%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU198+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 10:43:22 AM UTC 2026
% Result : Theorem 14.08s 2.67s
% Output : CNFRefutation 14.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 55
% Syntax : Number of formulae : 491 ( 282 unt; 0 typ; 0 def)
% Number of atoms : 2613 ( 776 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 4264 ( 850 ~; 594 |; 54 &;2656 @)
% ( 12 <=>; 98 =>; 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 : 41 ( 38 usr; 7 con; 0-3 aty)
% Number of variables : 932 ( 0 ^; 926 !; 6 ?; 932 :)
% Comments :
%------------------------------------------------------------------------------
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_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_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_field,type,
relation_field: $i > $i ).
thf(tp_relation_inverse,type,
relation_inverse: $i > $i ).
thf(tp_relation_rng,type,
relation_rng: $i > $i ).
thf(tp_relation_rng_restriction,type,
relation_rng_restriction: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY81,type,
sK2_SY81: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY133,type,
sK5_SY133: $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_meet,type,
set_meet: $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset_complement,type,
subset_complement: $i > $i > $i ).
thf(tp_subset_difference,type,
subset_difference: $i > $i > $i > $i ).
thf(tp_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(16,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(22,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(25,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(28,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
thf(33,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(35,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(50,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(56,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(59,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(60,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(61,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(62,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(63,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(65,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(66,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(67,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(68,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(70,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(71,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(72,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(73,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(74,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(75,axiom,
$true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(90,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(109,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
thf(123,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(132,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(146,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
thf(150,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(158,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(162,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(165,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(171,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(173,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
thf(191,conjecture,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
thf(192,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[191]) ).
thf(193,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ A @ B ) ) @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[192]) ).
thf(194,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(195,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(196,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(197,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(198,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(199,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(200,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(201,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(202,plain,
$true = $true,
inference(unfold_def,[status(thm)],[50]) ).
thf(203,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(204,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(205,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(206,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(207,plain,
$true = $true,
inference(unfold_def,[status(thm)],[59]) ).
thf(208,plain,
$true = $true,
inference(unfold_def,[status(thm)],[60]) ).
thf(209,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(210,plain,
$true = $true,
inference(unfold_def,[status(thm)],[62]) ).
thf(211,plain,
$true = $true,
inference(unfold_def,[status(thm)],[63]) ).
thf(212,plain,
$true = $true,
inference(unfold_def,[status(thm)],[65]) ).
thf(213,plain,
$true = $true,
inference(unfold_def,[status(thm)],[66]) ).
thf(214,plain,
$true = $true,
inference(unfold_def,[status(thm)],[67]) ).
thf(215,plain,
$true = $true,
inference(unfold_def,[status(thm)],[68]) ).
thf(216,plain,
$true = $true,
inference(unfold_def,[status(thm)],[70]) ).
thf(217,plain,
$true = $true,
inference(unfold_def,[status(thm)],[71]) ).
thf(218,plain,
$true = $true,
inference(unfold_def,[status(thm)],[72]) ).
thf(219,plain,
$true = $true,
inference(unfold_def,[status(thm)],[73]) ).
thf(220,plain,
$true = $true,
inference(unfold_def,[status(thm)],[74]) ).
thf(221,plain,
$true = $true,
inference(unfold_def,[status(thm)],[75]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(225,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(226,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(227,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(228,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(230,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(231,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(232,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(233,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(234,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(235,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(236,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(237,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(238,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(239,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(240,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)],[165]) ).
thf(241,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(242,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(243,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(245,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(246,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(247,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(248,plain,
( ( ! [SY81: $i] :
( ( relation @ SY81 )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ sK1_A @ SY81 ) ) @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[193]) ).
thf(249,plain,
( ( ( relation @ sK2_SY81 )
=> ( subset @ ( relation_rng @ ( relation_rng_restriction @ sK1_A @ sK2_SY81 ) ) @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[248]) ).
thf(250,plain,
( ( relation @ sK2_SY81 )
= $true ),
inference(standard_cnf,[status(thm)],[249]) ).
thf(251,plain,
( ( subset @ ( relation_rng @ ( relation_rng_restriction @ sK1_A @ sK2_SY81 ) ) @ sK1_A )
= $false ),
inference(standard_cnf,[status(thm)],[249]) ).
thf(252,plain,
( ( ~ ( subset @ ( relation_rng @ ( relation_rng_restriction @ sK1_A @ sK2_SY81 ) ) @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[251]) ).
thf(253,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(254,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(255,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ D ) )
=> ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(256,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(257,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(258,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(259,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(260,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)],[240]) ).
thf(261,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(263,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(264,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(265,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(266,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(267,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(268,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(269,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(270,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(271,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(272,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(273,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(274,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(275,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(276,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(277,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(278,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(279,plain,
$true = $true,
inference(copy,[status(thm)],[221]) ).
thf(280,plain,
$true = $true,
inference(copy,[status(thm)],[220]) ).
thf(281,plain,
$true = $true,
inference(copy,[status(thm)],[219]) ).
thf(282,plain,
$true = $true,
inference(copy,[status(thm)],[218]) ).
thf(283,plain,
$true = $true,
inference(copy,[status(thm)],[217]) ).
thf(284,plain,
$true = $true,
inference(copy,[status(thm)],[216]) ).
thf(285,plain,
$true = $true,
inference(copy,[status(thm)],[215]) ).
thf(286,plain,
$true = $true,
inference(copy,[status(thm)],[214]) ).
thf(287,plain,
$true = $true,
inference(copy,[status(thm)],[213]) ).
thf(288,plain,
$true = $true,
inference(copy,[status(thm)],[212]) ).
thf(289,plain,
$true = $true,
inference(copy,[status(thm)],[211]) ).
thf(290,plain,
$true = $true,
inference(copy,[status(thm)],[210]) ).
thf(291,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(292,plain,
$true = $true,
inference(copy,[status(thm)],[208]) ).
thf(293,plain,
$true = $true,
inference(copy,[status(thm)],[207]) ).
thf(294,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(295,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(296,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(297,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(298,plain,
$true = $true,
inference(copy,[status(thm)],[202]) ).
thf(299,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(300,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(301,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(302,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(303,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(304,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(305,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(306,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(307,plain,
( ( relation @ sK2_SY81 )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(308,plain,
( ( ~ ( subset @ ( relation_rng @ ( relation_rng_restriction @ sK1_A @ sK2_SY81 ) ) @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(309,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)],[260]) ).
