%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU085+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 10:42:52 AM UTC 2026
% Result : Theorem 0.07s 0.26s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 110 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 543 ( 152 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 767 ( 200 ~; 104 |; 15 &; 422 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 7 con; 0-2 aty)
% Number of variables : 152 ( 0 ^; 146 !; 6 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $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_epsilon_connected,type,
epsilon_connected: $i > $o ).
thf(tp_epsilon_transitive,type,
epsilon_transitive: $i > $o ).
thf(tp_finite,type,
finite: $i > $o ).
thf(tp_function,type,
function: $i > $o ).
thf(tp_function_yielding,type,
function_yielding: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_natural,type,
natural: $i > $o ).
thf(tp_one_to_one,type,
one_to_one: $i > $o ).
thf(tp_ordinal,type,
ordinal: $i > $o ).
thf(tp_ordinal_yielding,type,
ordinal_yielding: $i > $o ).
thf(tp_positive_rationals,type,
positive_rationals: $i ).
thf(tp_powerset,type,
powerset: $i > $i ).
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_A,type,
sK1_A: $i ).
thf(tp_sK2_SY18,type,
sK2_SY18: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY20,type,
sK4_SY20: $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_transfinite_sequence,type,
transfinite_sequence: $i > $o ).
thf(6,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(8,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(9,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(20,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(37,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(52,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(57,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(60,conjecture,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finset_1) ).
thf(61,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[60]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[61]) ).
thf(63,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(64,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(65,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(67,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(68,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(69,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(70,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(71,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(72,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(73,plain,
( ( ! [SY18: $i] :
( ( finite @ sK1_A )
=> ( finite @ ( set_difference @ sK1_A @ SY18 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(74,plain,
( ( ( finite @ sK1_A )
=> ( finite @ ( set_difference @ sK1_A @ sK2_SY18 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[73]) ).
thf(75,plain,
( ( finite @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[74]) ).
thf(76,plain,
( ( finite @ ( set_difference @ sK1_A @ sK2_SY18 ) )
= $false ),
inference(standard_cnf,[status(thm)],[74]) ).
thf(77,plain,
( ( ~ ( finite @ ( set_difference @ sK1_A @ sK2_SY18 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[76]) ).
thf(78,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(79,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(82,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(83,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(84,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(85,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(86,plain,
( ( ! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(87,plain,
( ( ! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(88,plain,
( ( finite @ sK1_A )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(89,plain,
( ( ~ ( finite @ ( set_difference @ sK1_A @ sK2_SY18 ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(90,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( finite @ SX1 ) )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(92,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( relation @ SX0 )
| ~ ( relation @ SX1 ) )
| ( relation @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(93,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(94,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(95,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(96,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( finite @ SX0 )
| ( finite @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(97,plain,
! [SV1: $i] :
( ( ! [SY19: $i] : ( subset @ ( set_difference @ SV1 @ SY19 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(98,plain,
! [SV2: $i] :
( ( ( set_difference @ SV2 @ empty_set )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(99,plain,
! [SV3: $i] :
( ( ( set_difference @ empty_set @ SV3 )
= empty_set )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(100,plain,
( ( finite @ ( set_difference @ sK1_A @ sK2_SY18 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(101,plain,
! [SV4: $i] :
( ( ~ ~ ( empty @ SV4 )
| ~ ! [SY20: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY20 @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ SY20 ) )
| ~ ( finite @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(102,plain,
! [SV5: $i] :
( ( ! [SY21: $i] :
( ~ ~ ( ~ ( subset @ SV5 @ SY21 )
| ~ ( finite @ SY21 ) )
| ( finite @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(103,plain,
! [SV6: $i] :
( ( ! [SY22: $i] :
( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( relation @ SY22 ) )
| ( relation @ ( set_difference @ SV6 @ SY22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(104,plain,
! [SV7: $i] :
( ( ~ ( empty @ SV7 )
| ( finite @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV8: $i] :
( ( ~ ( finite @ SV8 )
| ! [SY23: $i] :
( ~ ( element @ SY23 @ ( powerset @ SV8 ) )
| ( finite @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(106,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(107,plain,
! [SV9: $i] :
( ( ! [SY24: $i] :
( ~ ( finite @ SV9 )
| ( finite @ ( set_difference @ SV9 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(108,plain,
! [SV10: $i,SV1: $i] :
( ( subset @ ( set_difference @ SV1 @ SV10 ) @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(109,plain,
! [SV4: $i] :
( ( ( ~ ~ ( empty @ SV4 ) )
= $true )
| ( ( ~ ! [SY20: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY20 @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ SY20 ) )
| ~ ( finite @ SY20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(110,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ~ ( ~ ( subset @ SV5 @ SV11 )
| ~ ( finite @ SV11 ) )
| ( finite @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV12: $i,SV6: $i] :
( ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( relation @ SV12 ) )
| ( relation @ ( set_difference @ SV6 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(112,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $true )
| ( ( finite @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV8: $i] :
( ( ( ~ ( finite @ SV8 ) )
= $true )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( powerset @ SV8 ) )
| ( finite @ SY23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(114,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[106]) ).
