%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU188+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 10:43:20 AM UTC 2026
% Result : Theorem 0.46s 0.34s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 41
% Syntax : Number of formulae : 288 ( 189 unt; 0 typ; 0 def)
% Number of atoms : 1328 ( 478 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 1537 ( 366 ~; 232 |; 36 &; 847 @)
% ( 3 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 34 usr; 6 con; 0-3 aty)
% Number of variables : 255 ( 0 ^; 249 !; 6 ?; 255 :)
% 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_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_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_SX0,type,
sK2_SX0: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY29,type,
sK4_SY29: $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(4,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(7,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(9,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(12,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(14,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
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(32,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(33,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(34,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(35,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(37,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(42,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(44,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(47,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(52,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(53,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(54,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_tarski) ).
thf(55,axiom,
! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relat_1) ).
thf(56,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(57,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(59,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_relat_1) ).
thf(60,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_zfmisc_1) ).
thf(61,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(62,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(64,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_relat_1) ).
thf(65,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(66,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(67,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(68,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_setfam_1) ).
thf(69,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_relat_1) ).
thf(90,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(98,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(113,axiom,
( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
thf(130,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(137,axiom,
! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_relat_1) ).
thf(142,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(145,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(169,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(170,conjecture,
! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
thf(171,negated_conjecture,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[170]) ).
thf(172,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( ( relation_dom @ A )
= empty_set )
| ( ( relation_rng @ A )
= empty_set ) )
=> ( A = empty_set ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[171]) ).
thf(173,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(174,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(175,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(176,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(177,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(178,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(179,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(180,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(181,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(182,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(183,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(184,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(185,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(186,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(187,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(188,plain,
$true = $true,
inference(unfold_def,[status(thm)],[47]) ).
thf(189,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(190,plain,
$true = $true,
inference(unfold_def,[status(thm)],[53]) ).
thf(191,plain,
$true = $true,
inference(unfold_def,[status(thm)],[54]) ).
thf(192,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(193,plain,
$true = $true,
inference(unfold_def,[status(thm)],[56]) ).
thf(194,plain,
$true = $true,
inference(unfold_def,[status(thm)],[57]) ).
thf(195,plain,
$true = $true,
inference(unfold_def,[status(thm)],[59]) ).
thf(196,plain,
$true = $true,
inference(unfold_def,[status(thm)],[60]) ).
thf(197,plain,
$true = $true,
inference(unfold_def,[status(thm)],[61]) ).
thf(198,plain,
$true = $true,
inference(unfold_def,[status(thm)],[62]) ).
thf(199,plain,
$true = $true,
inference(unfold_def,[status(thm)],[64]) ).
thf(200,plain,
$true = $true,
inference(unfold_def,[status(thm)],[65]) ).
thf(201,plain,
$true = $true,
inference(unfold_def,[status(thm)],[66]) ).
thf(202,plain,
$true = $true,
inference(unfold_def,[status(thm)],[67]) ).
thf(203,plain,
$true = $true,
inference(unfold_def,[status(thm)],[68]) ).
thf(204,plain,
$true = $true,
inference(unfold_def,[status(thm)],[69]) ).
thf(205,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(206,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(207,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(208,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(209,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(210,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(211,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)],[145]) ).
thf(212,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(213,plain,
( ( ( relation @ sK1_A )
=> ( ( ( ( relation_dom @ sK1_A )
= empty_set )
| ( ( relation_rng @ sK1_A )
= empty_set ) )
=> ( sK1_A = empty_set ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[172]) ).
thf(214,plain,
( ( relation @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[213]) ).
thf(215,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
| ( ( relation_rng @ sK1_A )
= empty_set ) )
= $true ),
inference(standard_cnf,[status(thm)],[213]) ).
thf(216,plain,
( ( sK1_A = empty_set )
= $false ),
inference(standard_cnf,[status(thm)],[213]) ).