thf(310,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ! [SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_composition @ SX0 @ SX1 ) ) @ ( relation_rng @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(311,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX3 ) )
| ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(312,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( proper_subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( ( SX0 != SX1 ) ) )
| ( proper_subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(313,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(314,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( proper_subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(315,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(316,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(317,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(318,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SX0 @ SX2 ) @ ( cartesian_product2 @ SX1 @ SX2 ) )
| ~ ( subset @ ( cartesian_product2 @ SX2 @ SX0 ) @ ( cartesian_product2 @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(319,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_intersection2 @ SX0 @ SX2 ) @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(320,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SX1 @ SX0 ) ) @ ( relation_rng @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(321,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( disjoint @ SX1 @ SX2 ) )
| ( disjoint @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(322,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(323,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(324,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(325,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX0 @ SX2 ) )
| ( subset @ SX0 @ ( set_intersection2 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(326,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(327,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( relation @ SX2 )
| ~ ( ~ ( ~ ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX0 @ ( relation_rng @ SX2 ) ) )
| ( in @ SX0 @ ( relation_rng @ ( relation_rng_restriction @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(328,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(329,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX2 @ SX1 ) )
| ( subset @ ( set_union2 @ SX0 @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(330,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_inverse @ ( relation_inverse @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(331,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(332,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(333,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(334,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(335,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(336,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(337,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( set_difference @ SX0 @ SX2 ) @ ( set_difference @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(338,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( relation @ ( relation_rng_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(339,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(340,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom_restriction @ SX1 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(341,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_rng @ SX0 ) )
| ~ ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(342,plain,
! [SV1: $i] :
( ( ! [SY82: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY82 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(343,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(344,plain,
! [SV3: $i] :
( ( ! [SY83: $i] : ( subset @ ( set_difference @ SV3 @ SY83 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(345,plain,
! [SV4: $i] :
( ( ! [SY84: $i] : ( subset @ SV4 @ ( set_union2 @ SV4 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(346,plain,
! [SV5: $i] :
( ( relation @ ( identity_relation @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(347,plain,
! [SV6: $i] :
( ( ! [SY85: $i] : ( subset @ SV6 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(348,plain,
( ( subset @ ( relation_rng @ ( relation_rng_restriction @ sK1_A @ sK2_SY81 ) ) @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(349,plain,
! [SV7: $i] :
( ( ~ ( relation @ SV7 )
| ! [SY86: $i] :
( ~ ( relation @ SY86 )
| ~ ( subset @ SV7 @ SY86 )
| ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SY86 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SY86 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(350,plain,
! [SV8: $i] :
( ( ~ ( relation @ SV8 )
| ! [SY87: $i] :
( ~ ( relation @ SY87 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV8 @ SY87 ) ) @ ( relation_rng @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(351,plain,
! [SV9: $i] :
( ( ! [SY88: $i,SY89: $i,SY90: $i] :
( ~ ~ ( ~ ( subset @ SV9 @ SY88 )
| ~ ( subset @ SY89 @ SY90 ) )
| ( subset @ ( cartesian_product2 @ SV9 @ SY89 ) @ ( cartesian_product2 @ SY88 @ SY90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(352,plain,
! [SV10: $i] :
( ( ! [SY91: $i] :
~ ( ~ ( ~ ( proper_subset @ SV10 @ SY91 )
| ~ ( ~ ( subset @ SV10 @ SY91 )
| ~ ( ( SV10 != SY91 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV10 @ SY91 )
| ~ ( ( SV10 != SY91 ) ) )
| ( proper_subset @ SV10 @ SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(353,plain,
! [SV11: $i] :
( ( ! [SY92: $i] :
( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( relation @ SY92 ) )
| ( relation @ ( set_union2 @ SV11 @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(354,plain,
! [SV12: $i] :
( ( ! [SY93: $i] :
~ ~ ( ~ ( subset @ SV12 @ SY93 )
| ~ ( proper_subset @ SY93 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(355,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(356,plain,
! [SV13: $i] :
( ( ! [SY94: $i] :
( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( relation @ SY94 ) )
| ( relation @ ( set_intersection2 @ SV13 @ SY94 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(357,plain,
! [SV14: $i] :
( ( ~ ( subset @ SV14 @ empty_set )
| ( SV14 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(358,plain,
! [SV15: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ~ ( subset @ SV15 @ SY95 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV15 @ SY96 ) @ ( cartesian_product2 @ SY95 @ SY96 ) )
| ~ ( subset @ ( cartesian_product2 @ SY96 @ SV15 ) @ ( cartesian_product2 @ SY96 @ SY95 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(359,plain,
! [SV16: $i] :
( ( ! [SY97: $i,SY98: $i] :
( ~ ( subset @ SV16 @ SY97 )
| ( subset @ ( set_intersection2 @ SV16 @ SY98 ) @ ( set_intersection2 @ SY97 @ SY98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(360,plain,
! [SV17: $i] :
( ( ! [SY99: $i] :
( ~ ( relation @ SY99 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY99 @ SV17 ) ) @ ( relation_rng @ SY99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(361,plain,
! [SV18: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ~ ~ ( ~ ( subset @ SV18 @ SY100 )
| ~ ( disjoint @ SY100 @ SY101 ) )
| ( disjoint @ SV18 @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(362,plain,
! [SV19: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ~ ~ ( ~ ( subset @ SV19 @ SY102 )
| ~ ( subset @ SY102 @ SY103 ) )
| ( subset @ SV19 @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(363,plain,
! [SV20: $i] :
( ( ! [SY104: $i] :
( ~ ( relation @ SV20 )
| ( relation @ ( relation_dom_restriction @ SV20 @ SY104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(364,plain,
! [SV21: $i] :
( ( ~ ( empty @ SV21 )
| ( relation @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(365,plain,
! [SV22: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ~ ~ ( ~ ( subset @ SV22 @ SY105 )
| ~ ( subset @ SV22 @ SY106 ) )
| ( subset @ SV22 @ ( set_intersection2 @ SY105 @ SY106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(366,plain,
! [SV23: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV23 )
| ~ ( relation @ SV23 ) )
| ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(367,plain,
! [SV24: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ~ ( relation @ SY108 )
| ~ ( ~ ( ~ ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SY107 @ SY108 ) ) )
| ~ ( ~ ( in @ SV24 @ SY107 )
| ~ ( in @ SV24 @ ( relation_rng @ SY108 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV24 @ SY107 )
| ~ ( in @ SV24 @ ( relation_rng @ SY108 ) ) )
| ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SY107 @ SY108 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(368,plain,
! [SV25: $i] :
( ( ! [SY109: $i] :
( ~ ( subset @ SV25 @ SY109 )
| ( ( set_union2 @ SV25 @ SY109 )
= SY109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(369,plain,
! [SV26: $i] :
( ( ! [SY110: $i,SY111: $i] :
( ~ ~ ( ~ ( subset @ SV26 @ SY110 )
| ~ ( subset @ SY111 @ SY110 ) )
