%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU196+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:43:22 AM UTC 2026
% Result : Theorem 3.59s 0.86s
% Output : CNFRefutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 52
% Syntax : Number of formulae : 448 ( 266 unt; 0 typ; 0 def)
% Number of atoms : 2296 ( 696 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 3584 ( 720 ~; 495 |; 51 &;2220 @)
% ( 9 <=>; 89 =>; 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 : 40 ( 37 usr; 7 con; 0-3 aty)
% Number of variables : 819 ( 0 ^; 813 !; 6 ?; 819 :)
% 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_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY74,type,
sK2_SY74: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_sK5_SY114,type,
sK5_SY114: $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/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(22,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(25,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(28,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(35,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(50,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
thf(55,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(58,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(59,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(60,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(61,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(62,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(64,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(65,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(66,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(67,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(69,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(70,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(71,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(72,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(73,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(74,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(107,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
thf(120,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(123,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(129,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(143,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_relat_1) ).
thf(147,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(155,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(159,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(160,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(162,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( ( subset @ A @ B )
=> ( ( subset @ ( relation_dom @ A ) @ ( relation_dom @ B ) )
& ( subset @ ( relation_rng @ A ) @ ( relation_rng @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_relat_1) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(168,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(170,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(171,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/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(187,conjecture,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_relat_1) ).
thf(188,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[187]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ B @ A ) ) @ ( relation_rng @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[188]) ).
thf(190,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(191,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(192,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(193,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(194,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(195,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(196,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(197,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(198,plain,
$true = $true,
inference(unfold_def,[status(thm)],[50]) ).
thf(199,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(200,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(201,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(202,plain,
$true = $true,
inference(unfold_def,[status(thm)],[58]) ).
thf(203,plain,
$true = $true,
inference(unfold_def,[status(thm)],[59]) ).
thf(204,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(205,plain,
$true = $true,
inference(unfold_def,[status(thm)],[61]) ).
thf(206,plain,
$true = $true,
inference(unfold_def,[status(thm)],[62]) ).
thf(207,plain,
$true = $true,
inference(unfold_def,[status(thm)],[64]) ).
thf(208,plain,
$true = $true,
inference(unfold_def,[status(thm)],[65]) ).
thf(209,plain,
$true = $true,
inference(unfold_def,[status(thm)],[66]) ).
thf(210,plain,
$true = $true,
inference(unfold_def,[status(thm)],[67]) ).
thf(211,plain,
$true = $true,
inference(unfold_def,[status(thm)],[69]) ).
thf(212,plain,
$true = $true,
inference(unfold_def,[status(thm)],[70]) ).
thf(213,plain,
$true = $true,
inference(unfold_def,[status(thm)],[71]) ).
thf(214,plain,
$true = $true,
inference(unfold_def,[status(thm)],[72]) ).
thf(215,plain,
$true = $true,
inference(unfold_def,[status(thm)],[73]) ).
thf(216,plain,
$true = $true,
inference(unfold_def,[status(thm)],[74]) ).
thf(217,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(218,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(219,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(220,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(221,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)],[116]) ).
thf(222,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(225,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(226,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(227,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)],[143]) ).
thf(228,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(230,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)],[157]) ).
thf(231,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(232,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(233,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)],[161]) ).
thf(234,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)],[162]) ).
thf(235,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(236,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)],[167]) ).
thf(237,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(238,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(239,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)],[171]) ).
thf(240,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)],[172]) ).
thf(241,plain,
( ( ! [SY74: $i] :
( ( relation @ SY74 )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ SY74 @ sK1_A ) ) @ ( relation_rng @ SY74 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[189]) ).
thf(242,plain,
( ( ( relation @ sK2_SY74 )
=> ( subset @ ( relation_rng @ ( relation_dom_restriction @ sK2_SY74 @ sK1_A ) ) @ ( relation_rng @ sK2_SY74 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[241]) ).
thf(243,plain,
( ( relation @ sK2_SY74 )
= $true ),
inference(standard_cnf,[status(thm)],[242]) ).
thf(244,plain,
( ( subset @ ( relation_rng @ ( relation_dom_restriction @ sK2_SY74 @ sK1_A ) ) @ ( relation_rng @ sK2_SY74 ) )
= $false ),
inference(standard_cnf,[status(thm)],[242]) ).
thf(245,plain,
( ( ~ ( subset @ ( relation_rng @ ( relation_dom_restriction @ sK2_SY74 @ sK1_A ) ) @ ( relation_rng @ sK2_SY74 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[244]) ).
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(copy,[status(thm)],[240]) ).
thf(247,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)],[239]) ).
thf(248,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(249,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(250,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(251,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(252,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)],[234]) ).
thf(253,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(254,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(255,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(256,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(257,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(258,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(259,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_rng @ ( relation_composition @ A @ B ) ) @ ( relation_rng @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(260,plain,
( ( ! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(261,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(263,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(264,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ B )
=> ( subset @ ( relation_dom_restriction @ B @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(265,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(266,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(267,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(268,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(269,plain,
( ( ! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(270,plain,
$true = $true,
inference(copy,[status(thm)],[216]) ).
thf(271,plain,
$true = $true,
inference(copy,[status(thm)],[215]) ).
thf(272,plain,
$true = $true,
inference(copy,[status(thm)],[214]) ).
thf(273,plain,
$true = $true,
inference(copy,[status(thm)],[213]) ).
thf(274,plain,
$true = $true,
inference(copy,[status(thm)],[212]) ).
thf(275,plain,
$true = $true,
inference(copy,[status(thm)],[211]) ).
thf(276,plain,
$true = $true,
inference(copy,[status(thm)],[210]) ).
thf(277,plain,
$true = $true,
inference(copy,[status(thm)],[209]) ).
thf(278,plain,
$true = $true,
inference(copy,[status(thm)],[208]) ).
thf(279,plain,
$true = $true,
inference(copy,[status(thm)],[207]) ).
thf(280,plain,
$true = $true,
inference(copy,[status(thm)],[206]) ).
thf(281,plain,
$true = $true,
inference(copy,[status(thm)],[205]) ).
thf(282,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(283,plain,
$true = $true,
inference(copy,[status(thm)],[203]) ).
thf(284,plain,
$true = $true,
inference(copy,[status(thm)],[202]) ).
thf(285,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(286,plain,
( ( ! [A: $i] : ( relation @ ( identity_relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(287,plain,
( ( ! [A: $i,B: $i] :
( ( relation @ A )
=> ( relation @ ( relation_dom_restriction @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(288,plain,
$true = $true,
inference(copy,[status(thm)],[198]) ).
thf(289,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_intersection2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(290,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(291,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(292,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(293,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(294,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(295,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(296,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(297,plain,
( ( relation @ sK2_SY74 )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(298,plain,
( ( ~ ( subset @ ( relation_rng @ ( relation_dom_restriction @ sK2_SY74 @ sK1_A ) ) @ ( relation_rng @ sK2_SY74 ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(299,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_dom_restriction @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(300,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(301,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_union2 @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(302,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)],[265]) ).
thf(303,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(304,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( proper_subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(305,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)],[267]) ).
thf(306,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)],[268]) ).
thf(307,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(308,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( set_intersection2 @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(309,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( disjoint @ SX1 @ SX2 ) )
| ( disjoint @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(310,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)],[269]) ).
thf(311,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)],[259]) ).
thf(312,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(313,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)],[253]) ).
thf(314,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)],[252]) ).
thf(315,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_inverse @ ( relation_inverse @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(316,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)],[256]) ).
thf(317,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(318,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(319,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)],[250]) ).
