%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU089+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 : n007.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 : 22
% Number of leaves : 7
% Syntax : Number of formulae : 89 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 501 ( 140 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 773 ( 221 ~; 99 |; 27 &; 408 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 8 con; 0-3 aty)
% Number of variables : 153 ( 0 ^; 150 !; 3 ?; 153 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_being_limit_ordinal,type,
being_limit_ordinal: $i > $o ).
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_cartesian_product3,type,
cartesian_product3: $i > $i > $i > $i ).
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_SY15,type,
sK2_SY15: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_sK4_SX0,type,
sK4_SX0: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_transfinite_sequence,type,
transfinite_sequence: $i > $o ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_finset_1) ).
thf(34,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ~ ( empty @ C ) )
=> ~ ( empty @ ( cartesian_product3 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_subset_1) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( cartesian_product3 @ A @ B @ C )
= ( cartesian_product2 @ ( cartesian_product2 @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_zfmisc_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,C: $i] :
( ( ( finite @ A )
& ( finite @ B )
& ( finite @ C ) )
=> ( finite @ ( cartesian_product3 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_finset_1) ).
thf(61,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( finite @ A )
& ( finite @ B )
& ( finite @ C ) )
=> ( finite @ ( cartesian_product3 @ A @ B @ C ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[60]) ).
thf(62,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( finite @ A )
& ( finite @ B )
& ( finite @ C ) )
=> ( finite @ ( cartesian_product3 @ A @ B @ C ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[61]) ).
thf(63,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(64,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(65,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ~ ( empty @ C ) )
=> ~ ( empty @ ( cartesian_product3 @ A @ B @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(66,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(67,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( cartesian_product3 @ A @ B @ C )
= ( cartesian_product2 @ ( cartesian_product2 @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(68,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(69,plain,
( ( ! [SY15: $i,SY16: $i] :
( ( ( finite @ sK1_A )
& ( finite @ SY15 )
& ( finite @ SY16 ) )
=> ( finite @ ( cartesian_product3 @ sK1_A @ SY15 @ SY16 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[62]) ).
thf(70,plain,
( ( ! [SY17: $i] :
( ( ( finite @ sK1_A )
& ( finite @ sK2_SY15 )
& ( finite @ SY17 ) )
=> ( finite @ ( cartesian_product3 @ sK1_A @ sK2_SY15 @ SY17 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[69]) ).
thf(71,plain,
( ( ( ( finite @ sK1_A )
& ( finite @ sK2_SY15 )
& ( finite @ sK3_SY17 ) )
=> ( finite @ ( cartesian_product3 @ sK1_A @ sK2_SY15 @ sK3_SY17 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[70]) ).
thf(72,plain,
( ( finite @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(73,plain,
( ( finite @ sK2_SY15 )
= $true ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(74,plain,
( ( finite @ sK3_SY17 )
= $true ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(75,plain,
( ( finite @ ( cartesian_product3 @ sK1_A @ sK2_SY15 @ sK3_SY17 ) )
= $false ),
inference(standard_cnf,[status(thm)],[71]) ).
thf(76,plain,
( ( ~ ( finite @ ( cartesian_product3 @ sK1_A @ sK2_SY15 @ sK3_SY17 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[75]) ).
thf(77,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(78,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( cartesian_product3 @ A @ B @ C )
= ( cartesian_product2 @ ( cartesian_product2 @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(80,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B )
& ~ ( empty @ C ) )
=> ~ ( empty @ ( cartesian_product3 @ A @ B @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(81,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(82,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( cartesian_product2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(83,plain,
( ( finite @ sK3_SY17 )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(84,plain,
( ( finite @ sK2_SY15 )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(85,plain,
( ( finite @ sK1_A )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(86,plain,
( ( ~ ( finite @ ( cartesian_product3 @ sK1_A @ sK2_SY15 @ sK3_SY17 ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(87,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(88,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(89,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( finite @ SX0 )
| ~ ( finite @ SX1 ) )
| ( finite @ ( cartesian_product2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(90,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( finite @ SX0 )
| ~ ( finite @ SX1 ) )
| ( finite @ ( cartesian_product2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(91,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ~ ( empty @ SX1 ) )
| ~ ~ ( empty @ SX2 ) )
| ~ ( empty @ ( cartesian_product3 @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(92,plain,
! [SV1: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ( cartesian_product3 @ SV1 @ SY18 @ SY19 )
= ( cartesian_product2 @ ( cartesian_product2 @ SV1 @ SY18 ) @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(93,plain,
( ( finite @ ( cartesian_product3 @ sK1_A @ sK2_SY15 @ sK3_SY17 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(94,plain,
! [SV2: $i] :
( ( ~ ( empty @ SV2 )
| ( finite @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(95,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV3: $i] :
( ( ! [SY20: $i] :
( ~ ~ ( ~ ( finite @ SV3 )
| ~ ( finite @ SY20 ) )
| ( finite @ ( cartesian_product2 @ SV3 @ SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV4: $i] :
( ( ! [SY21: $i] :
( ~ ~ ( ~ ( finite @ SV4 )
| ~ ( finite @ SY21 ) )
| ( finite @ ( cartesian_product2 @ SV4 @ SY21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV5: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV5 )
| ~ ~ ( empty @ SY22 ) )
| ~ ~ ( empty @ SY23 ) )
| ~ ( empty @ ( cartesian_product3 @ SV5 @ SY22 @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(99,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY24: $i] :
( ( cartesian_product3 @ SV1 @ SV6 @ SY24 )
= ( cartesian_product2 @ ( cartesian_product2 @ SV1 @ SV6 ) @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(100,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $true )
| ( ( finite @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(101,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( finite @ sK4_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[95]) ).