| ( subset @ ( set_union2 @ SV26 @ SY111 ) @ SY110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(370,plain,
! [SV27: $i] :
( ( ~ ( relation @ SV27 )
| ( ( relation_inverse @ ( relation_inverse @ SV27 ) )
= SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(371,plain,
! [SV28: $i] :
( ( ! [SY112: $i] :
( ~ ( subset @ ( singleton @ SV28 ) @ ( singleton @ SY112 ) )
| ( SV28 = SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(372,plain,
! [SV29: $i] :
( ( ~ ( relation @ SV29 )
| ( relation @ ( relation_inverse @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(373,plain,
! [SV30: $i] :
( ( ! [SY113: $i] :
~ ( ~ ( ~ ( subset @ SV30 @ SY113 )
| ! [SY114: $i] :
( ~ ( in @ SY114 @ SV30 )
| ( in @ SY114 @ SY113 ) ) )
| ~ ( ~ ! [SY115: $i] :
( ~ ( in @ SY115 @ SV30 )
| ( in @ SY115 @ SY113 ) )
| ( subset @ SV30 @ SY113 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(374,plain,
! [SV31: $i] :
( ( ! [SY116: $i] :
( ~ ~ ( ~ ( relation @ SV31 )
| ~ ( relation @ SY116 ) )
| ( relation @ ( relation_composition @ SV31 @ SY116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(375,plain,
! [SV32: $i] :
( ( ! [SY117: $i] :
~ ( ~ ( ( SV32 != SY117 )
| ~ ( ~ ( subset @ SV32 @ SY117 )
| ~ ( subset @ SY117 @ SV32 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV32 @ SY117 )
| ~ ( subset @ SY117 @ SV32 ) )
| ( SV32 = SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(376,plain,
! [SV33: $i] :
( ( ! [SY118: $i] :
( ~ ( subset @ SV33 @ SY118 )
| ( ( set_intersection2 @ SV33 @ SY118 )
= SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(377,plain,
! [SV34: $i] :
( ( ! [SY119: $i,SY120: $i] :
( ~ ( subset @ SV34 @ SY119 )
| ( subset @ ( set_difference @ SV34 @ SY120 ) @ ( set_difference @ SY119 @ SY120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(378,plain,
! [SV35: $i] :
( ( ! [SY121: $i] :
( ~ ( relation @ SY121 )
| ( relation @ ( relation_rng_restriction @ SV35 @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(379,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(380,plain,
! [SV36: $i] :
( ( ! [SY122: $i] :
( ~ ( relation @ SY122 )
| ( subset @ ( relation_dom_restriction @ SY122 @ SV36 ) @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(381,plain,
! [SV37: $i] :
( ( ~ ( empty @ SV37 )
| ~ ( ~ ( empty @ ( relation_rng @ SV37 ) )
| ~ ( relation @ ( relation_rng @ SV37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(382,plain,
! [SV38: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV38 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(383,plain,
! [SV39: $i,SV3: $i] :
( ( subset @ ( set_difference @ SV3 @ SV39 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(384,plain,
! [SV40: $i,SV4: $i] :
( ( subset @ SV4 @ ( set_union2 @ SV4 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(385,plain,
! [SV6: $i] :
( ( subset @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(386,plain,
! [SV7: $i] :
( ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( ! [SY86: $i] :
( ~ ( relation @ SY86 )
| ~ ( subset @ SV7 @ SY86 )
| ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SY86 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SY86 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(387,plain,
! [SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ! [SY87: $i] :
( ~ ( relation @ SY87 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV8 @ SY87 ) ) @ ( relation_rng @ SY87 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(388,plain,
! [SV42: $i,SV9: $i] :
( ( ! [SY123: $i,SY124: $i] :
( ~ ~ ( ~ ( subset @ SV9 @ SV42 )
| ~ ( subset @ SY123 @ SY124 ) )
| ( subset @ ( cartesian_product2 @ SV9 @ SY123 ) @ ( cartesian_product2 @ SV42 @ SY124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(389,plain,
! [SV43: $i,SV10: $i] :
( ( ~ ( ~ ( ~ ( proper_subset @ SV10 @ SV43 )
| ~ ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) )
| ( proper_subset @ SV10 @ SV43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(390,plain,
! [SV44: $i,SV11: $i] :
( ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( relation @ SV44 ) )
| ( relation @ ( set_union2 @ SV11 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(391,plain,
! [SV45: $i,SV12: $i] :
( ( ~ ~ ( ~ ( subset @ SV12 @ SV45 )
| ~ ( proper_subset @ SV45 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(392,plain,
( ( ~ ~ ( ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[355]) ).
thf(393,plain,
! [SV46: $i,SV13: $i] :
( ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( relation @ SV46 ) )
| ( relation @ ( set_intersection2 @ SV13 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(394,plain,
! [SV14: $i] :
( ( ( ~ ( subset @ SV14 @ empty_set ) )
= $true )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(395,plain,
! [SV47: $i,SV15: $i] :
( ( ! [SY125: $i] :
( ~ ( subset @ SV15 @ SV47 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV15 @ SY125 ) @ ( cartesian_product2 @ SV47 @ SY125 ) )
| ~ ( subset @ ( cartesian_product2 @ SY125 @ SV15 ) @ ( cartesian_product2 @ SY125 @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(396,plain,
! [SV48: $i,SV16: $i] :
( ( ! [SY126: $i] :
( ~ ( subset @ SV16 @ SV48 )
| ( subset @ ( set_intersection2 @ SV16 @ SY126 ) @ ( set_intersection2 @ SV48 @ SY126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(397,plain,
! [SV17: $i,SV49: $i] :
( ( ~ ( relation @ SV49 )
| ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV49 @ SV17 ) ) @ ( relation_rng @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(398,plain,
! [SV50: $i,SV18: $i] :
( ( ! [SY127: $i] :
( ~ ~ ( ~ ( subset @ SV18 @ SV50 )
| ~ ( disjoint @ SV50 @ SY127 ) )
| ( disjoint @ SV18 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(399,plain,
! [SV51: $i,SV19: $i] :
( ( ! [SY128: $i] :
( ~ ~ ( ~ ( subset @ SV19 @ SV51 )
| ~ ( subset @ SV51 @ SY128 ) )
| ( subset @ SV19 @ SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(400,plain,
! [SV52: $i,SV20: $i] :
( ( ~ ( relation @ SV20 )
| ( relation @ ( relation_dom_restriction @ SV20 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(401,plain,
! [SV21: $i] :
( ( ( ~ ( empty @ SV21 ) )
= $true )
| ( ( relation @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(402,plain,
! [SV53: $i,SV22: $i] :
( ( ! [SY129: $i] :
( ~ ~ ( ~ ( subset @ SV22 @ SV53 )
| ~ ( subset @ SV22 @ SY129 ) )
| ( subset @ SV22 @ ( set_intersection2 @ SV53 @ SY129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(403,plain,
! [SV23: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV23 )
| ~ ( relation @ SV23 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(404,plain,
! [SV54: $i,SV24: $i] :
( ( ! [SY130: $i] :
( ~ ( relation @ SY130 )
| ~ ( ~ ( ~ ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SY130 ) ) )
| ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SY130 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SY130 ) ) )
| ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SY130 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(405,plain,
! [SV55: $i,SV25: $i] :
( ( ~ ( subset @ SV25 @ SV55 )
| ( ( set_union2 @ SV25 @ SV55 )
= SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(406,plain,
! [SV56: $i,SV26: $i] :
( ( ! [SY131: $i] :
( ~ ~ ( ~ ( subset @ SV26 @ SV56 )
| ~ ( subset @ SY131 @ SV56 ) )
| ( subset @ ( set_union2 @ SV26 @ SY131 ) @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(407,plain,
! [SV27: $i] :
( ( ( ~ ( relation @ SV27 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV27 ) )
= SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(408,plain,
! [SV57: $i,SV28: $i] :
( ( ~ ( subset @ ( singleton @ SV28 ) @ ( singleton @ SV57 ) )
| ( SV28 = SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(409,plain,
! [SV29: $i] :
( ( ( ~ ( relation @ SV29 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(410,plain,
! [SV58: $i,SV30: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV30 @ SV58 )
| ! [SY132: $i] :
( ~ ( in @ SY132 @ SV30 )
| ( in @ SY132 @ SV58 ) ) )
| ~ ( ~ ! [SY133: $i] :
( ~ ( in @ SY133 @ SV30 )
| ( in @ SY133 @ SV58 ) )
| ( subset @ SV30 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(411,plain,
! [SV59: $i,SV31: $i] :
( ( ~ ~ ( ~ ( relation @ SV31 )
| ~ ( relation @ SV59 ) )
| ( relation @ ( relation_composition @ SV31 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(412,plain,
! [SV60: $i,SV32: $i] :
( ( ~ ( ~ ( ( SV32 != SV60 )
| ~ ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) )
| ( SV32 = SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(413,plain,
! [SV61: $i,SV33: $i] :
( ( ~ ( subset @ SV33 @ SV61 )
| ( ( set_intersection2 @ SV33 @ SV61 )
= SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(414,plain,
! [SV62: $i,SV34: $i] :
( ( ! [SY134: $i] :
( ~ ( subset @ SV34 @ SV62 )
| ( subset @ ( set_difference @ SV34 @ SY134 ) @ ( set_difference @ SV62 @ SY134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(415,plain,
! [SV35: $i,SV63: $i] :
( ( ~ ( relation @ SV63 )
| ( relation @ ( relation_rng_restriction @ SV35 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(416,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[379]) ).