thf(320,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(321,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_rng @ SX0 ) )
| ~ ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(322,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 ) )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(323,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_intersection2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(324,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(325,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(326,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( relation @ SX1 )
| ( subset @ ( relation_dom_restriction @ SX1 @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(327,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)],[247]) ).
thf(328,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)],[246]) ).
thf(329,plain,
! [SV1: $i] :
( ( ! [SY75: $i] : ( subset @ ( set_intersection2 @ SV1 @ SY75 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(330,plain,
! [SV2: $i] :
( ( subset @ empty_set @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(331,plain,
! [SV3: $i] :
( ( ! [SY76: $i] : ( subset @ ( set_difference @ SV3 @ SY76 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(332,plain,
! [SV4: $i] :
( ( ! [SY77: $i] : ( subset @ SV4 @ ( set_union2 @ SV4 @ SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(333,plain,
! [SV5: $i] :
( ( relation @ ( identity_relation @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(334,plain,
! [SV6: $i] :
( ( ! [SY78: $i] : ( subset @ SV6 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(335,plain,
( ( subset @ ( relation_rng @ ( relation_dom_restriction @ sK2_SY74 @ sK1_A ) ) @ ( relation_rng @ sK2_SY74 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(336,plain,
! [SV7: $i] :
( ( ! [SY79: $i] :
( ~ ( relation @ SV7 )
| ( relation @ ( relation_dom_restriction @ SV7 @ SY79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(337,plain,
! [SV8: $i] :
( ( ! [SY80: $i] :
( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( relation @ SY80 ) )
| ( relation @ ( set_union2 @ SV8 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(338,plain,
! [SV9: $i] :
( ( ! [SY81: $i] :
( ~ ( subset @ SV9 @ SY81 )
| ( ( set_union2 @ SV9 @ SY81 )
= SY81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(339,plain,
! [SV10: $i] :
( ( ! [SY82: $i,SY83: $i] :
( ~ ~ ( ~ ( subset @ SV10 @ SY82 )
| ~ ( subset @ SY83 @ SY82 ) )
| ( subset @ ( set_union2 @ SV10 @ SY83 ) @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(340,plain,
! [SV11: $i] :
( ( ~ ( relation @ SV11 )
| ( relation @ ( relation_inverse @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(341,plain,
! [SV12: $i] :
( ( ! [SY84: $i] :
~ ~ ( ~ ( subset @ SV12 @ SY84 )
| ~ ( proper_subset @ SY84 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(342,plain,
! [SV13: $i] :
( ( ! [SY85: $i] :
~ ( ~ ( ( SV13 != SY85 )
| ~ ( ~ ( subset @ SV13 @ SY85 )
| ~ ( subset @ SY85 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV13 @ SY85 )
| ~ ( subset @ SY85 @ SV13 ) )
| ( SV13 = SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(343,plain,
! [SV14: $i] :
( ( ! [SY86: $i] :
~ ( ~ ( ~ ( subset @ SV14 @ SY86 )
| ! [SY87: $i] :
( ~ ( in @ SY87 @ SV14 )
| ( in @ SY87 @ SY86 ) ) )
| ~ ( ~ ! [SY88: $i] :
( ~ ( in @ SY88 @ SV14 )
| ( in @ SY88 @ SY86 ) )
| ( subset @ SV14 @ SY86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(344,plain,
! [SV15: $i] :
( ( ~ ( empty @ SV15 )
| ( relation @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(345,plain,
! [SV16: $i] :
( ( ! [SY89: $i] :
( ~ ( subset @ SV16 @ SY89 )
| ( ( set_intersection2 @ SV16 @ SY89 )
= SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(346,plain,
! [SV17: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ~ ( ~ ( subset @ SV17 @ SY90 )
| ~ ( disjoint @ SY90 @ SY91 ) )
| ( disjoint @ SV17 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(347,plain,
! [SV18: $i] :
( ( ! [SY92: $i] :
~ ( ~ ( ~ ( proper_subset @ SV18 @ SY92 )
| ~ ( ~ ( subset @ SV18 @ SY92 )
| ~ ( ( SV18 != SY92 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV18 @ SY92 )
| ~ ( ( SV18 != SY92 ) ) )
| ( proper_subset @ SV18 @ SY92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(348,plain,
! [SV19: $i] :
( ( ~ ( relation @ SV19 )
| ! [SY93: $i] :
( ~ ( relation @ SY93 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV19 @ SY93 ) ) @ ( relation_rng @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(349,plain,
! [SV20: $i] :
( ( ~ ( subset @ SV20 @ empty_set )
| ( SV20 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(350,plain,
! [SV21: $i] :
( ( ! [SY94: $i,SY95: $i] :
( ~ ( subset @ SV21 @ SY94 )
| ( subset @ ( set_intersection2 @ SV21 @ SY95 ) @ ( set_intersection2 @ SY94 @ SY95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(351,plain,
! [SV22: $i] :
( ( ~ ( relation @ SV22 )
| ! [SY96: $i] :
( ~ ( relation @ SY96 )
| ~ ( subset @ SV22 @ SY96 )
| ~ ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_dom @ SY96 ) )
| ~ ( subset @ ( relation_rng @ SV22 ) @ ( relation_rng @ SY96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(352,plain,
! [SV23: $i] :
( ( ~ ( relation @ SV23 )
| ( ( relation_inverse @ ( relation_inverse @ SV23 ) )
= SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(353,plain,
! [SV24: $i] :
( ( ! [SY97: $i,SY98: $i] :
( ~ ( subset @ SV24 @ SY97 )
| ( subset @ ( set_difference @ SV24 @ SY98 ) @ ( set_difference @ SY97 @ SY98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(354,plain,
! [SV25: $i] :
( ( ! [SY99: $i] :
( ~ ~ ( ~ ( relation @ SV25 )
| ~ ( relation @ SY99 ) )
| ( relation @ ( relation_composition @ SV25 @ SY99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(355,plain,
! [SV26: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV26 )
| ~ ( relation @ SV26 ) )
| ~ ( empty @ ( relation_rng @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(356,plain,
! [SV27: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ~ ~ ( ~ ( subset @ SV27 @ SY100 )
| ~ ( subset @ SV27 @ SY101 ) )
| ( subset @ SV27 @ ( set_intersection2 @ SY100 @ SY101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(357,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(358,plain,
! [SV28: $i] :
( ( ~ ( empty @ SV28 )
| ~ ( ~ ( empty @ ( relation_rng @ SV28 ) )
| ~ ( relation @ ( relation_rng @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(359,plain,
! [SV29: $i] :
( ( ! [SY102: $i,SY103: $i] :
( ~ ~ ( ~ ( subset @ SV29 @ SY102 )
| ~ ( subset @ SY102 @ SY103 ) )
| ( subset @ SV29 @ SY103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(360,plain,
! [SV30: $i] :
( ( ! [SY104: $i] :