thf(217,plain,
( ( sK1_A != empty_set )
= $true ),
inference(polarity_switch,[status(thm)],[216]) ).
thf(218,plain,
( ( ! [A: $i] :
( ( singleton @ A )
!= empty_set ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(219,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)],[211]) ).
thf(220,plain,
( ( ! [A: $i] : ( subset @ empty_set @ A ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(221,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( ( relation_rng @ A )
= ( relation_dom @ ( relation_inverse @ A ) ) )
& ( ( relation_dom @ A )
= ( relation_rng @ ( relation_inverse @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(222,plain,
( ( ! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(223,plain,
( ( ( ( relation_dom @ empty_set )
= empty_set )
& ( ( relation_rng @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(224,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(225,plain,
( ( ! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(226,plain,
$true = $true,
inference(copy,[status(thm)],[204]) ).
thf(227,plain,
$true = $true,
inference(copy,[status(thm)],[203]) ).
thf(228,plain,
$true = $true,
inference(copy,[status(thm)],[202]) ).
thf(229,plain,
$true = $true,
inference(copy,[status(thm)],[201]) ).
thf(230,plain,
$true = $true,
inference(copy,[status(thm)],[200]) ).
thf(231,plain,
$true = $true,
inference(copy,[status(thm)],[199]) ).
thf(232,plain,
$true = $true,
inference(copy,[status(thm)],[198]) ).
thf(233,plain,
$true = $true,
inference(copy,[status(thm)],[197]) ).
thf(234,plain,
$true = $true,
inference(copy,[status(thm)],[196]) ).
thf(235,plain,
$true = $true,
inference(copy,[status(thm)],[195]) ).
thf(236,plain,
$true = $true,
inference(copy,[status(thm)],[194]) ).
thf(237,plain,
$true = $true,
inference(copy,[status(thm)],[193]) ).
thf(238,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( relation @ ( relation_inverse @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(239,plain,
$true = $true,
inference(copy,[status(thm)],[191]) ).
thf(240,plain,
$true = $true,
inference(copy,[status(thm)],[190]) ).
thf(241,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(242,plain,
$true = $true,
inference(copy,[status(thm)],[188]) ).
thf(243,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(245,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(246,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(247,plain,
( ( ! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(248,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(249,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(250,plain,
( ( ! [A: $i] :
( ( relation @ A )
=> ( ( relation_inverse @ ( relation_inverse @ A ) )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(251,plain,
( ( ? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(252,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(253,plain,
( ( ! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(254,plain,
( ( ! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(255,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(256,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(257,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(258,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
| ( ( relation_rng @ sK1_A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(259,plain,
( ( relation @ sK1_A )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(260,plain,
( ( sK1_A != empty_set )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(261,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( relation @ ( relation_inverse @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(262,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_dom @ SX0 ) )
| ~ ( relation @ ( relation_dom @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(263,plain,
( ( ~ ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(264,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(265,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( SX0 != empty_set )
| ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) )
| ~ ( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(266,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(267,plain,
( ( ! [SX0: $i] :
( ( singleton @ SX0 )
!= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(268,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ~ ( ~ ( empty @ ( relation_rng @ SX0 ) )
| ~ ( relation @ ( relation_rng @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(269,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(270,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(271,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ( ( relation_inverse @ ( relation_inverse @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(272,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(273,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ empty_set )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(274,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(275,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( relation_composition @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(276,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_rng @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(277,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) )
| ~ ( empty @ ( relation_dom @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(278,plain,
( ( ! [SX0: $i] :
( ~ ( relation @ SX0 )
| ~ ( ( ( relation_rng @ SX0 )
!= ( relation_dom @ ( relation_inverse @ SX0 ) ) )
| ( ( relation_dom @ SX0 )
!= ( relation_rng @ ( relation_inverse @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(279,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)],[219]) ).