thf(417,plain,
! [SV36: $i,SV64: $i] :
( ( ~ ( relation @ SV64 )
| ( subset @ ( relation_dom_restriction @ SV64 @ SV36 ) @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(418,plain,
! [SV37: $i] :
( ( ( ~ ( empty @ SV37 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV37 ) )
| ~ ( relation @ ( relation_rng @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(419,plain,
! [SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( ! [SY86: $i] :
( ~ ( relation @ SY86 )
| ~ ( subset @ SV7 @ SY86 )
| ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SY86 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SY86 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(420,plain,
! [SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ! [SY87: $i] :
( ~ ( relation @ SY87 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV8 @ SY87 ) ) @ ( relation_rng @ SY87 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(421,plain,
! [SV65: $i,SV42: $i,SV9: $i] :
( ( ! [SY135: $i] :
( ~ ~ ( ~ ( subset @ SV9 @ SV42 )
| ~ ( subset @ SV65 @ SY135 ) )
| ( subset @ ( cartesian_product2 @ SV9 @ SV65 ) @ ( cartesian_product2 @ SV42 @ SY135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(422,plain,
! [SV43: $i,SV10: $i] :
( ( ~ ( ~ ( proper_subset @ SV10 @ SV43 )
| ~ ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) )
| ( proper_subset @ SV10 @ SV43 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(423,plain,
! [SV44: $i,SV11: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV11 )
| ~ ( relation @ SV44 ) ) )
= $true )
| ( ( relation @ ( set_union2 @ SV11 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(424,plain,
! [SV45: $i,SV12: $i] :
( ( ~ ( ~ ( subset @ SV12 @ SV45 )
| ~ ( proper_subset @ SV45 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(425,plain,
( ( ~ ( ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[392]) ).
thf(426,plain,
! [SV46: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV13 )
| ~ ( relation @ SV46 ) ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV13 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(427,plain,
! [SV14: $i] :
( ( ( subset @ SV14 @ empty_set )
= $false )
| ( ( SV14 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(428,plain,
! [SV66: $i,SV47: $i,SV15: $i] :
( ( ~ ( subset @ SV15 @ SV47 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV15 @ SV66 ) @ ( cartesian_product2 @ SV47 @ SV66 ) )
| ~ ( subset @ ( cartesian_product2 @ SV66 @ SV15 ) @ ( cartesian_product2 @ SV66 @ SV47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(429,plain,
! [SV67: $i,SV48: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV48 )
| ( subset @ ( set_intersection2 @ SV16 @ SV67 ) @ ( set_intersection2 @ SV48 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(430,plain,
! [SV17: $i,SV49: $i] :
( ( ( ~ ( relation @ SV49 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV49 @ SV17 ) ) @ ( relation_rng @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(431,plain,
! [SV68: $i,SV50: $i,SV18: $i] :
( ( ~ ~ ( ~ ( subset @ SV18 @ SV50 )
| ~ ( disjoint @ SV50 @ SV68 ) )
| ( disjoint @ SV18 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(432,plain,
! [SV69: $i,SV51: $i,SV19: $i] :
( ( ~ ~ ( ~ ( subset @ SV19 @ SV51 )
| ~ ( subset @ SV51 @ SV69 ) )
| ( subset @ SV19 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(433,plain,
! [SV52: $i,SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( relation @ ( relation_dom_restriction @ SV20 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(434,plain,
! [SV21: $i] :
( ( ( empty @ SV21 )
= $false )
| ( ( relation @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(435,plain,
! [SV70: $i,SV53: $i,SV22: $i] :
( ( ~ ~ ( ~ ( subset @ SV22 @ SV53 )
| ~ ( subset @ SV22 @ SV70 ) )
| ( subset @ SV22 @ ( set_intersection2 @ SV53 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(436,plain,
! [SV23: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV23 )
| ~ ( relation @ SV23 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(437,plain,
! [SV54: $i,SV24: $i,SV71: $i] :
( ( ~ ( relation @ SV71 )
| ~ ( ~ ( ~ ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
| ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) )
| ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(438,plain,
! [SV55: $i,SV25: $i] :
( ( ( ~ ( subset @ SV25 @ SV55 ) )
= $true )
| ( ( ( set_union2 @ SV25 @ SV55 )
= SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(439,plain,
! [SV72: $i,SV56: $i,SV26: $i] :
( ( ~ ~ ( ~ ( subset @ SV26 @ SV56 )
| ~ ( subset @ SV72 @ SV56 ) )
| ( subset @ ( set_union2 @ SV26 @ SV72 ) @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(440,plain,
! [SV27: $i] :
( ( ( relation @ SV27 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV27 ) )
= SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(441,plain,
! [SV57: $i,SV28: $i] :
( ( ( ~ ( subset @ ( singleton @ SV28 ) @ ( singleton @ SV57 ) ) )
= $true )
| ( ( SV28 = SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(442,plain,
! [SV29: $i] :
( ( ( relation @ SV29 )
= $false )
| ( ( relation @ ( relation_inverse @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(443,plain,
! [SV58: $i,SV30: $i] :
( ( ~ ( ~ ( subset @ SV30 @ SV58 )
| ! [SY132: $i] :
( ~ ( in @ SY132 @ SV30 )
| ( in @ SY132 @ SV58 ) ) )
| ~ ( ~ ! [SY133: $i] :
( ~ ( in @ SY133 @ SV30 )
| ( in @ SY133 @ SV58 ) )
| ( subset @ SV30 @ SV58 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(444,plain,
! [SV59: $i,SV31: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV31 )
| ~ ( relation @ SV59 ) ) )
= $true )
| ( ( relation @ ( relation_composition @ SV31 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(445,plain,
! [SV60: $i,SV32: $i] :
( ( ~ ( ( SV32 != SV60 )
| ~ ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) )
| ( SV32 = SV60 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(446,plain,
! [SV61: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV61 ) )
= $true )
| ( ( ( set_intersection2 @ SV33 @ SV61 )
= SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(447,plain,
! [SV73: $i,SV62: $i,SV34: $i] :
( ( ~ ( subset @ SV34 @ SV62 )
| ( subset @ ( set_difference @ SV34 @ SV73 ) @ ( set_difference @ SV62 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(448,plain,
! [SV35: $i,SV63: $i] :
( ( ( ~ ( relation @ SV63 ) )
= $true )
| ( ( relation @ ( relation_rng_restriction @ SV35 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(449,plain,
( ( ~ ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(450,plain,
! [SV36: $i,SV64: $i] :
( ( ( ~ ( relation @ SV64 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV64 @ SV36 ) @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(451,plain,
! [SV37: $i] :
( ( ( empty @ SV37 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV37 ) )
| ~ ( relation @ ( relation_rng @ SV37 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(452,plain,
! [SV7: $i,SV74: $i] :
( ( ( ~ ( relation @ SV74 )
| ~ ( subset @ SV7 @ SV74 )
| ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV74 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV74 ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(453,plain,
! [SV8: $i,SV75: $i] :
( ( ( ~ ( relation @ SV75 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV8 @ SV75 ) ) @ ( relation_rng @ SV75 ) ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(454,plain,
! [SV76: $i,SV65: $i,SV42: $i,SV9: $i] :
( ( ~ ~ ( ~ ( subset @ SV9 @ SV42 )
| ~ ( subset @ SV65 @ SV76 ) )
| ( subset @ ( cartesian_product2 @ SV9 @ SV65 ) @ ( cartesian_product2 @ SV42 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(455,plain,
! [SV43: $i,SV10: $i] :
( ( ~ ( ~ ( proper_subset @ SV10 @ SV43 )
| ~ ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(456,plain,
! [SV43: $i,SV10: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) )
| ( proper_subset @ SV10 @ SV43 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(457,plain,
! [SV44: $i,SV11: $i] :
( ( ( ~ ( ~ ( relation @ SV11 )
| ~ ( relation @ SV44 ) ) )
= $false )
| ( ( relation @ ( set_union2 @ SV11 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(458,plain,
! [SV45: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV45 )
| ~ ( proper_subset @ SV45 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[424]) ).