( ~ ~ ( ~ ( relation @ SV30 )
| ~ ( relation @ SY104 ) )
| ( relation @ ( set_intersection2 @ SV30 @ SY104 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(361,plain,
! [SV31: $i] :
( ( ! [SY105: $i] :
( ~ ( subset @ ( singleton @ SV31 ) @ ( singleton @ SY105 ) )
| ( SV31 = SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(362,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(363,plain,
! [SV32: $i] :
( ( ! [SY106: $i] :
( ~ ( relation @ SY106 )
| ( subset @ ( relation_dom_restriction @ SY106 @ SV32 ) @ SY106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(364,plain,
! [SV33: $i] :
( ( ! [SY107: $i,SY108: $i,SY109: $i] :
( ~ ~ ( ~ ( subset @ SV33 @ SY107 )
| ~ ( subset @ SY108 @ SY109 ) )
| ( subset @ ( cartesian_product2 @ SV33 @ SY108 ) @ ( cartesian_product2 @ SY107 @ SY109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(365,plain,
! [SV34: $i] :
( ( ! [SY110: $i,SY111: $i] :
( ~ ( subset @ SV34 @ SY110 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SY111 ) @ ( cartesian_product2 @ SY110 @ SY111 ) )
| ~ ( subset @ ( cartesian_product2 @ SY111 @ SV34 ) @ ( cartesian_product2 @ SY111 @ SY110 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(366,plain,
! [SV35: $i,SV1: $i] :
( ( subset @ ( set_intersection2 @ SV1 @ SV35 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(367,plain,
! [SV36: $i,SV3: $i] :
( ( subset @ ( set_difference @ SV3 @ SV36 ) @ SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(368,plain,
! [SV37: $i,SV4: $i] :
( ( subset @ SV4 @ ( set_union2 @ SV4 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(369,plain,
! [SV6: $i] :
( ( subset @ SV6 @ SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(370,plain,
! [SV39: $i,SV7: $i] :
( ( ~ ( relation @ SV7 )
| ( relation @ ( relation_dom_restriction @ SV7 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(371,plain,
! [SV40: $i,SV8: $i] :
( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( relation @ SV40 ) )
| ( relation @ ( set_union2 @ SV8 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(372,plain,
! [SV41: $i,SV9: $i] :
( ( ~ ( subset @ SV9 @ SV41 )
| ( ( set_union2 @ SV9 @ SV41 )
= SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(373,plain,
! [SV42: $i,SV10: $i] :
( ( ! [SY112: $i] :
( ~ ~ ( ~ ( subset @ SV10 @ SV42 )
| ~ ( subset @ SY112 @ SV42 ) )
| ( subset @ ( set_union2 @ SV10 @ SY112 ) @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(374,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ SV11 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(375,plain,
! [SV43: $i,SV12: $i] :
( ( ~ ~ ( ~ ( subset @ SV12 @ SV43 )
| ~ ( proper_subset @ SV43 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(376,plain,
! [SV44: $i,SV13: $i] :
( ( ~ ( ~ ( ( SV13 != SV44 )
| ~ ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) )
| ( SV13 = SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(377,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV14 @ SV45 )
| ! [SY113: $i] :
( ~ ( in @ SY113 @ SV14 )
| ( in @ SY113 @ SV45 ) ) )
| ~ ( ~ ! [SY114: $i] :
( ~ ( in @ SY114 @ SV14 )
| ( in @ SY114 @ SV45 ) )
| ( subset @ SV14 @ SV45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(378,plain,
! [SV15: $i] :
( ( ( ~ ( empty @ SV15 ) )
= $true )
| ( ( relation @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(379,plain,
! [SV46: $i,SV16: $i] :
( ( ~ ( subset @ SV16 @ SV46 )
| ( ( set_intersection2 @ SV16 @ SV46 )
= SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(380,plain,
! [SV47: $i,SV17: $i] :
( ( ! [SY115: $i] :
( ~ ~ ( ~ ( subset @ SV17 @ SV47 )
| ~ ( disjoint @ SV47 @ SY115 ) )
| ( disjoint @ SV17 @ SY115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(381,plain,
! [SV48: $i,SV18: $i] :
( ( ~ ( ~ ( ~ ( proper_subset @ SV18 @ SV48 )
| ~ ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) )
| ( proper_subset @ SV18 @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(382,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ! [SY93: $i] :
( ~ ( relation @ SY93 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV19 @ SY93 ) ) @ ( relation_rng @ SY93 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(383,plain,
! [SV20: $i] :
( ( ( ~ ( subset @ SV20 @ empty_set ) )
= $true )
| ( ( SV20 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(384,plain,
! [SV49: $i,SV21: $i] :
( ( ! [SY116: $i] :
( ~ ( subset @ SV21 @ SV49 )
| ( subset @ ( set_intersection2 @ SV21 @ SY116 ) @ ( set_intersection2 @ SV49 @ SY116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(385,plain,
! [SV22: $i] :
( ( ( ~ ( relation @ SV22 ) )
= $true )
| ( ( ! [SY96: $i] :
( ~ ( relation @ SY96 )
| ~ ( subset @ SV22 @ SY96 )
| ~ ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_dom @ SY96 ) )
| ~ ( subset @ ( relation_rng @ SV22 ) @ ( relation_rng @ SY96 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(386,plain,
! [SV23: $i] :
( ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV23 ) )
= SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(387,plain,
! [SV50: $i,SV24: $i] :
( ( ! [SY117: $i] :
( ~ ( subset @ SV24 @ SV50 )
| ( subset @ ( set_difference @ SV24 @ SY117 ) @ ( set_difference @ SV50 @ SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(388,plain,
! [SV51: $i,SV25: $i] :
( ( ~ ~ ( ~ ( relation @ SV25 )
| ~ ( relation @ SV51 ) )
| ( relation @ ( relation_composition @ SV25 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(389,plain,
! [SV26: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV26 )
| ~ ( relation @ SV26 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(390,plain,
! [SV52: $i,SV27: $i] :
( ( ! [SY118: $i] :
( ~ ~ ( ~ ( subset @ SV27 @ SV52 )
| ~ ( subset @ SV27 @ SY118 ) )
| ( subset @ SV27 @ ( set_intersection2 @ SV52 @ SY118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(391,plain,
( ( ~ ~ ( ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[357]) ).
thf(392,plain,
! [SV28: $i] :
( ( ( ~ ( empty @ SV28 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV28 ) )
| ~ ( relation @ ( relation_rng @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(393,plain,
! [SV53: $i,SV29: $i] :
( ( ! [SY119: $i] :
( ~ ~ ( ~ ( subset @ SV29 @ SV53 )
| ~ ( subset @ SV53 @ SY119 ) )
| ( subset @ SV29 @ SY119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(394,plain,
! [SV54: $i,SV30: $i] :
( ( ~ ~ ( ~ ( relation @ SV30 )
| ~ ( relation @ SV54 ) )
| ( relation @ ( set_intersection2 @ SV30 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(395,plain,
! [SV55: $i,SV31: $i] :
( ( ~ ( subset @ ( singleton @ SV31 ) @ ( singleton @ SV55 ) )
| ( SV31 = SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(396,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[362]) ).