thf(115,plain,
! [SV13: $i,SV9: $i] :
( ( ~ ( finite @ SV9 )
| ( finite @ ( set_difference @ SV9 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(116,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ SV4 ) )
= $false )
| ( ( ~ ! [SY20: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY20 @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ SY20 ) )
| ~ ( finite @ SY20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(117,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV5 @ SV11 )
| ~ ( finite @ SV11 ) ) )
= $true )
| ( ( finite @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( relation @ SV6 )
| ~ ( relation @ SV12 ) ) )
= $true )
| ( ( relation @ ( set_difference @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(119,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $false )
| ( ( finite @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(120,plain,
! [SV8: $i] :
( ( ( finite @ SV8 )
= $false )
| ( ( ! [SY23: $i] :
( ~ ( element @ SY23 @ ( powerset @ SV8 ) )
| ( finite @ SY23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(121,plain,
( ( ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(122,plain,
! [SV13: $i,SV9: $i] :
( ( ( ~ ( finite @ SV9 ) )
= $true )
| ( ( finite @ ( set_difference @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(123,plain,
! [SV4: $i] :
( ( ( empty @ SV4 )
= $true )
| ( ( ~ ! [SY20: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY20 @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ SY20 ) )
| ~ ( finite @ SY20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(124,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( ~ ( subset @ SV5 @ SV11 )
| ~ ( finite @ SV11 ) ) )
= $false )
| ( ( finite @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(125,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ( relation @ SV6 )
| ~ ( relation @ SV12 ) ) )
= $false )
| ( ( relation @ ( set_difference @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(126,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ ( powerset @ SV8 ) )
| ( finite @ SV14 ) )
= $true )
| ( ( finite @ SV8 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(127,plain,
( ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(128,plain,
! [SV13: $i,SV9: $i] :
( ( ( finite @ SV9 )
= $false )
| ( ( finite @ ( set_difference @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(129,plain,
! [SV4: $i] :
( ( ( ! [SY20: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY20 @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ SY20 ) )
| ~ ( finite @ SY20 ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(130,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ SV11 )
| ~ ( finite @ SV11 ) )
= $true )
| ( ( finite @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(131,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( relation @ SV6 )
| ~ ( relation @ SV12 ) )
= $true )
| ( ( relation @ ( set_difference @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[125]) ).
thf(132,plain,
! [SV8: $i,SV14: $i] :
( ( ( ~ ( element @ SV14 @ ( powerset @ SV8 ) ) )
= $true )
| ( ( finite @ SV14 )
= $true )
| ( ( finite @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(133,plain,
( ( ~ ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(134,plain,
( ( ~ ( finite @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(135,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK4_SY20 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ ( sK4_SY20 @ SV4 ) ) )
| ~ ( finite @ ( sK4_SY20 @ SV4 ) ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[129]) ).