thf(459,plain,
( ( ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(460,plain,
! [SV46: $i,SV13: $i] :
( ( ( ~ ( ~ ( relation @ SV13 )
| ~ ( relation @ SV46 ) ) )
= $false )
| ( ( relation @ ( set_intersection2 @ SV13 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(461,plain,
! [SV66: $i,SV47: $i,SV15: $i] :
( ( ( ~ ( subset @ SV15 @ SV47 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( cartesian_product2 @ SV15 @ SV66 ) @ ( cartesian_product2 @ SV47 @ SV66 ) )
| ~ ( subset @ ( cartesian_product2 @ SV66 @ SV15 ) @ ( cartesian_product2 @ SV66 @ SV47 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(462,plain,
! [SV67: $i,SV48: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV48 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV16 @ SV67 ) @ ( set_intersection2 @ SV48 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(463,plain,
! [SV17: $i,SV49: $i] :
( ( ( relation @ SV49 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_dom_restriction @ SV49 @ SV17 ) ) @ ( relation_rng @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(464,plain,
! [SV68: $i,SV50: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV18 @ SV50 )
| ~ ( disjoint @ SV50 @ SV68 ) ) )
= $true )
| ( ( disjoint @ SV18 @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(465,plain,
! [SV69: $i,SV51: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV19 @ SV51 )
| ~ ( subset @ SV51 @ SV69 ) ) )
= $true )
| ( ( subset @ SV19 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(466,plain,
! [SV52: $i,SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( relation @ ( relation_dom_restriction @ SV20 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(467,plain,
! [SV70: $i,SV53: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV22 @ SV53 )
| ~ ( subset @ SV22 @ SV70 ) ) )
= $true )
| ( ( subset @ SV22 @ ( set_intersection2 @ SV53 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[435]) ).
thf(468,plain,
! [SV23: $i] :
( ( ( ~ ~ ( empty @ SV23 )
| ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(469,plain,
! [SV54: $i,SV24: $i,SV71: $i] :
( ( ( ~ ( relation @ SV71 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
| ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) )
| ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[437]) ).
thf(470,plain,
! [SV55: $i,SV25: $i] :
( ( ( subset @ SV25 @ SV55 )
= $false )
| ( ( ( set_union2 @ SV25 @ SV55 )
= SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(471,plain,
! [SV72: $i,SV56: $i,SV26: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV26 @ SV56 )
| ~ ( subset @ SV72 @ SV56 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV26 @ SV72 ) @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(472,plain,
! [SV57: $i,SV28: $i] :
( ( ( subset @ ( singleton @ SV28 ) @ ( singleton @ SV57 ) )
= $false )
| ( ( SV28 = SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(473,plain,
! [SV58: $i,SV30: $i] :
( ( ~ ( ~ ( subset @ SV30 @ SV58 )
| ! [SY132: $i] :
( ~ ( in @ SY132 @ SV30 )
| ( in @ SY132 @ SV58 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(474,plain,
! [SV58: $i,SV30: $i] :
( ( ~ ( ~ ! [SY133: $i] :
( ~ ( in @ SY133 @ SV30 )
| ( in @ SY133 @ SV58 ) )
| ( subset @ SV30 @ SV58 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[443]) ).
thf(475,plain,
! [SV59: $i,SV31: $i] :
( ( ( ~ ( ~ ( relation @ SV31 )
| ~ ( relation @ SV59 ) ) )
= $false )
| ( ( relation @ ( relation_composition @ SV31 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(476,plain,
! [SV60: $i,SV32: $i] :
( ( ~ ( ( SV32 != SV60 )
| ~ ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(477,plain,
! [SV60: $i,SV32: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) )
| ( SV32 = SV60 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[445]) ).
thf(478,plain,
! [SV61: $i,SV33: $i] :
( ( ( subset @ SV33 @ SV61 )
= $false )
| ( ( ( set_intersection2 @ SV33 @ SV61 )
= SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(479,plain,
! [SV73: $i,SV62: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV62 ) )
= $true )
| ( ( subset @ ( set_difference @ SV34 @ SV73 ) @ ( set_difference @ SV62 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(480,plain,
! [SV35: $i,SV63: $i] :
( ( ( relation @ SV63 )
= $false )
| ( ( relation @ ( relation_rng_restriction @ SV35 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(481,plain,
( ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(482,plain,
! [SV36: $i,SV64: $i] :
( ( ( relation @ SV64 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV64 @ SV36 ) @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[450]) ).
thf(483,plain,
! [SV37: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV37 ) )
| ~ ( relation @ ( relation_rng @ SV37 ) ) )
= $false )
| ( ( empty @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[451]) ).
thf(484,plain,
! [SV7: $i,SV74: $i] :
( ( ( ~ ( relation @ SV74 ) )
= $true )
| ( ( ~ ( subset @ SV7 @ SV74 )
| ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV74 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV74 ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(485,plain,
! [SV8: $i,SV75: $i] :
( ( ( ~ ( relation @ SV75 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV8 @ SV75 ) ) @ ( relation_rng @ SV75 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(486,plain,
! [SV76: $i,SV65: $i,SV42: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV9 @ SV42 )
| ~ ( subset @ SV65 @ SV76 ) ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV9 @ SV65 ) @ ( cartesian_product2 @ SV42 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(487,plain,
! [SV43: $i,SV10: $i] :
( ( ~ ( proper_subset @ SV10 @ SV43 )
| ~ ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[455]) ).
thf(488,plain,
! [SV43: $i,SV10: $i] :
( ( ~ ~ ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) )
| ( proper_subset @ SV10 @ SV43 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[456]) ).
thf(489,plain,
! [SV44: $i,SV11: $i] :
( ( ( ~ ( relation @ SV11 )
| ~ ( relation @ SV44 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV11 @ SV44 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(490,plain,
! [SV45: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV45 ) )
= $true )
| ( ( ~ ( proper_subset @ SV45 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(491,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(492,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[459]) ).
thf(493,plain,
! [SV46: $i,SV13: $i] :
( ( ( ~ ( relation @ SV13 )
| ~ ( relation @ SV46 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV13 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(494,plain,
! [SV66: $i,SV47: $i,SV15: $i] :
( ( ( subset @ SV15 @ SV47 )
= $false )
| ( ( ~ ( ~ ( subset @ ( cartesian_product2 @ SV15 @ SV66 ) @ ( cartesian_product2 @ SV47 @ SV66 ) )
| ~ ( subset @ ( cartesian_product2 @ SV66 @ SV15 ) @ ( cartesian_product2 @ SV66 @ SV47 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(495,plain,
! [SV67: $i,SV48: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV48 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV16 @ SV67 ) @ ( set_intersection2 @ SV48 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(496,plain,
! [SV68: $i,SV50: $i,SV18: $i] :
( ( ( ~ ( ~ ( subset @ SV18 @ SV50 )
| ~ ( disjoint @ SV50 @ SV68 ) ) )
= $false )
| ( ( disjoint @ SV18 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(497,plain,
! [SV69: $i,SV51: $i,SV19: $i] :
( ( ( ~ ( ~ ( subset @ SV19 @ SV51 )
| ~ ( subset @ SV51 @ SV69 ) ) )
= $false )
| ( ( subset @ SV19 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(498,plain,
! [SV70: $i,SV53: $i,SV22: $i] :
( ( ( ~ ( ~ ( subset @ SV22 @ SV53 )
| ~ ( subset @ SV22 @ SV70 ) ) )
= $false )
| ( ( subset @ SV22 @ ( set_intersection2 @ SV53 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(499,plain,
! [SV23: $i] :
( ( ( ~ ~ ( empty @ SV23 ) )
= $true )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(500,plain,
! [SV54: $i,SV24: $i,SV71: $i] :
( ( ( relation @ SV71 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
| ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) )
| ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(501,plain,
! [SV72: $i,SV56: $i,SV26: $i] :
( ( ( ~ ( ~ ( subset @ SV26 @ SV56 )
| ~ ( subset @ SV72 @ SV56 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV26 @ SV72 ) @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(502,plain,
! [SV58: $i,SV30: $i] :
( ( ~ ( subset @ SV30 @ SV58 )
| ! [SY132: $i] :
( ~ ( in @ SY132 @ SV30 )
| ( in @ SY132 @ SV58 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(503,plain,
! [SV58: $i,SV30: $i] :
( ( ~ ! [SY133: $i] :
( ~ ( in @ SY133 @ SV30 )
| ( in @ SY133 @ SV58 ) )
| ( subset @ SV30 @ SV58 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(504,plain,
! [SV59: $i,SV31: $i] :
( ( ( ~ ( relation @ SV31 )
| ~ ( relation @ SV59 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV31 @ SV59 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(505,plain,
! [SV60: $i,SV32: $i] :
( ( ( SV32 != SV60 )
| ~ ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(506,plain,
! [SV60: $i,SV32: $i] :
( ( ~ ~ ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) )
| ( SV32 = SV60 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(507,plain,
! [SV73: $i,SV62: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV62 )
= $false )
| ( ( subset @ ( set_difference @ SV34 @ SV73 ) @ ( set_difference @ SV62 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(508,plain,
( ( ~ ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(509,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(510,plain,
! [SV37: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV37 ) ) )
= $false )
| ( ( empty @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(511,plain,
! [SV37: $i] :
( ( ( ~ ( relation @ ( relation_rng @ SV37 ) ) )
= $false )
| ( ( empty @ SV37 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[483]) ).