thf(102,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ~ ( ~ ( finite @ SV3 )
| ~ ( finite @ SV7 ) )
| ( finite @ ( cartesian_product2 @ SV3 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(103,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ~ ( ~ ( finite @ SV4 )
| ~ ( finite @ SV8 ) )
| ( finite @ ( cartesian_product2 @ SV4 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(104,plain,
! [SV9: $i,SV5: $i] :
( ( ! [SY25: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV5 )
| ~ ~ ( empty @ SV9 ) )
| ~ ~ ( empty @ SY25 ) )
| ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(105,plain,
! [SV10: $i,SV6: $i,SV1: $i] :
( ( ( cartesian_product3 @ SV1 @ SV6 @ SV10 )
= ( cartesian_product2 @ ( cartesian_product2 @ SV1 @ SV6 ) @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(106,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $false )
| ( ( finite @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(107,plain,
( ( ~ ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( finite @ sK4_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(108,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( finite @ SV3 )
| ~ ( finite @ SV7 ) ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( finite @ SV4 )
| ~ ( finite @ SV8 ) ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(110,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV5 )
| ~ ~ ( empty @ SV9 ) )
| ~ ~ ( empty @ SV11 ) )
| ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(111,plain,
( ( ~ ~ ( empty @ sK4_SX0 )
| ~ ( finite @ sK4_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( ~ ( finite @ SV3 )
| ~ ( finite @ SV7 ) ) )
= $false )
| ( ( finite @ ( cartesian_product2 @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( ~ ( finite @ SV4 )
| ~ ( finite @ SV8 ) ) )
= $false )
| ( ( finite @ ( cartesian_product2 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( empty @ SV5 )
| ~ ~ ( empty @ SV9 ) )
| ~ ~ ( empty @ SV11 ) ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(115,plain,
( ( ~ ~ ( empty @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(116,plain,
( ( ~ ( finite @ sK4_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(117,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( finite @ SV3 )
| ~ ( finite @ SV7 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(118,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( finite @ SV4 )
| ~ ( finite @ SV8 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(119,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( empty @ SV5 )
| ~ ~ ( empty @ SV9 ) )
| ~ ~ ( empty @ SV11 ) ) )
= $false )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(120,plain,
( ( ~ ( empty @ sK4_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(121,plain,
( ( finite @ sK4_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(122,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( finite @ SV3 ) )
= $true )
| ( ( ~ ( finite @ SV7 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(123,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( finite @ SV4 ) )
= $true )
| ( ( ~ ( finite @ SV8 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(124,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV5 )
| ~ ~ ( empty @ SV9 ) )
| ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(125,plain,
( ( empty @ sK4_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(126,plain,
! [SV7: $i,SV3: $i] :
( ( ( finite @ SV3 )
= $false )
| ( ( ~ ( finite @ SV7 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(127,plain,
! [SV8: $i,SV4: $i] :
( ( ( finite @ SV4 )
= $false )
| ( ( ~ ( finite @ SV8 ) )
= $true )
| ( ( finite @ ( cartesian_product2 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(128,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( empty @ SV5 )
| ~ ~ ( empty @ SV9 ) ) )
= $true )
| ( ( ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(129,plain,
! [SV3: $i,SV7: $i] :
( ( ( finite @ SV7 )
= $false )
| ( ( finite @ SV3 )
= $false )
| ( ( finite @ ( cartesian_product2 @ SV3 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(130,plain,
! [SV4: $i,SV8: $i] :
( ( ( finite @ SV8 )
= $false )
| ( ( finite @ SV4 )
= $false )
| ( ( finite @ ( cartesian_product2 @ SV4 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(131,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( empty @ SV5 )
| ~ ~ ( empty @ SV9 ) ) )
= $false )
| ( ( ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(132,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ~ ( empty @ SV5 )
| ~ ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(133,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ~ ( empty @ SV5 ) )
= $true )
| ( ( ~ ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(134,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( empty @ SV5 ) )
= $false )
| ( ( ~ ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(135,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( empty @ SV5 )
= $true )
| ( ( ~ ~ ( empty @ SV9 ) )
= $true )
| ( ( ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(136,plain,
! [SV11: $i,SV5: $i,SV9: $i] :
( ( ( ~ ( empty @ SV9 ) )
= $false )
| ( ( empty @ SV5 )
= $true )
| ( ( ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(137,plain,
! [SV11: $i,SV5: $i,SV9: $i] :
( ( ( empty @ SV9 )
= $true )
| ( ( empty @ SV5 )
= $true )
| ( ( ~ ~ ( empty @ SV11 ) )
= $true )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(138,plain,
! [SV9: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( empty @ SV11 ) )
= $false )
| ( ( empty @ SV5 )
= $true )
| ( ( empty @ SV9 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(139,plain,
! [SV9: $i,SV5: $i,SV11: $i] :
( ( ( empty @ SV11 )
= $true )
| ( ( empty @ SV5 )
= $true )
| ( ( empty @ SV9 )
= $true )
| ( ( ~ ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(140,plain,
! [SV11: $i,SV9: $i,SV5: $i] :
( ( ( empty @ ( cartesian_product3 @ SV5 @ SV9 @ SV11 ) )
= $false )
| ( ( empty @ SV9 )
= $true )
| ( ( empty @ SV5 )
= $true )
| ( ( empty @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(141,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[83,140,130,129,125,121,106,105,93,85,84]) ).
thf(142,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU089+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 : n007.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
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 14:58:31 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: 6
% 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: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:141,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: 89 ****
% 0.07/0.26 %**** clause counter: 141 ****
% 0.07/0.26
% 0.07/0.26 % SZS status Theorem for /export/starexec/sandbox2/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:141,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------