thf(280,plain,
! [SV1: $i] :
( ( subset @ empty_set @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(281,plain,
! [SV2: $i] :
( ( ( set_union2 @ SV2 @ empty_set )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(282,plain,
! [SV3: $i] :
( ( ( set_intersection2 @ SV3 @ empty_set )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(283,plain,
! [SV4: $i] :
( ( ( set_difference @ SV4 @ empty_set )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(284,plain,
! [SV5: $i] :
( ( ( set_difference @ empty_set @ SV5 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(285,plain,
( ( ( ( relation_dom @ sK1_A )
= empty_set )
= $true )
| ( ( ( relation_rng @ sK1_A )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(286,plain,
( ( sK1_A = empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(287,plain,
! [SV6: $i] :
( ( ~ ( relation @ SV6 )
| ( relation @ ( relation_inverse @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(288,plain,
! [SV7: $i] :
( ( ~ ( empty @ SV7 )
| ~ ( ~ ( empty @ ( relation_dom @ SV7 ) )
| ~ ( relation @ ( relation_dom @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(289,plain,
( ( ( ( relation_dom @ empty_set )
!= empty_set )
| ( ( relation_rng @ empty_set )
!= empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(290,plain,
! [SV8: $i] :
( ( ! [SY27: $i] :
( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( relation @ SY27 ) )
| ( relation @ ( set_union2 @ SV8 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(291,plain,
! [SV9: $i] :
( ( ~ ( ~ ( ( SV9 != empty_set )
| ! [SY28: $i] :
~ ( in @ SY28 @ SV9 ) )
| ~ ( ~ ! [SY29: $i] :
~ ( in @ SY29 @ SV9 )
| ( SV9 = empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(292,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(293,plain,
! [SV10: $i] :
( ( ( singleton @ SV10 )
!= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(294,plain,
! [SV11: $i] :
( ( ~ ( empty @ SV11 )
| ~ ( ~ ( empty @ ( relation_rng @ SV11 ) )
| ~ ( relation @ ( relation_rng @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(295,plain,
! [SV12: $i] :
( ( ~ ( empty @ SV12 )
| ( SV12 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(296,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(297,plain,
! [SV13: $i] :
( ( ~ ( relation @ SV13 )
| ( ( relation_inverse @ ( relation_inverse @ SV13 ) )
= SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(298,plain,
! [SV14: $i] :
( ( ~ ( empty @ SV14 )
| ( relation @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(299,plain,
! [SV15: $i] :
( ( ~ ( subset @ SV15 @ empty_set )
| ( SV15 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(300,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( empty @ SX0 )
| ~ ( relation @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(301,plain,
! [SV16: $i] :
( ( ! [SY30: $i] :
( ~ ~ ( ~ ( relation @ SV16 )
| ~ ( relation @ SY30 ) )
| ( relation @ ( relation_composition @ SV16 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(302,plain,
! [SV17: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV17 )
| ~ ( relation @ SV17 ) )
| ~ ( empty @ ( relation_rng @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(303,plain,
! [SV18: $i] :
( ( ~ ~ ( ~ ~ ( empty @ SV18 )
| ~ ( relation @ SV18 ) )
| ~ ( empty @ ( relation_dom @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(304,plain,
! [SV19: $i] :
( ( ~ ( relation @ SV19 )
| ~ ( ( ( relation_rng @ SV19 )
!= ( relation_dom @ ( relation_inverse @ SV19 ) ) )
| ( ( relation_dom @ SV19 )
!= ( relation_rng @ ( relation_inverse @ SV19 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(305,plain,
! [SV20: $i] :
( ( ~ ( relation @ SV20 )
| ! [SY31: $i] :
( ~ ( relation @ SY31 )
| ~ ( subset @ SV20 @ SY31 )
| ~ ( ~ ( subset @ ( relation_dom @ SV20 ) @ ( relation_dom @ SY31 ) )
| ~ ( subset @ ( relation_rng @ SV20 ) @ ( relation_rng @ SY31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(306,plain,
! [SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( relation @ ( relation_inverse @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[287]) ).