thf(397,plain,
! [SV32: $i,SV56: $i] :
( ( ~ ( relation @ SV56 )
| ( subset @ ( relation_dom_restriction @ SV56 @ SV32 ) @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(398,plain,
! [SV57: $i,SV33: $i] :
( ( ! [SY120: $i,SY121: $i] :
( ~ ~ ( ~ ( subset @ SV33 @ SV57 )
| ~ ( subset @ SY120 @ SY121 ) )
| ( subset @ ( cartesian_product2 @ SV33 @ SY120 ) @ ( cartesian_product2 @ SV57 @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(399,plain,
! [SV58: $i,SV34: $i] :
( ( ! [SY122: $i] :
( ~ ( subset @ SV34 @ SV58 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SY122 ) @ ( cartesian_product2 @ SV58 @ SY122 ) )
| ~ ( subset @ ( cartesian_product2 @ SY122 @ SV34 ) @ ( cartesian_product2 @ SY122 @ SV58 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(400,plain,
! [SV39: $i,SV7: $i] :
( ( ( ~ ( relation @ SV7 ) )
= $true )
| ( ( relation @ ( relation_dom_restriction @ SV7 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(401,plain,
! [SV40: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( relation @ SV40 ) ) )
= $true )
| ( ( relation @ ( set_union2 @ SV8 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(402,plain,
! [SV41: $i,SV9: $i] :
( ( ( ~ ( subset @ SV9 @ SV41 ) )
= $true )
| ( ( ( set_union2 @ SV9 @ SV41 )
= SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(403,plain,
! [SV59: $i,SV42: $i,SV10: $i] :
( ( ~ ~ ( ~ ( subset @ SV10 @ SV42 )
| ~ ( subset @ SV59 @ SV42 ) )
| ( subset @ ( set_union2 @ SV10 @ SV59 ) @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(404,plain,
! [SV11: $i] :
( ( ( relation @ SV11 )
= $false )
| ( ( relation @ ( relation_inverse @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(405,plain,
! [SV43: $i,SV12: $i] :
( ( ~ ( ~ ( subset @ SV12 @ SV43 )
| ~ ( proper_subset @ SV43 @ SV12 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(406,plain,
! [SV44: $i,SV13: $i] :
( ( ~ ( ( SV13 != SV44 )
| ~ ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) )
| ( SV13 = SV44 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(407,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ SV14 @ SV45 )
| ! [SY113: $i] :
( ~ ( in @ SY113 @ SV14 )
| ( in @ SY113 @ SV45 ) ) )
| ~ ( ~ ! [SY114: $i] :
( ~ ( in @ SY114 @ SV14 )
| ( in @ SY114 @ SV45 ) )
| ( subset @ SV14 @ SV45 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(408,plain,
! [SV15: $i] :
( ( ( empty @ SV15 )
= $false )
| ( ( relation @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(409,plain,
! [SV46: $i,SV16: $i] :
( ( ( ~ ( subset @ SV16 @ SV46 ) )
= $true )
| ( ( ( set_intersection2 @ SV16 @ SV46 )
= SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(410,plain,
! [SV60: $i,SV47: $i,SV17: $i] :
( ( ~ ~ ( ~ ( subset @ SV17 @ SV47 )
| ~ ( disjoint @ SV47 @ SV60 ) )
| ( disjoint @ SV17 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(411,plain,
! [SV48: $i,SV18: $i] :
( ( ~ ( ~ ( proper_subset @ SV18 @ SV48 )
| ~ ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) )
| ( proper_subset @ SV18 @ SV48 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(412,plain,
! [SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( ! [SY93: $i] :
( ~ ( relation @ SY93 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV19 @ SY93 ) ) @ ( relation_rng @ SY93 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(413,plain,
! [SV20: $i] :
( ( ( subset @ SV20 @ empty_set )
= $false )
| ( ( SV20 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(414,plain,
! [SV61: $i,SV49: $i,SV21: $i] :
( ( ~ ( subset @ SV21 @ SV49 )
| ( subset @ ( set_intersection2 @ SV21 @ SV61 ) @ ( set_intersection2 @ SV49 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(415,plain,
! [SV22: $i] :
( ( ( relation @ SV22 )
= $false )
| ( ( ! [SY96: $i] :
( ~ ( relation @ SY96 )
| ~ ( subset @ SV22 @ SY96 )
| ~ ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_dom @ SY96 ) )
| ~ ( subset @ ( relation_rng @ SV22 ) @ ( relation_rng @ SY96 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(416,plain,
! [SV23: $i] :
( ( ( relation @ SV23 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV23 ) )
= SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(417,plain,
! [SV62: $i,SV50: $i,SV24: $i] :
( ( ~ ( subset @ SV24 @ SV50 )
| ( subset @ ( set_difference @ SV24 @ SV62 ) @ ( set_difference @ SV50 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(418,plain,
! [SV51: $i,SV25: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV25 )
| ~ ( relation @ SV51 ) ) )
= $true )
| ( ( relation @ ( relation_composition @ SV25 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(419,plain,
! [SV26: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV26 )
| ~ ( relation @ SV26 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(420,plain,
! [SV63: $i,SV52: $i,SV27: $i] :
( ( ~ ~ ( ~ ( subset @ SV27 @ SV52 )
| ~ ( subset @ SV27 @ SV63 ) )
| ( subset @ SV27 @ ( set_intersection2 @ SV52 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(421,plain,
( ( ~ ( ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[391]) ).
thf(422,plain,
! [SV28: $i] :
( ( ( empty @ SV28 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV28 ) )
| ~ ( relation @ ( relation_rng @ SV28 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(423,plain,
! [SV64: $i,SV53: $i,SV29: $i] :
( ( ~ ~ ( ~ ( subset @ SV29 @ SV53 )
| ~ ( subset @ SV53 @ SV64 ) )
| ( subset @ SV29 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(424,plain,
! [SV54: $i,SV30: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV30 )
| ~ ( relation @ SV54 ) ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV30 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(425,plain,
! [SV55: $i,SV31: $i] :
( ( ( ~ ( subset @ ( singleton @ SV31 ) @ ( singleton @ SV55 ) ) )
= $true )
| ( ( SV31 = SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(426,plain,
( ( ~ ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(427,plain,
! [SV32: $i,SV56: $i] :
( ( ( ~ ( relation @ SV56 ) )
= $true )
| ( ( subset @ ( relation_dom_restriction @ SV56 @ SV32 ) @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(428,plain,
! [SV65: $i,SV57: $i,SV33: $i] :
( ( ! [SY123: $i] :
( ~ ~ ( ~ ( subset @ SV33 @ SV57 )
| ~ ( subset @ SV65 @ SY123 ) )
| ( subset @ ( cartesian_product2 @ SV33 @ SV65 ) @ ( cartesian_product2 @ SV57 @ SY123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(429,plain,
! [SV66: $i,SV58: $i,SV34: $i] :
( ( ~ ( subset @ SV34 @ SV58 )
| ~ ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SV66 ) @ ( cartesian_product2 @ SV58 @ SV66 ) )
| ~ ( subset @ ( cartesian_product2 @ SV66 @ SV34 ) @ ( cartesian_product2 @ SV66 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(430,plain,
! [SV39: $i,SV7: $i] :
( ( ( relation @ SV7 )
= $false )
| ( ( relation @ ( relation_dom_restriction @ SV7 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(431,plain,
! [SV40: $i,SV8: $i] :
( ( ( ~ ( ~ ( relation @ SV8 )
| ~ ( relation @ SV40 ) ) )
= $false )
| ( ( relation @ ( set_union2 @ SV8 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(432,plain,
! [SV41: $i,SV9: $i] :
( ( ( subset @ SV9 @ SV41 )
= $false )
| ( ( ( set_union2 @ SV9 @ SV41 )
= SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(433,plain,
! [SV59: $i,SV42: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV10 @ SV42 )
| ~ ( subset @ SV59 @ SV42 ) ) )
= $true )
| ( ( subset @ ( set_union2 @ SV10 @ SV59 ) @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(434,plain,
! [SV43: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV43 )
| ~ ( proper_subset @ SV43 @ SV12 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[405]) ).
