ( relation @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[963]) ).
thf(982,plain,
! [SV42: $i] :
( ( ( relation @ SV42 )
= $false )
| ( ( ~ ( empty @ SV42 ) )
= $true )
| ( ( ~ ( function @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
| ~ ( one_to_one @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(983,plain,
! [SV44: $i] :
( ( ( relation @ SV44 )
= $false )
| ( ( ~ ( function @ SV44 ) )
= $true )
| ( ( ~ ( one_to_one @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV44 ) )
| ~ ( function @ ( relation_inverse @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(984,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV46 )
| ~ ( function @ SV46 ) ) )
= $true )
| ( ( ~ ( relation @ SV61 ) )
= $true )
| ( ( ~ ( function @ SV61 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(985,plain,
! [SV52: $i] :
( ( ( empty @ ( relation_rng @ SV52 ) )
= $false )
| ( ( empty @ SV52 )
= $true )
| ( ( relation @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(986,plain,
( ( relation @ sK13_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[972]) ).
thf(987,plain,
( ( empty @ sK13_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[973]) ).
thf(988,plain,
! [SV66: $i,SV38: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV38 ) @ ( relation_dom @ SV66 ) ) )
= $false )
| ( ( subset @ SV38 @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[978]) ).
thf(989,plain,
! [SV66: $i,SV38: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV38 ) @ ( relation_rng @ SV66 ) ) )
= $false )
| ( ( subset @ SV38 @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[978]) ).
thf(990,plain,
! [SV40: $i] :
( ( ( relation @ ( function_inverse @ SV40 ) )
= $true )
| ( ( relation @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[980]) ).
thf(991,plain,
! [SV40: $i] :
( ( ( function @ ( function_inverse @ SV40 ) )
= $true )
| ( ( relation @ SV40 )
= $false )
| ( ( function @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[981]) ).
thf(992,plain,
! [SV42: $i] :
( ( ( empty @ SV42 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( ~ ( function @ SV42 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
| ~ ( one_to_one @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(993,plain,
! [SV44: $i] :
( ( ( function @ SV44 )
= $false )
| ( ( relation @ SV44 )
= $false )
| ( ( ~ ( one_to_one @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV44 ) )
| ~ ( function @ ( relation_inverse @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(994,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ( ~ ( relation @ SV46 )
| ~ ( function @ SV46 ) ) )
= $false )
| ( ( ~ ( relation @ SV61 ) )
= $true )
| ( ( ~ ( function @ SV61 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(995,plain,
! [SV66: $i,SV38: $i] :
( ( ( subset @ ( relation_dom @ SV38 ) @ ( relation_dom @ SV66 ) )
= $true )
| ( ( subset @ SV38 @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[988]) ).
thf(996,plain,
! [SV66: $i,SV38: $i] :
( ( ( subset @ ( relation_rng @ SV38 ) @ ( relation_rng @ SV66 ) )
= $true )
| ( ( subset @ SV38 @ SV66 )
= $false )
| ( ( relation @ SV66 )
= $false )
| ( ( relation @ SV38 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[989]) ).
thf(997,plain,
! [SV42: $i] :
( ( ( function @ SV42 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( empty @ SV42 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
| ~ ( one_to_one @ SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(998,plain,
! [SV44: $i] :
( ( ( one_to_one @ SV44 )
= $false )
| ( ( relation @ SV44 )
= $false )
| ( ( function @ SV44 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_inverse @ SV44 ) )
| ~ ( function @ ( relation_inverse @ SV44 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(999,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ( relation @ SV46 )
| ~ ( function @ SV46 ) )
= $true )
| ( ( ~ ( relation @ SV61 ) )
= $true )
| ( ( ~ ( function @ SV61 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[994]) ).
thf(1000,plain,
! [SV42: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
| ~ ( one_to_one @ SV42 ) )
= $false )
| ( ( empty @ SV42 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( function @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1001,plain,
! [SV44: $i] :
( ( ( ~ ( relation @ ( relation_inverse @ SV44 ) )
| ~ ( function @ ( relation_inverse @ SV44 ) ) )
= $false )
| ( ( function @ SV44 )
= $false )
| ( ( relation @ SV44 )
= $false )
| ( ( one_to_one @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1002,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( ~ ( function @ SV46 ) )
= $true )
| ( ( ~ ( relation @ SV61 ) )
= $true )
| ( ( ~ ( function @ SV61 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1003,plain,
! [SV42: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) ) )
= $false )
| ( ( empty @ SV42 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( function @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1000]) ).
thf(1004,plain,
! [SV42: $i] :
( ( ( ~ ( one_to_one @ SV42 ) )
= $false )
| ( ( empty @ SV42 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( function @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1000]) ).
thf(1005,plain,
! [SV44: $i] :
( ( ( ~ ( relation @ ( relation_inverse @ SV44 ) ) )
= $false )
| ( ( function @ SV44 )
= $false )
| ( ( relation @ SV44 )
= $false )
| ( ( one_to_one @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1006,plain,
! [SV44: $i] :
( ( ( ~ ( function @ ( relation_inverse @ SV44 ) ) )
= $false )
| ( ( function @ SV44 )
= $false )
| ( ( relation @ SV44 )
= $false )
| ( ( one_to_one @ SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1001]) ).