thf(512,plain,
! [SV7: $i,SV74: $i] :
( ( ( relation @ SV74 )
= $false )
| ( ( ~ ( subset @ SV7 @ SV74 )
| ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV74 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV74 ) ) ) )
= $true )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(513,plain,
! [SV8: $i,SV75: $i] :
( ( ( relation @ SV75 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV8 @ SV75 ) ) @ ( relation_rng @ SV75 ) )
= $true )
| ( ( relation @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(514,plain,
! [SV76: $i,SV65: $i,SV42: $i,SV9: $i] :
( ( ( ~ ( ~ ( subset @ SV9 @ SV42 )
| ~ ( subset @ SV65 @ SV76 ) ) )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV9 @ SV65 ) @ ( cartesian_product2 @ SV42 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(515,plain,
! [SV43: $i,SV10: $i] :
( ( ( ~ ( proper_subset @ SV10 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(516,plain,
! [SV43: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) ) )
= $true )
| ( ( proper_subset @ SV10 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(517,plain,
! [SV44: $i,SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( ~ ( relation @ SV44 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV11 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[489]) ).
thf(518,plain,
! [SV45: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV45 )
= $false )
| ( ( ~ ( proper_subset @ SV45 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(519,plain,
( ( empty @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(520,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(521,plain,
! [SV46: $i,SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV13 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(522,plain,
! [SV47: $i,SV66: $i,SV15: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV15 @ SV66 ) @ ( cartesian_product2 @ SV47 @ SV66 ) )
| ~ ( subset @ ( cartesian_product2 @ SV66 @ SV15 ) @ ( cartesian_product2 @ SV66 @ SV47 ) ) )
= $false )
| ( ( subset @ SV15 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(523,plain,
! [SV68: $i,SV50: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV50 )
| ~ ( disjoint @ SV50 @ SV68 ) )
= $true )
| ( ( disjoint @ SV18 @ SV68 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(524,plain,
! [SV69: $i,SV51: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV51 )
| ~ ( subset @ SV51 @ SV69 ) )
= $true )
| ( ( subset @ SV19 @ SV69 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(525,plain,
! [SV70: $i,SV53: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV53 )
| ~ ( subset @ SV22 @ SV70 ) )
= $true )
| ( ( subset @ SV22 @ ( set_intersection2 @ SV53 @ SV70 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(526,plain,
! [SV23: $i] :
( ( ( ~ ( empty @ SV23 ) )
= $false )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(527,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( ~ ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
| ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) ) )
| ~ ( ~ ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) )
| ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) ) ) )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(528,plain,
! [SV72: $i,SV56: $i,SV26: $i] :
( ( ( ~ ( subset @ SV26 @ SV56 )
| ~ ( subset @ SV72 @ SV56 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV26 @ SV72 ) @ SV56 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(529,plain,
! [SV58: $i,SV30: $i] :
( ( ( ~ ( subset @ SV30 @ SV58 ) )
= $true )
| ( ( ! [SY132: $i] :
( ~ ( in @ SY132 @ SV30 )
| ( in @ SY132 @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(530,plain,
! [SV58: $i,SV30: $i] :
( ( ( ~ ! [SY133: $i] :
( ~ ( in @ SY133 @ SV30 )
| ( in @ SY133 @ SV58 ) ) )
= $true )
| ( ( subset @ SV30 @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(531,plain,
! [SV59: $i,SV31: $i] :
( ( ( ~ ( relation @ SV31 ) )
= $true )
| ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV31 @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(532,plain,
! [SV60: $i,SV32: $i] :
( ( ( SV32 != SV60 )
= $true )
| ( ( ~ ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(533,plain,
! [SV60: $i,SV32: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) ) )
= $true )
| ( ( SV32 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(534,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(535,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(536,plain,
! [SV37: $i] :
( ( ( empty @ ( relation_rng @ SV37 ) )
= $true )
| ( ( empty @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(537,plain,
! [SV37: $i] :
( ( ( relation @ ( relation_rng @ SV37 ) )
= $true )
| ( ( empty @ SV37 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(538,plain,
! [SV74: $i,SV7: $i] :
( ( ( ~ ( subset @ SV7 @ SV74 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV74 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV74 ) ) ) )
= $true )
| ( ( relation @ SV74 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(539,plain,
! [SV76: $i,SV65: $i,SV42: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV42 )
| ~ ( subset @ SV65 @ SV76 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV9 @ SV65 ) @ ( cartesian_product2 @ SV42 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(540,plain,
! [SV43: $i,SV10: $i] :
( ( ( proper_subset @ SV10 @ SV43 )
= $false )
| ( ( ~ ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[515]) ).
thf(541,plain,
! [SV43: $i,SV10: $i] :
( ( ( ~ ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) ) )
= $false )
| ( ( proper_subset @ SV10 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(542,plain,
! [SV44: $i,SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( ~ ( relation @ SV44 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV11 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(543,plain,
! [SV12: $i,SV45: $i] :
( ( ( proper_subset @ SV45 @ SV12 )
= $false )
| ( ( subset @ SV12 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(544,plain,
! [SV46: $i,SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( ~ ( relation @ SV46 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV13 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(545,plain,
! [SV47: $i,SV66: $i,SV15: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV15 @ SV66 ) @ ( cartesian_product2 @ SV47 @ SV66 ) ) )
= $false )
| ( ( subset @ SV15 @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(546,plain,
! [SV47: $i,SV15: $i,SV66: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV66 @ SV15 ) @ ( cartesian_product2 @ SV66 @ SV47 ) ) )
= $false )
| ( ( subset @ SV15 @ SV47 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[522]) ).
thf(547,plain,
! [SV68: $i,SV50: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV50 ) )
= $true )
| ( ( ~ ( disjoint @ SV50 @ SV68 ) )
= $true )
| ( ( disjoint @ SV18 @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(548,plain,
! [SV69: $i,SV51: $i,SV19: $i] :
( ( ( ~ ( subset @ SV19 @ SV51 ) )
= $true )
| ( ( ~ ( subset @ SV51 @ SV69 ) )
= $true )
| ( ( subset @ SV19 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(549,plain,
! [SV70: $i,SV53: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV53 ) )
= $true )
| ( ( ~ ( subset @ SV22 @ SV70 ) )
= $true )
| ( ( subset @ SV22 @ ( set_intersection2 @ SV53 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(550,plain,
! [SV23: $i] :
( ( ( empty @ SV23 )
= $true )
| ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(551,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( ~ ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
| ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) ) ) )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[527]) ).