thf(435,plain,
! [SV44: $i,SV13: $i] :
( ( ~ ( ( SV13 != SV44 )
| ~ ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(436,plain,
! [SV44: $i,SV13: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) )
| ( SV13 = SV44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(437,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ( ~ ( subset @ SV14 @ SV45 )
| ! [SY113: $i] :
( ~ ( in @ SY113 @ SV14 )
| ( in @ SY113 @ SV45 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(438,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ( ~ ! [SY114: $i] :
( ~ ( in @ SY114 @ SV14 )
| ( in @ SY114 @ SV45 ) )
| ( subset @ SV14 @ SV45 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(439,plain,
! [SV46: $i,SV16: $i] :
( ( ( subset @ SV16 @ SV46 )
= $false )
| ( ( ( set_intersection2 @ SV16 @ SV46 )
= SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(440,plain,
! [SV60: $i,SV47: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV17 @ SV47 )
| ~ ( disjoint @ SV47 @ SV60 ) ) )
= $true )
| ( ( disjoint @ SV17 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(441,plain,
! [SV48: $i,SV18: $i] :
( ( ~ ( ~ ( proper_subset @ SV18 @ SV48 )
| ~ ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(442,plain,
! [SV48: $i,SV18: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) )
| ( proper_subset @ SV18 @ SV48 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(443,plain,
! [SV19: $i,SV67: $i] :
( ( ( ~ ( relation @ SV67 )
| ( subset @ ( relation_rng @ ( relation_composition @ SV19 @ SV67 ) ) @ ( relation_rng @ SV67 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(444,plain,
! [SV61: $i,SV49: $i,SV21: $i] :
( ( ( ~ ( subset @ SV21 @ SV49 ) )
= $true )
| ( ( subset @ ( set_intersection2 @ SV21 @ SV61 ) @ ( set_intersection2 @ SV49 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(445,plain,
! [SV22: $i,SV68: $i] :
( ( ( ~ ( relation @ SV68 )
| ~ ( subset @ SV22 @ SV68 )
| ~ ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_dom @ SV68 ) )
| ~ ( subset @ ( relation_rng @ SV22 ) @ ( relation_rng @ SV68 ) ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(446,plain,
! [SV62: $i,SV50: $i,SV24: $i] :
( ( ( ~ ( subset @ SV24 @ SV50 ) )
= $true )
| ( ( subset @ ( set_difference @ SV24 @ SV62 ) @ ( set_difference @ SV50 @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(447,plain,
! [SV51: $i,SV25: $i] :
( ( ( ~ ( ~ ( relation @ SV25 )
| ~ ( relation @ SV51 ) ) )
= $false )
| ( ( relation @ ( relation_composition @ SV25 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(448,plain,
! [SV26: $i] :
( ( ( ~ ~ ( empty @ SV26 )
| ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(449,plain,
! [SV63: $i,SV52: $i,SV27: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV27 @ SV52 )
| ~ ( subset @ SV27 @ SV63 ) ) )
= $true )
| ( ( subset @ SV27 @ ( set_intersection2 @ SV52 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(450,plain,
( ( ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[421]) ).
thf(451,plain,
! [SV28: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV28 ) )
| ~ ( relation @ ( relation_rng @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(452,plain,
! [SV64: $i,SV53: $i,SV29: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV29 @ SV53 )
| ~ ( subset @ SV53 @ SV64 ) ) )
= $true )
| ( ( subset @ SV29 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(453,plain,
! [SV54: $i,SV30: $i] :
( ( ( ~ ( ~ ( relation @ SV30 )
| ~ ( relation @ SV54 ) ) )
= $false )
| ( ( relation @ ( set_intersection2 @ SV30 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(454,plain,
! [SV55: $i,SV31: $i] :
( ( ( subset @ ( singleton @ SV31 ) @ ( singleton @ SV55 ) )
= $false )
| ( ( SV31 = SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(455,plain,
( ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(456,plain,
! [SV32: $i,SV56: $i] :
( ( ( relation @ SV56 )
= $false )
| ( ( subset @ ( relation_dom_restriction @ SV56 @ SV32 ) @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(457,plain,
! [SV69: $i,SV65: $i,SV57: $i,SV33: $i] :
( ( ~ ~ ( ~ ( subset @ SV33 @ SV57 )
| ~ ( subset @ SV65 @ SV69 ) )
| ( subset @ ( cartesian_product2 @ SV33 @ SV65 ) @ ( cartesian_product2 @ SV57 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(458,plain,
! [SV66: $i,SV58: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV58 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SV66 ) @ ( cartesian_product2 @ SV58 @ SV66 ) )
| ~ ( subset @ ( cartesian_product2 @ SV66 @ SV34 ) @ ( cartesian_product2 @ SV66 @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(459,plain,
! [SV40: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 )
| ~ ( relation @ SV40 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV8 @ SV40 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(460,plain,
! [SV59: $i,SV42: $i,SV10: $i] :
( ( ( ~ ( ~ ( subset @ SV10 @ SV42 )
| ~ ( subset @ SV59 @ SV42 ) ) )
= $false )
| ( ( subset @ ( set_union2 @ SV10 @ SV59 ) @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(461,plain,
! [SV43: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV43 ) )
= $true )
| ( ( ~ ( proper_subset @ SV43 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(462,plain,
! [SV44: $i,SV13: $i] :
( ( ( SV13 != SV44 )
| ~ ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(463,plain,
! [SV44: $i,SV13: $i] :
( ( ~ ~ ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) )
| ( SV13 = SV44 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[436]) ).
thf(464,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ( subset @ SV14 @ SV45 )
| ! [SY113: $i] :
( ~ ( in @ SY113 @ SV14 )
| ( in @ SY113 @ SV45 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(465,plain,
! [SV45: $i,SV14: $i] :
( ( ~ ! [SY114: $i] :
( ~ ( in @ SY114 @ SV14 )
| ( in @ SY114 @ SV45 ) )
| ( subset @ SV14 @ SV45 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(466,plain,
! [SV60: $i,SV47: $i,SV17: $i] :
( ( ( ~ ( ~ ( subset @ SV17 @ SV47 )
| ~ ( disjoint @ SV47 @ SV60 ) ) )
= $false )
| ( ( disjoint @ SV17 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(467,plain,
! [SV48: $i,SV18: $i] :
( ( ~ ( proper_subset @ SV18 @ SV48 )
| ~ ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(468,plain,
! [SV48: $i,SV18: $i] :
( ( ~ ~ ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) )
| ( proper_subset @ SV18 @ SV48 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(469,plain,
! [SV19: $i,SV67: $i] :
( ( ( ~ ( relation @ SV67 ) )
= $true )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV19 @ SV67 ) ) @ ( relation_rng @ SV67 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(470,plain,
! [SV61: $i,SV49: $i,SV21: $i] :
( ( ( subset @ SV21 @ SV49 )
= $false )
| ( ( subset @ ( set_intersection2 @ SV21 @ SV61 ) @ ( set_intersection2 @ SV49 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(471,plain,
! [SV22: $i,SV68: $i] :
( ( ( ~ ( relation @ SV68 ) )
= $true )
| ( ( ~ ( subset @ SV22 @ SV68 )
| ~ ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_dom @ SV68 ) )
| ~ ( subset @ ( relation_rng @ SV22 ) @ ( relation_rng @ SV68 ) ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[445]) ).
thf(472,plain,
! [SV62: $i,SV50: $i,SV24: $i] :
( ( ( subset @ SV24 @ SV50 )
= $false )
| ( ( subset @ ( set_difference @ SV24 @ SV62 ) @ ( set_difference @ SV50 @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(473,plain,
! [SV51: $i,SV25: $i] :
( ( ( ~ ( relation @ SV25 )
| ~ ( relation @ SV51 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV25 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(474,plain,
! [SV26: $i] :
( ( ( ~ ~ ( empty @ SV26 ) )
= $true )
| ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(475,plain,
! [SV63: $i,SV52: $i,SV27: $i] :
( ( ( ~ ( ~ ( subset @ SV27 @ SV52 )
| ~ ( subset @ SV27 @ SV63 ) ) )
= $false )
| ( ( subset @ SV27 @ ( set_intersection2 @ SV52 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[449]) ).