thf(307,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV7 ) )
| ~ ( relation @ ( relation_dom @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(308,plain,
( ( ( relation_dom @ empty_set )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(309,plain,
( ( ( relation_rng @ empty_set )
!= empty_set )
= $false ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(310,plain,
! [SV21: $i,SV8: $i] :
( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( relation @ SV21 ) )
| ( relation @ ( set_union2 @ SV8 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(311,plain,
! [SV9: $i] :
( ( ~ ( ( SV9 != empty_set )
| ! [SY28: $i] :
~ ( in @ SY28 @ SV9 ) )
| ~ ( ~ ! [SY29: $i] :
~ ( in @ SY29 @ SV9 )
| ( SV9 = empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(312,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[292]) ).
thf(313,plain,
! [SV10: $i] :
( ( ( singleton @ SV10 )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(314,plain,
! [SV11: $i] :
( ( ( ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV11 ) )
| ~ ( relation @ ( relation_rng @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(315,plain,
! [SV12: $i] :
( ( ( ~ ( empty @ SV12 ) )
= $true )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(316,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(317,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(318,plain,
! [SV13: $i] :
( ( ( ~ ( relation @ SV13 ) )
= $true )
| ( ( ( relation_inverse @ ( relation_inverse @ SV13 ) )
= SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(319,plain,
! [SV14: $i] :
( ( ( ~ ( empty @ SV14 ) )
= $true )
| ( ( relation @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(320,plain,
! [SV15: $i] :
( ( ( ~ ( subset @ SV15 @ empty_set ) )
= $true )
| ( ( SV15 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(321,plain,
( ( ~ ~ ( ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[300]) ).
thf(322,plain,
! [SV22: $i,SV16: $i] :
( ( ~ ~ ( ~ ( relation @ SV16 )
| ~ ( relation @ SV22 ) )
| ( relation @ ( relation_composition @ SV16 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(323,plain,
! [SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV17 )
| ~ ( relation @ SV17 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[302]) ).
thf(324,plain,
! [SV18: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV18 )
| ~ ( relation @ SV18 ) ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(325,plain,
! [SV19: $i] :
( ( ( ~ ( relation @ SV19 ) )
= $true )
| ( ( ~ ( ( ( relation_rng @ SV19 )
!= ( relation_dom @ ( relation_inverse @ SV19 ) ) )
| ( ( relation_dom @ SV19 )
!= ( relation_rng @ ( relation_inverse @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(326,plain,
! [SV20: $i] :
( ( ( ~ ( relation @ SV20 ) )
= $true )
| ( ( ! [SY31: $i] :
( ~ ( relation @ SY31 )
| ~ ( subset @ SV20 @ SY31 )
| ~ ( ~ ( subset @ ( relation_dom @ SV20 ) @ ( relation_dom @ SY31 ) )
| ~ ( subset @ ( relation_rng @ SV20 ) @ ( relation_rng @ SY31 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(327,plain,
! [SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( relation @ ( relation_inverse @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(328,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_dom @ SV7 ) )
| ~ ( relation @ ( relation_dom @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(329,plain,
( ( ( relation_dom @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[308]) ).
thf(330,plain,
( ( ( relation_rng @ empty_set )
= empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(331,plain,
! [SV21: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV8 )
| ~ ( relation @ SV21 ) ) )
= $true )
| ( ( relation @ ( set_union2 @ SV8 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(332,plain,
! [SV9: $i] :
( ( ~ ( ( SV9 != empty_set )
| ! [SY28: $i] :
~ ( in @ SY28 @ SV9 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(333,plain,
! [SV9: $i] :
( ( ~ ( ~ ! [SY29: $i] :
~ ( in @ SY29 @ SV9 )
| ( SV9 = empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(334,plain,
( ( ~ ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[312]) ).