thf(552,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) )
| ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) ) ) )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[527]) ).
thf(553,plain,
! [SV72: $i,SV56: $i,SV26: $i] :
( ( ( ~ ( subset @ SV26 @ SV56 ) )
= $true )
| ( ( ~ ( subset @ SV72 @ SV56 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV26 @ SV72 ) @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(554,plain,
! [SV58: $i,SV30: $i] :
( ( ( subset @ SV30 @ SV58 )
= $false )
| ( ( ! [SY132: $i] :
( ~ ( in @ SY132 @ SV30 )
| ( in @ SY132 @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(555,plain,
! [SV58: $i,SV30: $i] :
( ( ( ! [SY133: $i] :
( ~ ( in @ SY133 @ SV30 )
| ( in @ SY133 @ SV58 ) ) )
= $false )
| ( ( subset @ SV30 @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(556,plain,
! [SV59: $i,SV31: $i] :
( ( ( relation @ SV31 )
= $false )
| ( ( ~ ( relation @ SV59 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV31 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(557,plain,
! [SV60: $i,SV32: $i] :
( ( ( SV32 = SV60 )
= $false )
| ( ( ~ ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(558,plain,
! [SV60: $i,SV32: $i] :
( ( ( ~ ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) ) )
= $false )
| ( ( SV32 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(559,plain,
( ( empty @ sK4_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(560,plain,
! [SV74: $i,SV7: $i] :
( ( ( subset @ SV7 @ SV74 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV74 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV74 ) ) ) )
= $true )
| ( ( relation @ SV74 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(561,plain,
! [SV76: $i,SV65: $i,SV42: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV42 ) )
= $true )
| ( ( ~ ( subset @ SV65 @ SV76 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV9 @ SV65 ) @ ( cartesian_product2 @ SV42 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(562,plain,
! [SV43: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) )
= $false )
| ( ( proper_subset @ SV10 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(563,plain,
! [SV43: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV43 )
| ~ ( ( SV10 != SV43 ) ) )
= $true )
| ( ( proper_subset @ SV10 @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(564,plain,
! [SV11: $i,SV44: $i] :
( ( ( relation @ SV44 )
= $false )
| ( ( relation @ SV11 )
= $false )
| ( ( relation @ ( set_union2 @ SV11 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(565,plain,
! [SV13: $i,SV46: $i] :
( ( ( relation @ SV46 )
= $false )
| ( ( relation @ SV13 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV13 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(566,plain,
! [SV47: $i,SV66: $i,SV15: $i] :
( ( ( subset @ ( cartesian_product2 @ SV15 @ SV66 ) @ ( cartesian_product2 @ SV47 @ SV66 ) )
= $true )
| ( ( subset @ SV15 @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[545]) ).
thf(567,plain,
! [SV47: $i,SV15: $i,SV66: $i] :
( ( ( subset @ ( cartesian_product2 @ SV66 @ SV15 ) @ ( cartesian_product2 @ SV66 @ SV47 ) )
= $true )
| ( ( subset @ SV15 @ SV47 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[546]) ).
thf(568,plain,
! [SV68: $i,SV50: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV50 )
= $false )
| ( ( ~ ( disjoint @ SV50 @ SV68 ) )
= $true )
| ( ( disjoint @ SV18 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(569,plain,
! [SV69: $i,SV51: $i,SV19: $i] :
( ( ( subset @ SV19 @ SV51 )
= $false )
| ( ( ~ ( subset @ SV51 @ SV69 ) )
= $true )
| ( ( subset @ SV19 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(570,plain,
! [SV70: $i,SV53: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV53 )
= $false )
| ( ( ~ ( subset @ SV22 @ SV70 ) )
= $true )
| ( ( subset @ SV22 @ ( set_intersection2 @ SV53 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(571,plain,
! [SV23: $i] :
( ( ( relation @ SV23 )
= $false )
| ( ( empty @ SV23 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(572,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
| ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(573,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) )
| ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[552]) ).
thf(574,plain,
! [SV72: $i,SV56: $i,SV26: $i] :
( ( ( subset @ SV26 @ SV56 )
= $false )
| ( ( ~ ( subset @ SV72 @ SV56 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV26 @ SV72 ) @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(575,plain,
! [SV58: $i,SV30: $i,SV77: $i] :
( ( ( ~ ( in @ SV77 @ SV30 )
| ( in @ SV77 @ SV58 ) )
= $true )
| ( ( subset @ SV30 @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(576,plain,
! [SV30: $i,SV58: $i] :
( ( ( ~ ( in @ ( sK5_SY133 @ SV58 @ SV30 ) @ SV30 )
| ( in @ ( sK5_SY133 @ SV58 @ SV30 ) @ SV58 ) )
= $false )
| ( ( subset @ SV30 @ SV58 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[555]) ).
thf(577,plain,
! [SV31: $i,SV59: $i] :
( ( ( relation @ SV59 )
= $false )
| ( ( relation @ SV31 )
= $false )
| ( ( relation @ ( relation_composition @ SV31 @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(578,plain,
! [SV60: $i,SV32: $i] :
( ( ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) )
= $false )
| ( ( SV32 = SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(579,plain,
! [SV60: $i,SV32: $i] :
( ( ( ~ ( subset @ SV32 @ SV60 )
| ~ ( subset @ SV60 @ SV32 ) )
= $true )
| ( ( SV32 = SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(580,plain,
! [SV74: $i,SV7: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV74 ) )
| ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV74 ) ) )
= $false )
| ( ( subset @ SV7 @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(581,plain,
! [SV76: $i,SV65: $i,SV42: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV42 )
= $false )
| ( ( ~ ( subset @ SV65 @ SV76 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV9 @ SV65 ) @ ( cartesian_product2 @ SV42 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(582,plain,
! [SV43: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV43 ) )
= $false )
| ( ( proper_subset @ SV10 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[562]) ).
thf(583,plain,
! [SV43: $i,SV10: $i] :
( ( ( ~ ( ( SV10 != SV43 ) ) )
= $false )
| ( ( proper_subset @ SV10 @ SV43 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[562]) ).
thf(584,plain,
! [SV43: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV43 ) )
= $true )
| ( ( ~ ( ( SV10 != SV43 ) ) )
= $true )
| ( ( proper_subset @ SV10 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(585,plain,
! [SV18: $i,SV68: $i,SV50: $i] :
( ( ( disjoint @ SV50 @ SV68 )
= $false )
| ( ( subset @ SV18 @ SV50 )
= $false )
| ( ( disjoint @ SV18 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(586,plain,
! [SV19: $i,SV69: $i,SV51: $i] :
( ( ( subset @ SV51 @ SV69 )
= $false )
| ( ( subset @ SV19 @ SV51 )
= $false )
| ( ( subset @ SV19 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(587,plain,
! [SV53: $i,SV70: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV70 )
= $false )
| ( ( subset @ SV22 @ SV53 )
= $false )
| ( ( subset @ SV22 @ ( set_intersection2 @ SV53 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(588,plain,
! [SV23: $i] :
( ( ( empty @ ( relation_rng @ SV23 ) )
= $false )
| ( ( empty @ SV23 )
= $true )
| ( ( relation @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(589,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(590,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) ) )
= $true )
| ( ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(591,plain,
! [SV26: $i,SV56: $i,SV72: $i] :
( ( ( subset @ SV72 @ SV56 )
= $false )
| ( ( subset @ SV26 @ SV56 )
= $false )
| ( ( subset @ ( set_union2 @ SV26 @ SV72 ) @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(592,plain,
! [SV58: $i,SV30: $i,SV77: $i] :
( ( ( ~ ( in @ SV77 @ SV30 ) )
= $true )
| ( ( in @ SV77 @ SV58 )
= $true )
| ( ( subset @ SV30 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(593,plain,
! [SV30: $i,SV58: $i] :
( ( ( ~ ( in @ ( sK5_SY133 @ SV58 @ SV30 ) @ SV30 ) )
= $false )
| ( ( subset @ SV30 @ SV58 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[576]) ).