thf(476,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(477,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(478,plain,
! [SV28: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(479,plain,
! [SV28: $i] :
( ( ( ~ ( relation @ ( relation_rng @ SV28 ) ) )
= $false )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(480,plain,
! [SV64: $i,SV53: $i,SV29: $i] :
( ( ( ~ ( ~ ( subset @ SV29 @ SV53 )
| ~ ( subset @ SV53 @ SV64 ) ) )
= $false )
| ( ( subset @ SV29 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(481,plain,
! [SV54: $i,SV30: $i] :
( ( ( ~ ( relation @ SV30 )
| ~ ( relation @ SV54 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV30 @ SV54 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(482,plain,
( ( ~ ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(483,plain,
( ( ~ ( relation @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(484,plain,
! [SV69: $i,SV65: $i,SV57: $i,SV33: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV33 @ SV57 )
| ~ ( subset @ SV65 @ SV69 ) ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV33 @ SV65 ) @ ( cartesian_product2 @ SV57 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(485,plain,
! [SV66: $i,SV58: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV58 )
= $false )
| ( ( ~ ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SV66 ) @ ( cartesian_product2 @ SV58 @ SV66 ) )
| ~ ( subset @ ( cartesian_product2 @ SV66 @ SV34 ) @ ( cartesian_product2 @ SV66 @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(486,plain,
! [SV40: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ~ ( relation @ SV40 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV8 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(487,plain,
! [SV59: $i,SV42: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV42 )
| ~ ( subset @ SV59 @ SV42 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV10 @ SV59 ) @ SV42 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(488,plain,
! [SV43: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV43 )
= $false )
| ( ( ~ ( proper_subset @ SV43 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(489,plain,
! [SV44: $i,SV13: $i] :
( ( ( SV13 != SV44 )
= $true )
| ( ( ~ ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(490,plain,
! [SV44: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) ) )
= $true )
| ( ( SV13 = SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(491,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ( subset @ SV14 @ SV45 ) )
= $true )
| ( ( ! [SY113: $i] :
( ~ ( in @ SY113 @ SV14 )
| ( in @ SY113 @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(492,plain,
! [SV45: $i,SV14: $i] :
( ( ( ~ ! [SY114: $i] :
( ~ ( in @ SY114 @ SV14 )
| ( in @ SY114 @ SV45 ) ) )
= $true )
| ( ( subset @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(493,plain,
! [SV60: $i,SV47: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV47 )
| ~ ( disjoint @ SV47 @ SV60 ) )
= $true )
| ( ( disjoint @ SV17 @ SV60 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(494,plain,
! [SV48: $i,SV18: $i] :
( ( ( ~ ( proper_subset @ SV18 @ SV48 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(495,plain,
! [SV48: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) ) )
= $true )
| ( ( proper_subset @ SV18 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(496,plain,
! [SV19: $i,SV67: $i] :
( ( ( relation @ SV67 )
= $false )
| ( ( subset @ ( relation_rng @ ( relation_composition @ SV19 @ SV67 ) ) @ ( relation_rng @ SV67 ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(497,plain,
! [SV22: $i,SV68: $i] :
( ( ( relation @ SV68 )
= $false )
| ( ( ~ ( subset @ SV22 @ SV68 )
| ~ ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_dom @ SV68 ) )
| ~ ( subset @ ( relation_rng @ SV22 ) @ ( relation_rng @ SV68 ) ) ) )
= $true )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(498,plain,
! [SV51: $i,SV25: $i] :
( ( ( ~ ( relation @ SV25 ) )
= $true )
| ( ( ~ ( relation @ SV51 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV25 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(499,plain,
! [SV26: $i] :
( ( ( ~ ( empty @ SV26 ) )
= $false )
| ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(500,plain,
! [SV63: $i,SV52: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ SV52 )
| ~ ( subset @ SV27 @ SV63 ) )
= $true )
| ( ( subset @ SV27 @ ( set_intersection2 @ SV52 @ SV63 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(501,plain,
( ( empty @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(502,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(503,plain,
! [SV28: $i] :
( ( ( empty @ ( relation_rng @ SV28 ) )
= $true )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(504,plain,
! [SV28: $i] :
( ( ( relation @ ( relation_rng @ SV28 ) )
= $true )
| ( ( empty @ SV28 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(505,plain,
! [SV64: $i,SV53: $i,SV29: $i] :
( ( ( ~ ( subset @ SV29 @ SV53 )
| ~ ( subset @ SV53 @ SV64 ) )
= $true )
| ( ( subset @ SV29 @ SV64 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(506,plain,
! [SV54: $i,SV30: $i] :
( ( ( ~ ( relation @ SV30 ) )
= $true )
| ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV30 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(507,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(508,plain,
( ( relation @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(509,plain,
! [SV69: $i,SV65: $i,SV57: $i,SV33: $i] :
( ( ( ~ ( ~ ( subset @ SV33 @ SV57 )
| ~ ( subset @ SV65 @ SV69 ) ) )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV33 @ SV65 ) @ ( cartesian_product2 @ SV57 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(510,plain,
! [SV58: $i,SV66: $i,SV34: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SV66 ) @ ( cartesian_product2 @ SV58 @ SV66 ) )
| ~ ( subset @ ( cartesian_product2 @ SV66 @ SV34 ) @ ( cartesian_product2 @ SV66 @ SV58 ) ) )
= $false )
| ( ( subset @ SV34 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[485]) ).
