%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : NUM395+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n026.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 10:33:35 AM UTC 2026
% Result : Theorem 0.11s 0.26s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 113 ( 77 unt; 0 typ; 0 def)
% Number of atoms : 527 ( 143 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 587 ( 199 ~; 103 |; 27 &; 246 @)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 55 !; 3 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_element,type,
element: $i > $i > $o ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_relation,type,
relation: $i > $o ).
thf(tp_relation_empty_yielding,type,
relation_empty_yielding: $i > $o ).
thf(tp_relation_non_empty,type,
relation_non_empty: $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(1,axiom,
( ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l18_ordinal1) ).
thf(2,axiom,
! [A: $i] :
( ( ordinal @ A )
<=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_ordinal1) ).
thf(3,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(6,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(10,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(11,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(17,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(18,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(19,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(29,conjecture,
ordinal @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_ordinal1) ).
thf(30,negated_conjecture,
( ( ordinal @ empty_set )
= $false ),
inference(negate_conjecture,[status(cth)],[29]) ).
thf(31,plain,
( ( ordinal @ empty_set )
= $false ),
inference(unfold_def,[status(thm)],[30]) ).
thf(32,plain,
( ( ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(33,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
<=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(34,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(35,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(36,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(37,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(38,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(39,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(40,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(41,plain,
( ( ~ ( ordinal @ empty_set ) )
= $true ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(42,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(44,plain,
( ( ? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(45,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(46,plain,
( ( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(47,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(48,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(49,plain,
( ( ! [A: $i] :
( ( ordinal @ A )
<=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(50,plain,
( ( ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(51,plain,
( ( ~ ( ordinal @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(52,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(53,plain,
( ( ~ ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(54,plain,
( ( ! [SX0: $i] :
( ~ ( ordinal @ SX0 )
| ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(55,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(56,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(57,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( SX0 = empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(58,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( ordinal @ SX0 )
| ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ( ordinal @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(59,plain,
( ( ~ ( ~ ( epsilon_transitive @ empty_set )
| ~ ( epsilon_connected @ empty_set ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(60,plain,
( ( ordinal @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV1: $i] :
( ( ~ ~ ( ~ ( epsilon_transitive @ SV1 )
| ~ ( epsilon_connected @ SV1 ) )
| ( ordinal @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(62,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
| ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV2: $i] :
( ( ~ ( ordinal @ SV2 )
| ~ ( ~ ( epsilon_transitive @ SV2 )
| ~ ( epsilon_connected @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(64,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( ~ ( epsilon_transitive @ SX0 )
| ~ ( epsilon_connected @ SX0 ) )
| ~ ( ordinal @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(65,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(66,plain,
! [SV3: $i] :
( ( ~ ( empty @ SV3 )
| ( SV3 = empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(67,plain,
! [SV4: $i] :
( ( ~ ( ~ ( ~ ( ordinal @ SV4 )
| ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) )
| ( ordinal @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(68,plain,
( ( ~ ( epsilon_transitive @ empty_set )
| ~ ( epsilon_connected @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV1: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV1 )
| ~ ( epsilon_connected @ SV1 ) ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(70,plain,
( ( ~ ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(71,plain,
( ( ~ ( relation_empty_yielding @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[62]) ).
thf(72,plain,
! [SV2: $i] :
( ( ( ~ ( ordinal @ SV2 ) )
= $true )
| ( ( ~ ( ~ ( epsilon_transitive @ SV2 )
| ~ ( epsilon_connected @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(73,plain,
( ( ~ ~ ( ~ ~ ( ~ ( epsilon_transitive @ sK1_SX0 )
| ~ ( epsilon_connected @ sK1_SX0 ) )
| ~ ( ordinal @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[64]) ).
thf(74,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(75,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(76,plain,
! [SV3: $i] :
( ( ( ~ ( empty @ SV3 ) )
= $true )
| ( ( SV3 = empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV4: $i] :
( ( ~ ( ~ ( ordinal @ SV4 )
| ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) ) )
| ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) )
| ( ordinal @ SV4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(78,plain,
( ( ~ ( epsilon_transitive @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(79,plain,
( ( ~ ( epsilon_connected @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(80,plain,
! [SV1: $i] :
( ( ( ~ ( ~ ( epsilon_transitive @ SV1 )
| ~ ( epsilon_connected @ SV1 ) ) )
= $false )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(81,plain,
( ( ~ ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(82,plain,
( ( relation_empty_yielding @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(83,plain,
! [SV2: $i] :
( ( ( ordinal @ SV2 )
= $false )
| ( ( ~ ( ~ ( epsilon_transitive @ SV2 )
| ~ ( epsilon_connected @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(84,plain,
( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ sK1_SX0 )
| ~ ( epsilon_connected @ sK1_SX0 ) )
| ~ ( ordinal @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(85,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(86,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(87,plain,
! [SV3: $i] :
( ( ( empty @ SV3 )
= $false )
| ( ( SV3 = empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(88,plain,
! [SV4: $i] :
( ( ~ ( ~ ( ordinal @ SV4 )
| ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(89,plain,
! [SV4: $i] :
( ( ~ ( ~ ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) )
| ( ordinal @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[77]) ).