thf(335,plain,
! [SV11: $i] :
( ( ( empty @ SV11 )
= $false )
| ( ( ~ ( ~ ( empty @ ( relation_rng @ SV11 ) )
| ~ ( relation @ ( relation_rng @ SV11 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(336,plain,
! [SV12: $i] :
( ( ( empty @ SV12 )
= $false )
| ( ( SV12 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(337,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[316]) ).
thf(338,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[317]) ).
thf(339,plain,
! [SV13: $i] :
( ( ( relation @ SV13 )
= $false )
| ( ( ( relation_inverse @ ( relation_inverse @ SV13 ) )
= SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(340,plain,
! [SV14: $i] :
( ( ( empty @ SV14 )
= $false )
| ( ( relation @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(341,plain,
! [SV15: $i] :
( ( ( subset @ SV15 @ empty_set )
= $false )
| ( ( SV15 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[320]) ).
thf(342,plain,
( ( ~ ( ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(343,plain,
! [SV22: $i,SV16: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV16 )
| ~ ( relation @ SV22 ) ) )
= $true )
| ( ( relation @ ( relation_composition @ SV16 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(344,plain,
! [SV17: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV17 )
| ~ ( relation @ SV17 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_rng @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(345,plain,
! [SV18: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV18 )
| ~ ( relation @ SV18 ) ) )
= $false )
| ( ( ~ ( empty @ ( relation_dom @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(346,plain,
! [SV19: $i] :
( ( ( relation @ SV19 )
= $false )
| ( ( ~ ( ( ( relation_rng @ SV19 )
!= ( relation_dom @ ( relation_inverse @ SV19 ) ) )
| ( ( relation_dom @ SV19 )
!= ( relation_rng @ ( relation_inverse @ SV19 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(347,plain,
! [SV20: $i] :
( ( ( relation @ SV20 )
= $false )
| ( ( ! [SY31: $i] :
( ~ ( relation @ SY31 )
| ~ ( subset @ SV20 @ SY31 )
| ~ ( ~ ( subset @ ( relation_dom @ SV20 ) @ ( relation_dom @ SY31 ) )
| ~ ( subset @ ( relation_rng @ SV20 ) @ ( relation_rng @ SY31 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(348,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV7 ) )
| ~ ( relation @ ( relation_dom @ SV7 ) ) )
= $false )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(349,plain,
! [SV21: $i,SV8: $i] :
( ( ( ~ ( ~ ( relation @ SV8 )
| ~ ( relation @ SV21 ) ) )
= $false )
| ( ( relation @ ( set_union2 @ SV8 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(350,plain,
! [SV9: $i] :
( ( ( SV9 != empty_set )
| ! [SY28: $i] :
~ ( in @ SY28 @ SV9 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(351,plain,
! [SV9: $i] :
( ( ~ ! [SY29: $i] :
~ ( in @ SY29 @ SV9 )
| ( SV9 = empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[333]) ).
thf(352,plain,
( ( ~ ~ ( empty @ sK2_SX0 )
| ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(353,plain,
! [SV11: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV11 ) )
| ~ ( relation @ ( relation_rng @ SV11 ) ) )
= $false )
| ( ( empty @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(354,plain,
( ( ~ ( empty @ sK3_SX0 )
| ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(355,plain,
! [SV22: $i,SV16: $i] :
( ( ( ~ ( ~ ( relation @ SV16 )
| ~ ( relation @ SV22 ) ) )
= $false )
| ( ( relation @ ( relation_composition @ SV16 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(356,plain,
! [SV17: $i] :
( ( ( ~ ~ ( empty @ SV17 )
| ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(357,plain,
! [SV18: $i] :
( ( ( ~ ~ ( empty @ SV18 )
| ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(358,plain,
! [SV19: $i] :
( ( ( ( ( relation_rng @ SV19 )
!= ( relation_dom @ ( relation_inverse @ SV19 ) ) )
| ( ( relation_dom @ SV19 )
!= ( relation_rng @ ( relation_inverse @ SV19 ) ) ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(359,plain,
! [SV20: $i,SV23: $i] :
( ( ( ~ ( relation @ SV23 )
| ~ ( subset @ SV20 @ SV23 )
| ~ ( ~ ( subset @ ( relation_dom @ SV20 ) @ ( relation_dom @ SV23 ) )
| ~ ( subset @ ( relation_rng @ SV20 ) @ ( relation_rng @ SV23 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(360,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ ( relation_dom @ SV7 ) ) )
= $false )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(361,plain,
! [SV7: $i] :
( ( ( ~ ( relation @ ( relation_dom @ SV7 ) ) )
= $false )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[348]) ).