thf(511,plain,
! [SV40: $i,SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ~ ( relation @ SV40 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV8 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(512,plain,
! [SV59: $i,SV42: $i,SV10: $i] :
( ( ( ~ ( subset @ SV10 @ SV42 ) )
= $true )
| ( ( ~ ( subset @ SV59 @ SV42 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV10 @ SV59 ) @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(513,plain,
! [SV12: $i,SV43: $i] :
( ( ( proper_subset @ SV43 @ SV12 )
= $false )
| ( ( subset @ SV12 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(514,plain,
! [SV44: $i,SV13: $i] :
( ( ( SV13 = SV44 )
= $false )
| ( ( ~ ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(515,plain,
! [SV44: $i,SV13: $i] :
( ( ( ~ ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) ) )
= $false )
| ( ( SV13 = SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(516,plain,
! [SV45: $i,SV14: $i] :
( ( ( subset @ SV14 @ SV45 )
= $false )
| ( ( ! [SY113: $i] :
( ~ ( in @ SY113 @ SV14 )
| ( in @ SY113 @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(517,plain,
! [SV45: $i,SV14: $i] :
( ( ( ! [SY114: $i] :
( ~ ( in @ SY114 @ SV14 )
| ( in @ SY114 @ SV45 ) ) )
= $false )
| ( ( subset @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(518,plain,
! [SV60: $i,SV47: $i,SV17: $i] :
( ( ( ~ ( subset @ SV17 @ SV47 ) )
= $true )
| ( ( ~ ( disjoint @ SV47 @ SV60 ) )
= $true )
| ( ( disjoint @ SV17 @ SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(519,plain,
! [SV48: $i,SV18: $i] :
( ( ( proper_subset @ SV18 @ SV48 )
= $false )
| ( ( ~ ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(520,plain,
! [SV48: $i,SV18: $i] :
( ( ( ~ ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) ) )
= $false )
| ( ( proper_subset @ SV18 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(521,plain,
! [SV68: $i,SV22: $i] :
( ( ( ~ ( subset @ SV22 @ SV68 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_dom @ SV68 ) )
| ~ ( subset @ ( relation_rng @ SV22 ) @ ( relation_rng @ SV68 ) ) ) )
= $true )
| ( ( relation @ SV68 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(522,plain,
! [SV51: $i,SV25: $i] :
( ( ( relation @ SV25 )
= $false )
| ( ( ~ ( relation @ SV51 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV25 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(523,plain,
! [SV26: $i] :
( ( ( empty @ SV26 )
= $true )
| ( ( ~ ( relation @ SV26 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(524,plain,
! [SV63: $i,SV52: $i,SV27: $i] :
( ( ( ~ ( subset @ SV27 @ SV52 ) )
= $true )
| ( ( ~ ( subset @ SV27 @ SV63 ) )
= $true )
| ( ( subset @ SV27 @ ( set_intersection2 @ SV52 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(525,plain,
! [SV64: $i,SV53: $i,SV29: $i] :
( ( ( ~ ( subset @ SV29 @ SV53 ) )
= $true )
| ( ( ~ ( subset @ SV53 @ SV64 ) )
= $true )
| ( ( subset @ SV29 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(526,plain,
! [SV54: $i,SV30: $i] :
( ( ( relation @ SV30 )
= $false )
| ( ( ~ ( relation @ SV54 ) )
= $true )
| ( ( relation @ ( set_intersection2 @ SV30 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(527,plain,
( ( empty @ sK4_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(528,plain,
! [SV69: $i,SV65: $i,SV57: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV57 )
| ~ ( subset @ SV65 @ SV69 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV33 @ SV65 ) @ ( cartesian_product2 @ SV57 @ SV69 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(529,plain,
! [SV58: $i,SV66: $i,SV34: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV34 @ SV66 ) @ ( cartesian_product2 @ SV58 @ SV66 ) ) )
= $false )
| ( ( subset @ SV34 @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(530,plain,
! [SV58: $i,SV34: $i,SV66: $i] :
( ( ( ~ ( subset @ ( cartesian_product2 @ SV66 @ SV34 ) @ ( cartesian_product2 @ SV66 @ SV58 ) ) )
= $false )
| ( ( subset @ SV34 @ SV58 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(531,plain,
! [SV8: $i,SV40: $i] :
( ( ( relation @ SV40 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( relation @ ( set_union2 @ SV8 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(532,plain,
! [SV59: $i,SV42: $i,SV10: $i] :
( ( ( subset @ SV10 @ SV42 )
= $false )
| ( ( ~ ( subset @ SV59 @ SV42 ) )
= $true )
| ( ( subset @ ( set_union2 @ SV10 @ SV59 ) @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(533,plain,
! [SV44: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) )
= $false )
| ( ( SV13 = SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[514]) ).
thf(534,plain,
! [SV44: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV44 )
| ~ ( subset @ SV44 @ SV13 ) )
= $true )
| ( ( SV13 = SV44 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(535,plain,
! [SV45: $i,SV14: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ SV14 )
| ( in @ SV70 @ SV45 ) )
= $true )
| ( ( subset @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(536,plain,
! [SV14: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK5_SY114 @ SV45 @ SV14 ) @ SV14 )
| ( in @ ( sK5_SY114 @ SV45 @ SV14 ) @ SV45 ) )
= $false )
| ( ( subset @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[517]) ).
thf(537,plain,
! [SV60: $i,SV47: $i,SV17: $i] :
( ( ( subset @ SV17 @ SV47 )
= $false )
| ( ( ~ ( disjoint @ SV47 @ SV60 ) )
= $true )
| ( ( disjoint @ SV17 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(538,plain,
! [SV48: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) )
= $false )
| ( ( proper_subset @ SV18 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(539,plain,
! [SV48: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV48 )
| ~ ( ( SV18 != SV48 ) ) )
= $true )
| ( ( proper_subset @ SV18 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(540,plain,
! [SV68: $i,SV22: $i] :
( ( ( subset @ SV22 @ SV68 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_dom @ SV68 ) )
| ~ ( subset @ ( relation_rng @ SV22 ) @ ( relation_rng @ SV68 ) ) ) )
= $true )
| ( ( relation @ SV68 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(541,plain,
! [SV25: $i,SV51: $i] :
( ( ( relation @ SV51 )
= $false )
| ( ( relation @ SV25 )
= $false )
| ( ( relation @ ( relation_composition @ SV25 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(542,plain,
! [SV26: $i] :
( ( ( relation @ SV26 )
= $false )
| ( ( empty @ SV26 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(543,plain,
! [SV63: $i,SV52: $i,SV27: $i] :
( ( ( subset @ SV27 @ SV52 )
= $false )
| ( ( ~ ( subset @ SV27 @ SV63 ) )
= $true )
| ( ( subset @ SV27 @ ( set_intersection2 @ SV52 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(544,plain,
! [SV64: $i,SV53: $i,SV29: $i] :
( ( ( subset @ SV29 @ SV53 )
= $false )
| ( ( ~ ( subset @ SV53 @ SV64 ) )
= $true )
| ( ( subset @ SV29 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(545,plain,
! [SV30: $i,SV54: $i] :
( ( ( relation @ SV54 )
= $false )
| ( ( relation @ SV30 )
= $false )
| ( ( relation @ ( set_intersection2 @ SV30 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(546,plain,
! [SV69: $i,SV65: $i,SV57: $i,SV33: $i] :
( ( ( ~ ( subset @ SV33 @ SV57 ) )
= $true )
| ( ( ~ ( subset @ SV65 @ SV69 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV33 @ SV65 ) @ ( cartesian_product2 @ SV57 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(547,plain,
! [SV58: $i,SV66: $i,SV34: $i] :
( ( ( subset @ ( cartesian_product2 @ SV34 @ SV66 ) @ ( cartesian_product2 @ SV58 @ SV66 ) )
= $true )
| ( ( subset @ SV34 @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(548,plain,
! [SV58: $i,SV34: $i,SV66: $i] :
( ( ( subset @ ( cartesian_product2 @ SV66 @ SV34 ) @ ( cartesian_product2 @ SV66 @ SV58 ) )
= $true )
| ( ( subset @ SV34 @ SV58 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(549,plain,
! [SV10: $i,SV42: $i,SV59: $i] :
( ( ( subset @ SV59 @ SV42 )
= $false )
| ( ( subset @ SV10 @ SV42 )
= $false )
| ( ( subset @ ( set_union2 @ SV10 @ SV59 ) @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(550,plain,
! [SV44: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV44 ) )
= $false )
| ( ( SV13 = SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(551,plain,
! [SV13: $i,SV44: $i] :
( ( ( ~ ( subset @ SV44 @ SV13 ) )
= $false )
| ( ( SV13 = SV44 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[533]) ).
thf(552,plain,
! [SV44: $i,SV13: $i] :
( ( ( ~ ( subset @ SV13 @ SV44 ) )
= $true )
| ( ( ~ ( subset @ SV44 @ SV13 ) )
= $true )
| ( ( SV13 = SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(553,plain,
! [SV45: $i,SV14: $i,SV70: $i] :
( ( ( ~ ( in @ SV70 @ SV14 ) )
= $true )
| ( ( in @ SV70 @ SV45 )
= $true )
| ( ( subset @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(554,plain,
! [SV14: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK5_SY114 @ SV45 @ SV14 ) @ SV14 ) )
= $false )
| ( ( subset @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(555,plain,
! [SV14: $i,SV45: $i] :
( ( ( in @ ( sK5_SY114 @ SV45 @ SV14 ) @ SV45 )
= $false )
| ( ( subset @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[536]) ).