thf(90,plain,
( ( epsilon_transitive @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(91,plain,
( ( epsilon_connected @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(92,plain,
! [SV1: $i] :
( ( ( ~ ( epsilon_transitive @ SV1 )
| ~ ( epsilon_connected @ SV1 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(93,plain,
( ( ~ ( empty @ empty_set )
| ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(94,plain,
! [SV2: $i] :
( ( ( ~ ( epsilon_transitive @ SV2 )
| ~ ( epsilon_connected @ SV2 ) )
= $false )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(95,plain,
( ( ~ ~ ( ~ ( epsilon_transitive @ sK1_SX0 )
| ~ ( epsilon_connected @ sK1_SX0 ) )
| ~ ( ordinal @ sK1_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(96,plain,
! [SV4: $i] :
( ( ~ ( ordinal @ SV4 )
| ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(97,plain,
! [SV4: $i] :
( ( ~ ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) )
| ( ordinal @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(98,plain,
! [SV1: $i] :
( ( ( ~ ( epsilon_transitive @ SV1 ) )
= $true )
| ( ( ~ ( epsilon_connected @ SV1 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(99,plain,
( ( ~ ( empty @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(100,plain,
( ( ~ ( relation @ empty_set ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(101,plain,
! [SV2: $i] :
( ( ( ~ ( epsilon_transitive @ SV2 ) )
= $false )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(102,plain,
! [SV2: $i] :
( ( ( ~ ( epsilon_connected @ SV2 ) )
= $false )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[94]) ).
thf(103,plain,
( ( ~ ~ ( ~ ( epsilon_transitive @ sK1_SX0 )
| ~ ( epsilon_connected @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(104,plain,
( ( ~ ( ordinal @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[95]) ).
thf(105,plain,
! [SV4: $i] :
( ( ( ~ ( ordinal @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) ) )
= $true )
| ( ( ordinal @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV1: $i] :
( ( ( epsilon_transitive @ SV1 )
= $false )
| ( ( ~ ( epsilon_connected @ SV1 ) )
= $true )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(108,plain,
( ( empty @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(109,plain,
( ( relation @ empty_set )
= $true ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(110,plain,
! [SV2: $i] :
( ( ( epsilon_transitive @ SV2 )
= $true )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(111,plain,
! [SV2: $i] :
( ( ( epsilon_connected @ SV2 )
= $true )
| ( ( ordinal @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(112,plain,
( ( ~ ( ~ ( epsilon_transitive @ sK1_SX0 )
| ~ ( epsilon_connected @ sK1_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(113,plain,
( ( ordinal @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(114,plain,
! [SV4: $i] :
( ( ( ordinal @ SV4 )
= $false )
| ( ( ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(115,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) ) )
= $false )
| ( ( ordinal @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(116,plain,
! [SV1: $i] :
( ( ( epsilon_connected @ SV1 )
= $false )
| ( ( epsilon_transitive @ SV1 )
= $false )
| ( ( ordinal @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(117,plain,
( ( ~ ( epsilon_transitive @ sK1_SX0 )
| ~ ( epsilon_connected @ sK1_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(118,plain,
! [SV4: $i] :
( ( ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) )
= $false )
| ( ( ordinal @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(119,plain,
! [SV4: $i] :
( ( ( ~ ( epsilon_transitive @ SV4 )
| ~ ( epsilon_connected @ SV4 ) )
= $true )
| ( ( ordinal @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(120,plain,
( ( ~ ( epsilon_transitive @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(121,plain,
( ( ~ ( epsilon_connected @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(122,plain,
! [SV4: $i] :
( ( ( ~ ( epsilon_transitive @ SV4 ) )
= $false )
| ( ( ordinal @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(123,plain,
! [SV4: $i] :
( ( ( ~ ( epsilon_connected @ SV4 ) )
= $false )
| ( ( ordinal @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[118]) ).
thf(124,plain,
! [SV4: $i] :
( ( ( ~ ( epsilon_transitive @ SV4 ) )
= $true )
| ( ( ~ ( epsilon_connected @ SV4 ) )
= $true )
| ( ( ordinal @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(125,plain,
( ( epsilon_transitive @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(126,plain,
( ( epsilon_connected @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(127,plain,
! [SV4: $i] :
( ( ( epsilon_transitive @ SV4 )
= $true )
| ( ( ordinal @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(128,plain,
! [SV4: $i] :
( ( ( epsilon_connected @ SV4 )
= $true )
| ( ( ordinal @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(129,plain,
! [SV4: $i] :
( ( ( epsilon_transitive @ SV4 )
= $false )
| ( ( ~ ( epsilon_connected @ SV4 ) )
= $true )
| ( ( ordinal @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(130,plain,
! [SV4: $i] :
( ( ( epsilon_connected @ SV4 )
= $false )
| ( ( epsilon_transitive @ SV4 )
= $false )
| ( ( ordinal @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(131,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[47,130,128,127,126,125,116,113,111,110,109,108,91,90,87,86,85,82,60]) ).
thf(132,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM395+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n026.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 13:14:16 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.26
% 0.11/0.26 No.of.Axioms: 9
% 0.11/0.26
% 0.11/0.26 Length.of.Defs: 0
% 0.11/0.26
% 0.11/0.26 Contains.Choice.Funs: false
% 0.11/0.26 .
% 0.11/0.26
% 0.11/0.26 ********************************
% 0.11/0.26 * All subproblems solved! *
% 0.11/0.26 ********************************
% 0.11/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:9,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:131,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.11/0.26
% 0.11/0.26 %**** Beginning of derivation protocol ****
% 0.11/0.26 % SZS output start CNFRefutation
% See solution above
% 0.11/0.26
% 0.11/0.26 %**** End of derivation protocol ****
% 0.11/0.26 %**** no. of clauses in derivation: 113 ****
% 0.11/0.26 %**** clause counter: 131 ****
% 0.11/0.26
% 0.11/0.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:9,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:131,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------