thf(362,plain,
! [SV21: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 )
| ~ ( relation @ SV21 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV8 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(363,plain,
! [SV9: $i] :
( ( ( SV9 != empty_set )
= $true )
| ( ( ! [SY28: $i] :
~ ( in @ SY28 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(364,plain,
! [SV9: $i] :
( ( ( ~ ! [SY29: $i] :
~ ( in @ SY29 @ SV9 ) )
= $true )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(365,plain,
( ( ~ ~ ( empty @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(366,plain,
( ( ~ ( relation @ sK2_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[352]) ).
thf(367,plain,
! [SV11: $i] :
( ( ( ~ ( empty @ ( relation_rng @ SV11 ) ) )
= $false )
| ( ( empty @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(368,plain,
! [SV11: $i] :
( ( ( ~ ( relation @ ( relation_rng @ SV11 ) ) )
= $false )
| ( ( empty @ SV11 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[353]) ).
thf(369,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(370,plain,
( ( ~ ( relation @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[354]) ).
thf(371,plain,
! [SV22: $i,SV16: $i] :
( ( ( ~ ( relation @ SV16 )
| ~ ( relation @ SV22 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV16 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(372,plain,
! [SV17: $i] :
( ( ( ~ ~ ( empty @ SV17 ) )
= $true )
| ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(373,plain,
! [SV18: $i] :
( ( ( ~ ~ ( empty @ SV18 ) )
= $true )
| ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(374,plain,
! [SV19: $i] :
( ( ( ( relation_rng @ SV19 )
!= ( relation_dom @ ( relation_inverse @ SV19 ) ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(375,plain,
! [SV19: $i] :
( ( ( ( relation_dom @ SV19 )
!= ( relation_rng @ ( relation_inverse @ SV19 ) ) )
= $false )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(376,plain,
! [SV20: $i,SV23: $i] :
( ( ( ~ ( relation @ SV23 ) )
= $true )
| ( ( ~ ( subset @ SV20 @ SV23 )
| ~ ( ~ ( subset @ ( relation_dom @ SV20 ) @ ( relation_dom @ SV23 ) )
| ~ ( subset @ ( relation_rng @ SV20 ) @ ( relation_rng @ SV23 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(377,plain,
! [SV7: $i] :
( ( ( empty @ ( relation_dom @ SV7 ) )
= $true )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(378,plain,
! [SV7: $i] :
( ( ( relation @ ( relation_dom @ SV7 ) )
= $true )
| ( ( empty @ SV7 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[361]) ).
thf(379,plain,
! [SV21: $i,SV8: $i] :
( ( ( ~ ( relation @ SV8 ) )
= $true )
| ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV8 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(380,plain,
! [SV9: $i] :
( ( ( SV9 = empty_set )
= $false )
| ( ( ! [SY28: $i] :
~ ( in @ SY28 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(381,plain,
! [SV9: $i] :
( ( ( ! [SY29: $i] :
~ ( in @ SY29 @ SV9 ) )
= $false )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(382,plain,
( ( ~ ( empty @ sK2_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(383,plain,
( ( relation @ sK2_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[366]) ).
thf(384,plain,
! [SV11: $i] :
( ( ( empty @ ( relation_rng @ SV11 ) )
= $true )
| ( ( empty @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[367]) ).