thf(1007,plain,
! [SV61: $i,SV46: $i] :
( ( ( relation @ SV46 )
= $false )
| ( ( ~ ( function @ SV46 ) )
= $true )
| ( ( ~ ( relation @ SV61 ) )
= $true )
| ( ( ~ ( function @ SV61 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1008,plain,
! [SV42: $i] :
( ( ( ~ ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) ) )
= $true )
| ( ( empty @ SV42 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( function @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1003]) ).
thf(1009,plain,
! [SV42: $i] :
( ( ( one_to_one @ SV42 )
= $true )
| ( ( empty @ SV42 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( function @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1010,plain,
! [SV44: $i] :
( ( ( relation @ ( relation_inverse @ SV44 ) )
= $true )
| ( ( function @ SV44 )
= $false )
| ( ( relation @ SV44 )
= $false )
| ( ( one_to_one @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1011,plain,
! [SV44: $i] :
( ( ( function @ ( relation_inverse @ SV44 ) )
= $true )
| ( ( function @ SV44 )
= $false )
| ( ( relation @ SV44 )
= $false )
| ( ( one_to_one @ SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1012,plain,
! [SV61: $i,SV46: $i] :
( ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( ~ ( relation @ SV61 ) )
= $true )
| ( ( ~ ( function @ SV61 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1013,plain,
! [SV42: $i] :
( ( ( ~ ( relation @ SV42 )
| ~ ( function @ SV42 ) )
= $false )
| ( ( empty @ SV42 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( function @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1014,plain,
! [SV46: $i,SV61: $i] :
( ( ( relation @ SV61 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( ~ ( function @ SV61 ) )
= $true )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1015,plain,
! [SV42: $i] :
( ( ( ~ ( relation @ SV42 ) )
= $false )
| ( ( empty @ SV42 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( function @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1013]) ).
thf(1016,plain,
! [SV42: $i] :
( ( ( ~ ( function @ SV42 ) )
= $false )
| ( ( empty @ SV42 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( function @ SV42 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1013]) ).
thf(1017,plain,
! [SV46: $i,SV61: $i] :
( ( ( function @ SV61 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV61 )
= $false )
| ( ( ~ ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1018,plain,
! [SV42: $i] :
( ( ( relation @ SV42 )
= $true )
| ( ( empty @ SV42 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( function @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1015]) ).
thf(1019,plain,
! [SV42: $i] :
( ( ( function @ SV42 )
= $true )
| ( ( empty @ SV42 )
= $false )
| ( ( relation @ SV42 )
= $false )
| ( ( function @ SV42 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1016]) ).
thf(1020,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) )
| ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) )
= $false )
| ( ( relation @ SV61 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( function @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1021,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ( relation @ ( relation_composition @ SV46 @ SV61 ) ) )
= $false )
| ( ( relation @ SV61 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( function @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1022,plain,
! [SV61: $i,SV46: $i] :
( ( ( ~ ( function @ ( relation_composition @ SV46 @ SV61 ) ) )
= $false )
| ( ( relation @ SV61 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( function @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1020]) ).
thf(1023,plain,
! [SV61: $i,SV46: $i] :
( ( ( relation @ ( relation_composition @ SV46 @ SV61 ) )
= $true )
| ( ( relation @ SV61 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( function @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1021]) ).
thf(1024,plain,
! [SV61: $i,SV46: $i] :
( ( ( function @ ( relation_composition @ SV46 @ SV61 ) )
= $true )
| ( ( relation @ SV61 )
= $false )
| ( ( relation @ SV46 )
= $false )
| ( ( function @ SV46 )
= $false )
| ( ( function @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1022]) ).
thf(1025,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[671,1024,1023,1019,1018,1011,1010,1009,996,995,991,990,987,986,985,979,977,976,975,974,970,969,966,965,946,940,938,937,936,935,934,933,929,928,927,926,925,924,917,916,915,910,876,867,866,861,860,851,847,846,843,825,818,817,816,748,747,713,712,711,694,693,688,687,685,684,683,682,681,680,679,677,676,675,674,673,672]) ).
thf(1026,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1025,659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU219+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.09 % Computer : n012.cluster.edu
% 0.00/0.09 % Model : x86_64 x86_64
% 0.00/0.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09 % Memory : 8046.5625MB
% 0.00/0.09 % OS : Linux 6.8.0-71-generic
% 0.00/0.09 % CPULimit : 300
% 0.00/0.09 % WCLimit : 300
% 0.00/0.09 % DateTime : Tue Oct 6 15:06:28 UTC 2026
% 0.00/0.09 % CPUTime :
% 0.00/0.09 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.38/0.43 .
% 1.38/0.43
% 1.38/0.43 No.of.Axioms: 51
% 1.38/0.43
% 1.38/0.43 Length.of.Defs: 0
% 1.38/0.43
% 1.38/0.43 Contains.Choice.Funs: false
% 1.38/0.43 ...................
% 1.38/0.43
% 1.38/0.43 ********************************
% 1.38/0.43 * All subproblems solved! *
% 1.38/0.43 ********************************
% 1.38/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:54,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:1025,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.38/0.43
% 1.38/0.43 %**** Beginning of derivation protocol ****
% 1.38/0.43 % SZS output start CNFRefutation
% See solution above
% 1.38/0.43
% 1.38/0.43 %**** End of derivation protocol ****
% 1.38/0.43 %**** no. of clauses in derivation: 847 ****
% 1.38/0.43 %**** clause counter: 1025 ****
% 1.38/0.43
% 1.38/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:54,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:1025,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------