thf(556,plain,
! [SV17: $i,SV60: $i,SV47: $i] :
( ( ( disjoint @ SV47 @ SV60 )
= $false )
| ( ( subset @ SV17 @ SV47 )
= $false )
| ( ( disjoint @ SV17 @ SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(557,plain,
! [SV48: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV48 ) )
= $false )
| ( ( proper_subset @ SV18 @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(558,plain,
! [SV48: $i,SV18: $i] :
( ( ( ~ ( ( SV18 != SV48 ) ) )
= $false )
| ( ( proper_subset @ SV18 @ SV48 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[538]) ).
thf(559,plain,
! [SV48: $i,SV18: $i] :
( ( ( ~ ( subset @ SV18 @ SV48 ) )
= $true )
| ( ( ~ ( ( SV18 != SV48 ) ) )
= $true )
| ( ( proper_subset @ SV18 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(560,plain,
! [SV68: $i,SV22: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_dom @ SV68 ) )
| ~ ( subset @ ( relation_rng @ SV22 ) @ ( relation_rng @ SV68 ) ) )
= $false )
| ( ( subset @ SV22 @ SV68 )
= $false )
| ( ( relation @ SV68 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(561,plain,
! [SV26: $i] :
( ( ( empty @ ( relation_rng @ SV26 ) )
= $false )
| ( ( empty @ SV26 )
= $true )
| ( ( relation @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(562,plain,
! [SV52: $i,SV63: $i,SV27: $i] :
( ( ( subset @ SV27 @ SV63 )
= $false )
| ( ( subset @ SV27 @ SV52 )
= $false )
| ( ( subset @ SV27 @ ( set_intersection2 @ SV52 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(563,plain,
! [SV29: $i,SV64: $i,SV53: $i] :
( ( ( subset @ SV53 @ SV64 )
= $false )
| ( ( subset @ SV29 @ SV53 )
= $false )
| ( ( subset @ SV29 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(564,plain,
! [SV69: $i,SV65: $i,SV57: $i,SV33: $i] :
( ( ( subset @ SV33 @ SV57 )
= $false )
| ( ( ~ ( subset @ SV65 @ SV69 ) )
= $true )
| ( ( subset @ ( cartesian_product2 @ SV33 @ SV65 ) @ ( cartesian_product2 @ SV57 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(565,plain,
! [SV44: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV44 )
= $true )
| ( ( SV13 = SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(566,plain,
! [SV13: $i,SV44: $i] :
( ( ( subset @ SV44 @ SV13 )
= $true )
| ( ( SV13 = SV44 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(567,plain,
! [SV44: $i,SV13: $i] :
( ( ( subset @ SV13 @ SV44 )
= $false )
| ( ( ~ ( subset @ SV44 @ SV13 ) )
= $true )
| ( ( SV13 = SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(568,plain,
! [SV45: $i,SV14: $i,SV70: $i] :
( ( ( in @ SV70 @ SV14 )
= $false )
| ( ( in @ SV70 @ SV45 )
= $true )
| ( ( subset @ SV14 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(569,plain,
! [SV14: $i,SV45: $i] :
( ( ( in @ ( sK5_SY114 @ SV45 @ SV14 ) @ SV14 )
= $true )
| ( ( subset @ SV14 @ SV45 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(570,plain,
! [SV48: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV48 )
= $true )
| ( ( proper_subset @ SV18 @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[557]) ).
thf(571,plain,
! [SV48: $i,SV18: $i] :
( ( ( SV18 != SV48 )
= $true )
| ( ( proper_subset @ SV18 @ SV48 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[558]) ).
thf(572,plain,
! [SV48: $i,SV18: $i] :
( ( ( subset @ SV18 @ SV48 )
= $false )
| ( ( ~ ( ( SV18 != SV48 ) ) )
= $true )
| ( ( proper_subset @ SV18 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(573,plain,
! [SV68: $i,SV22: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV22 ) @ ( relation_dom @ SV68 ) ) )
= $false )
| ( ( subset @ SV22 @ SV68 )
= $false )
| ( ( relation @ SV68 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(574,plain,
! [SV68: $i,SV22: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV22 ) @ ( relation_rng @ SV68 ) ) )
= $false )
| ( ( subset @ SV22 @ SV68 )
= $false )
| ( ( relation @ SV68 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[560]) ).
thf(575,plain,
! [SV57: $i,SV33: $i,SV69: $i,SV65: $i] :
( ( ( subset @ SV65 @ SV69 )
= $false )
| ( ( subset @ SV33 @ SV57 )
= $false )
| ( ( subset @ ( cartesian_product2 @ SV33 @ SV65 ) @ ( cartesian_product2 @ SV57 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(576,plain,
! [SV13: $i,SV44: $i] :
( ( ( subset @ SV44 @ SV13 )
= $false )
| ( ( subset @ SV13 @ SV44 )
= $false )
| ( ( SV13 = SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(577,plain,
! [SV48: $i,SV18: $i] :
( ( ( SV18 = SV48 )
= $false )
| ( ( proper_subset @ SV18 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(578,plain,
! [SV48: $i,SV18: $i] :
( ( ( SV18 != SV48 )
= $false )
| ( ( subset @ SV18 @ SV48 )
= $false )
| ( ( proper_subset @ SV18 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[572]) ).
thf(579,plain,
! [SV68: $i,SV22: $i] :
( ( ( subset @ ( relation_dom @ SV22 ) @ ( relation_dom @ SV68 ) )
= $true )
| ( ( subset @ SV22 @ SV68 )
= $false )
| ( ( relation @ SV68 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[573]) ).
thf(580,plain,
! [SV68: $i,SV22: $i] :
( ( ( subset @ ( relation_rng @ SV22 ) @ ( relation_rng @ SV68 ) )
= $true )
| ( ( subset @ SV22 @ SV68 )
= $false )
| ( ( relation @ SV68 )
= $false )
| ( ( relation @ SV22 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[574]) ).
thf(581,plain,
! [SV48: $i,SV18: $i] :
( ( ( SV18 = SV48 )
= $true )
| ( ( subset @ SV18 @ SV48 )
= $false )
| ( ( proper_subset @ SV18 @ SV48 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[578]) ).
thf(582,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[270,581,580,579,577,576,575,570,569,568,566,565,563,562,561,556,555,549,548,547,545,541,531,527,513,508,504,503,502,501,496,472,470,456,454,439,432,430,416,413,408,404,369,368,367,366,335,333,330,297,288,284,283,281,280,279,278,277,276,275,274,273,272,271]) ).
thf(583,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU196+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Oct 6 15:03:46 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.59/0.86 .
% 3.59/0.86
% 3.59/0.86 No.of.Axioms: 51
% 3.59/0.86
% 3.59/0.86 Length.of.Defs: 0
% 3.59/0.86
% 3.59/0.86 Contains.Choice.Funs: false
% 3.59/0.86 ............
% 3.59/0.86
% 3.59/0.86 ********************************
% 3.59/0.86 * All subproblems solved! *
% 3.59/0.86 ********************************
% 3.59/0.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:52,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:582,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.59/0.86
% 3.59/0.86 %**** Beginning of derivation protocol ****
% 3.59/0.86 % SZS output start CNFRefutation
% See solution above
% 3.59/0.86
% 3.59/0.86 %**** End of derivation protocol ****
% 3.59/0.86 %**** no. of clauses in derivation: 448 ****
% 3.59/0.86 %**** clause counter: 582 ****
% 3.59/0.86
% 3.59/0.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:52,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:582,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------