thf(594,plain,
! [SV30: $i,SV58: $i] :
( ( ( in @ ( sK5_SY133 @ SV58 @ SV30 ) @ SV58 )
= $false )
| ( ( subset @ SV30 @ SV58 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[576]) ).
thf(595,plain,
! [SV60: $i,SV32: $i] :
( ( ( ~ ( subset @ SV32 @ SV60 ) )
= $false )
| ( ( SV32 = SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[578]) ).
thf(596,plain,
! [SV32: $i,SV60: $i] :
( ( ( ~ ( subset @ SV60 @ SV32 ) )
= $false )
| ( ( SV32 = SV60 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[578]) ).
thf(597,plain,
! [SV60: $i,SV32: $i] :
( ( ( ~ ( subset @ SV32 @ SV60 ) )
= $true )
| ( ( ~ ( subset @ SV60 @ SV32 ) )
= $true )
| ( ( SV32 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(598,plain,
! [SV74: $i,SV7: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV74 ) ) )
= $false )
| ( ( subset @ SV7 @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[580]) ).
thf(599,plain,
! [SV74: $i,SV7: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV74 ) ) )
= $false )
| ( ( subset @ SV7 @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[580]) ).
thf(600,plain,
! [SV42: $i,SV9: $i,SV76: $i,SV65: $i] :
( ( ( subset @ SV65 @ SV76 )
= $false )
| ( ( subset @ SV9 @ SV42 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV9 @ SV65 ) @ ( cartesian_product2 @ SV42 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(601,plain,
! [SV43: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV43 )
= $true )
| ( ( proper_subset @ SV10 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(602,plain,
! [SV43: $i,SV10: $i] :
( ( ( SV10 != SV43 )
= $true )
| ( ( proper_subset @ SV10 @ SV43 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(603,plain,
! [SV43: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV43 )
= $false )
| ( ( ~ ( ( SV10 != SV43 ) ) )
= $true )
| ( ( proper_subset @ SV10 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(604,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(605,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) ) )
= $false )
| ( ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(606,plain,
! [SV58: $i,SV30: $i,SV77: $i] :
( ( ( in @ SV77 @ SV30 )
= $false )
| ( ( in @ SV77 @ SV58 )
= $true )
| ( ( subset @ SV30 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(607,plain,
! [SV30: $i,SV58: $i] :
( ( ( in @ ( sK5_SY133 @ SV58 @ SV30 ) @ SV30 )
= $true )
| ( ( subset @ SV30 @ SV58 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[593]) ).
thf(608,plain,
! [SV60: $i,SV32: $i] :
( ( ( subset @ SV32 @ SV60 )
= $true )
| ( ( SV32 = SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[595]) ).
thf(609,plain,
! [SV32: $i,SV60: $i] :
( ( ( subset @ SV60 @ SV32 )
= $true )
| ( ( SV32 = SV60 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[596]) ).
thf(610,plain,
! [SV60: $i,SV32: $i] :
( ( ( subset @ SV32 @ SV60 )
= $false )
| ( ( ~ ( subset @ SV60 @ SV32 ) )
= $true )
| ( ( SV32 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(611,plain,
! [SV74: $i,SV7: $i] :
( ( ( subset @ ( relation_dom @ SV7 ) @ ( relation_dom @ SV74 ) )
= $true )
| ( ( subset @ SV7 @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[598]) ).
thf(612,plain,
! [SV74: $i,SV7: $i] :
( ( ( subset @ ( relation_rng @ SV7 ) @ ( relation_rng @ SV74 ) )
= $true )
| ( ( subset @ SV7 @ SV74 )
= $false )
| ( ( relation @ SV74 )
= $false )
| ( ( relation @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[599]) ).
thf(613,plain,
! [SV43: $i,SV10: $i] :
( ( ( SV10 = SV43 )
= $false )
| ( ( proper_subset @ SV10 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(614,plain,
! [SV43: $i,SV10: $i] :
( ( ( SV10 != SV43 )
= $false )
| ( ( subset @ SV10 @ SV43 )
= $false )
| ( ( proper_subset @ SV10 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(615,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) )
= $false )
| ( ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(616,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV54 )
| ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) )
= $true )
| ( ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[605]) ).
thf(617,plain,
! [SV32: $i,SV60: $i] :
( ( ( subset @ SV60 @ SV32 )
= $false )
| ( ( subset @ SV32 @ SV60 )
= $false )
| ( ( SV32 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(618,plain,
! [SV43: $i,SV10: $i] :
( ( ( SV10 = SV43 )
= $true )
| ( ( subset @ SV10 @ SV43 )
= $false )
| ( ( proper_subset @ SV10 @ SV43 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[614]) ).
thf(619,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV54 ) )
= $false )
| ( ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(620,plain,
! [SV54: $i,SV71: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) )
= $false )
| ( ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[615]) ).
thf(621,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV54 ) )
= $true )
| ( ( ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) )
= $true )
| ( ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(622,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( in @ SV24 @ SV54 )
= $true )
| ( ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[619]) ).
thf(623,plain,
! [SV54: $i,SV71: $i,SV24: $i] :
( ( ( in @ SV24 @ ( relation_rng @ SV71 ) )
= $true )
| ( ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
= $false )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[620]) ).
thf(624,plain,
! [SV71: $i,SV54: $i,SV24: $i] :
( ( ( in @ SV24 @ SV54 )
= $false )
| ( ( ~ ( in @ SV24 @ ( relation_rng @ SV71 ) ) )
= $true )
| ( ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[621]) ).
thf(625,plain,
! [SV54: $i,SV71: $i,SV24: $i] :
( ( ( in @ SV24 @ ( relation_rng @ SV71 ) )
= $false )
| ( ( in @ SV24 @ SV54 )
= $false )
| ( ( in @ SV24 @ ( relation_rng @ ( relation_rng_restriction @ SV54 @ SV71 ) ) )
= $true )
| ( ( relation @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(626,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[279,625,623,622,618,617,613,612,611,609,608,607,606,601,600,594,591,588,587,586,585,577,567,566,565,564,559,543,537,536,535,520,519,513,507,495,482,480,478,472,470,466,463,442,440,434,427,385,384,383,382,348,346,343,307,298,293,292,290,289,288,287,286,285,284,283,282,281,280]) ).
thf(627,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[626]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU198+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.19 % Computer : n003.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Oct 6 15:06:09 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.08/2.67 .
% 14.08/2.67
% 14.08/2.67 No.of.Axioms: 54
% 14.08/2.67
% 14.08/2.67 Length.of.Defs: 0
% 14.08/2.67
% 14.08/2.67 Contains.Choice.Funs: false
% 14.08/2.67 .............
% 14.08/2.67
% 14.08/2.67 ********************************
% 14.08/2.67 * All subproblems solved! *
% 14.08/2.67 ********************************
% 14.08/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:55,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:626,loop_count:0,foatp_calls:1,translation:fof_full)
% 14.08/2.67
% 14.08/2.67 %**** Beginning of derivation protocol ****
% 14.08/2.67 % SZS output start CNFRefutation
% See solution above
% 14.08/2.68
% 14.08/2.68 %**** End of derivation protocol ****
% 14.08/2.68 %**** no. of clauses in derivation: 491 ****
% 14.08/2.68 %**** clause counter: 626 ****
% 14.08/2.68
% 14.08/2.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:55,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:626,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------