thf(385,plain,
! [SV11: $i] :
( ( ( relation @ ( relation_rng @ SV11 ) )
= $true )
| ( ( empty @ SV11 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[368]) ).
thf(386,plain,
( ( empty @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(387,plain,
( ( relation @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(388,plain,
! [SV22: $i,SV16: $i] :
( ( ( ~ ( relation @ SV16 ) )
= $true )
| ( ( ~ ( relation @ SV22 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV16 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(389,plain,
! [SV17: $i] :
( ( ( ~ ( empty @ SV17 ) )
= $false )
| ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(390,plain,
! [SV18: $i] :
( ( ( ~ ( empty @ SV18 ) )
= $false )
| ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(391,plain,
! [SV19: $i] :
( ( ( ( relation_rng @ SV19 )
= ( relation_dom @ ( relation_inverse @ SV19 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(392,plain,
! [SV19: $i] :
( ( ( ( relation_dom @ SV19 )
= ( relation_rng @ ( relation_inverse @ SV19 ) ) )
= $true )
| ( ( relation @ SV19 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(393,plain,
! [SV20: $i,SV23: $i] :
( ( ( relation @ SV23 )
= $false )
| ( ( ~ ( subset @ SV20 @ SV23 )
| ~ ( ~ ( subset @ ( relation_dom @ SV20 ) @ ( relation_dom @ SV23 ) )
| ~ ( subset @ ( relation_rng @ SV20 ) @ ( relation_rng @ SV23 ) ) ) )
= $true )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(394,plain,
! [SV21: $i,SV8: $i] :
( ( ( relation @ SV8 )
= $false )
| ( ( ~ ( relation @ SV21 ) )
= $true )
| ( ( relation @ ( set_union2 @ SV8 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(395,plain,
! [SV9: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV9 ) )
= $true )
| ( ( SV9 = empty_set )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(396,plain,
! [SV9: $i] :
( ( ( ~ ( in @ ( sK4_SY29 @ SV9 ) @ SV9 ) )
= $false )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[381]) ).
thf(397,plain,
( ( empty @ sK2_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(398,plain,
! [SV22: $i,SV16: $i] :
( ( ( relation @ SV16 )
= $false )
| ( ( ~ ( relation @ SV22 ) )
= $true )
| ( ( relation @ ( relation_composition @ SV16 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(399,plain,
! [SV17: $i] :
( ( ( empty @ SV17 )
= $true )
| ( ( ~ ( relation @ SV17 ) )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[389]) ).
thf(400,plain,
! [SV18: $i] :
( ( ( empty @ SV18 )
= $true )
| ( ( ~ ( relation @ SV18 ) )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(401,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV20 ) @ ( relation_dom @ SV23 ) )
| ~ ( subset @ ( relation_rng @ SV20 ) @ ( relation_rng @ SV23 ) ) ) )
= $true )
| ( ( relation @ SV23 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(402,plain,
! [SV8: $i,SV21: $i] :
( ( ( relation @ SV21 )
= $false )
| ( ( relation @ SV8 )
= $false )
| ( ( relation @ ( set_union2 @ SV8 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(403,plain,
! [SV9: $i,SV24: $i] :
( ( ( in @ SV24 @ SV9 )
= $false )
| ( ( SV9 = empty_set )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(404,plain,
! [SV9: $i] :
( ( ( in @ ( sK4_SY29 @ SV9 ) @ SV9 )
= $true )
| ( ( SV9 = empty_set )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[396]) ).