thf(136,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( subset @ SV5 @ SV11 ) )
= $true )
| ( ( ~ ( finite @ SV11 ) )
= $true )
| ( ( finite @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(137,plain,
! [SV12: $i,SV6: $i] :
( ( ( ~ ( relation @ SV6 ) )
= $true )
| ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( relation @ ( set_difference @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV8: $i,SV14: $i] :
( ( ( element @ SV14 @ ( powerset @ SV8 ) )
= $false )
| ( ( finite @ SV14 )
= $true )
| ( ( finite @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(139,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(140,plain,
( ( finite @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(141,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK4_SY20 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ ( sK4_SY20 @ SV4 ) ) )
| ~ ( finite @ ( sK4_SY20 @ SV4 ) ) ) )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(142,plain,
! [SV11: $i,SV5: $i] :
( ( ( subset @ SV5 @ SV11 )
= $false )
| ( ( ~ ( finite @ SV11 ) )
= $true )
| ( ( finite @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(143,plain,
! [SV12: $i,SV6: $i] :
( ( ( relation @ SV6 )
= $false )
| ( ( ~ ( relation @ SV12 ) )
= $true )
| ( ( relation @ ( set_difference @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(144,plain,
( ( empty @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(145,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK4_SY20 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ ( sK4_SY20 @ SV4 ) ) )
| ~ ( finite @ ( sK4_SY20 @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(146,plain,
! [SV5: $i,SV11: $i] :
( ( ( finite @ SV11 )
= $false )
| ( ( subset @ SV5 @ SV11 )
= $false )
| ( ( finite @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(147,plain,
! [SV6: $i,SV12: $i] :
( ( ( relation @ SV12 )
= $false )
| ( ( relation @ SV6 )
= $false )
| ( ( relation @ ( set_difference @ SV6 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(148,plain,
! [SV4: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK4_SY20 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ ( sK4_SY20 @ SV4 ) ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(149,plain,
! [SV4: $i] :
( ( ( ~ ( finite @ ( sK4_SY20 @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(150,plain,
! [SV4: $i] :
( ( ( ~ ( ~ ( element @ ( sK4_SY20 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ ( sK4_SY20 @ SV4 ) ) ) )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(151,plain,
! [SV4: $i] :
( ( ( finite @ ( sK4_SY20 @ SV4 ) )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(152,plain,
! [SV4: $i] :
( ( ( ~ ( element @ ( sK4_SY20 @ SV4 ) @ ( powerset @ SV4 ) )
| ~ ~ ( empty @ ( sK4_SY20 @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(153,plain,
! [SV4: $i] :
( ( ( ~ ( element @ ( sK4_SY20 @ SV4 ) @ ( powerset @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(154,plain,
! [SV4: $i] :
( ( ( ~ ~ ( empty @ ( sK4_SY20 @ SV4 ) ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[152]) ).
thf(155,plain,
! [SV4: $i] :
( ( ( element @ ( sK4_SY20 @ SV4 ) @ ( powerset @ SV4 ) )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(156,plain,
! [SV4: $i] :
( ( ( ~ ( empty @ ( sK4_SY20 @ SV4 ) ) )
= $true )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(157,plain,
! [SV4: $i] :
( ( ( empty @ ( sK4_SY20 @ SV4 ) )
= $false )
| ( ( empty @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(158,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[88,157,155,151,147,146,144,140,138,128,119,108,100,99,98]) ).
thf(159,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU085+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 15:02:52 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.26
% 0.07/0.26 No.of.Axioms: 10
% 0.07/0.26
% 0.07/0.26 Length.of.Defs: 0
% 0.07/0.26
% 0.07/0.26 Contains.Choice.Funs: false
% 0.07/0.26 ..
% 0.07/0.26
% 0.07/0.26 ********************************
% 0.07/0.26 * All subproblems solved! *
% 0.07/0.26 ********************************
% 0.07/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:11,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:158,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.26
% 0.07/0.26 %**** Beginning of derivation protocol ****
% 0.07/0.26 % SZS output start CNFRefutation
% See solution above
% 0.07/0.26
% 0.07/0.26 %**** End of derivation protocol ****
% 0.07/0.26 %**** no. of clauses in derivation: 110 ****
% 0.07/0.26 %**** clause counter: 158 ****
% 0.07/0.26
% 0.07/0.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:11,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:158,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------