thf(405,plain,
! [SV16: $i,SV22: $i] :
( ( ( relation @ SV22 )
= $false )
| ( ( relation @ SV16 )
= $false )
| ( ( relation @ ( relation_composition @ SV16 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(406,plain,
! [SV17: $i] :
( ( ( relation @ SV17 )
= $false )
| ( ( empty @ SV17 )
= $true )
| ( ( ~ ( empty @ ( relation_rng @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(407,plain,
! [SV18: $i] :
( ( ( relation @ SV18 )
= $false )
| ( ( empty @ SV18 )
= $true )
| ( ( ~ ( empty @ ( relation_dom @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(408,plain,
! [SV23: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV23 )
= $false )
| ( ( ~ ( ~ ( subset @ ( relation_dom @ SV20 ) @ ( relation_dom @ SV23 ) )
| ~ ( subset @ ( relation_rng @ SV20 ) @ ( relation_rng @ SV23 ) ) ) )
= $true )
| ( ( relation @ SV23 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(409,plain,
! [SV17: $i] :
( ( ( empty @ ( relation_rng @ SV17 ) )
= $false )
| ( ( empty @ SV17 )
= $true )
| ( ( relation @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(410,plain,
! [SV18: $i] :
( ( ( empty @ ( relation_dom @ SV18 ) )
= $false )
| ( ( empty @ SV18 )
= $true )
| ( ( relation @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(411,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV20 ) @ ( relation_dom @ SV23 ) )
| ~ ( subset @ ( relation_rng @ SV20 ) @ ( relation_rng @ SV23 ) ) )
= $false )
| ( ( subset @ SV20 @ SV23 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(412,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ( subset @ ( relation_dom @ SV20 ) @ ( relation_dom @ SV23 ) ) )
= $false )
| ( ( subset @ SV20 @ SV23 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(413,plain,
! [SV23: $i,SV20: $i] :
( ( ( ~ ( subset @ ( relation_rng @ SV20 ) @ ( relation_rng @ SV23 ) ) )
= $false )
| ( ( subset @ SV20 @ SV23 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(414,plain,
! [SV23: $i,SV20: $i] :
( ( ( subset @ ( relation_dom @ SV20 ) @ ( relation_dom @ SV23 ) )
= $true )
| ( ( subset @ SV20 @ SV23 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(415,plain,
! [SV23: $i,SV20: $i] :
( ( ( subset @ ( relation_rng @ SV20 ) @ ( relation_rng @ SV23 ) )
= $true )
| ( ( subset @ SV20 @ SV23 )
= $false )
| ( ( relation @ SV23 )
= $false )
| ( ( relation @ SV20 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[413]) ).
thf(416,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[226,415,414,410,409,405,404,403,402,397,392,391,387,386,385,384,383,378,377,341,340,339,338,337,336,330,329,327,313,286,285,284,283,282,281,280,259,243,242,240,239,237,236,235,234,233,232,231,230,229,228,227]) ).
thf(417,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU188+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
% 0.05/0.12 % Computer : n012.cluster.edu
% 0.05/0.12 % Model : x86_64 x86_64
% 0.05/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.12 % Memory : 8046.5625MB
% 0.05/0.12 % OS : Linux 6.8.0-71-generic
% 0.05/0.12 % CPULimit : 300
% 0.05/0.12 % WCLimit : 300
% 0.05/0.12 % DateTime : Tue Oct 6 15:03:31 UTC 2026
% 0.05/0.12 % CPUTime :
% 0.05/0.12 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.34 .
% 0.46/0.34
% 0.46/0.34 No.of.Axioms: 40
% 0.46/0.34
% 0.46/0.34 Length.of.Defs: 0
% 0.46/0.34
% 0.46/0.34 Contains.Choice.Funs: false
% 0.46/0.34 ......
% 0.46/0.34
% 0.46/0.34 ********************************
% 0.46/0.34 * All subproblems solved! *
% 0.46/0.34 ********************************
% 0.46/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:42,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:416,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.46/0.34
% 0.46/0.34 %**** Beginning of derivation protocol ****
% 0.46/0.34 % SZS output start CNFRefutation
% See solution above
% 0.46/0.34
% 0.46/0.34 %**** End of derivation protocol ****
% 0.46/0.34 %**** no. of clauses in derivation: 288 ****
% 0.46/0.34 %**** clause counter: 416 ****
% 0.46/0.34
% 0.46/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:42,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:416,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------