%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU294+3 : 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 10:43:50 AM UTC 2026
% Result : Theorem 0.45s 0.30s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of formulae : 87 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 422 ( 109 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 639 ( 175 ~; 83 |; 14 &; 347 @)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 7 con; 0-2 aty)
% Number of variables : 109 ( 0 ^; 103 !; 6 ?; 109 :)
% 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_SY12,type,
sK2_SY12: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY14,type,
sK4_SY14: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_transfinite_sequence,type,
transfinite_sequence: $i > $o ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(9,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(16,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(33,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(46,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(51,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(54,conjecture,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
thf(55,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[54]) ).
thf(56,plain,
( ( ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[55]) ).
thf(57,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(58,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(59,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(60,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(61,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(62,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(63,plain,
( ( ! [SY12: $i] :
( ( ( subset @ sK1_A @ SY12 )
& ( finite @ SY12 ) )
=> ( finite @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[56]) ).
thf(64,plain,
( ( ( ( subset @ sK1_A @ sK2_SY12 )
& ( finite @ sK2_SY12 ) )
=> ( finite @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(65,plain,
( ( subset @ sK1_A @ sK2_SY12 )
= $true ),
inference(standard_cnf,[status(thm)],[64]) ).
thf(66,plain,
( ( finite @ sK2_SY12 )
= $true ),
inference(standard_cnf,[status(thm)],[64]) ).
thf(67,plain,
( ( finite @ sK1_A )
= $false ),
inference(standard_cnf,[status(thm)],[64]) ).
thf(68,plain,
( ( ~ ( finite @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[67]) ).
thf(69,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(70,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(71,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(72,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(75,plain,
( ( finite @ sK2_SY12 )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(76,plain,
( ( subset @ sK1_A @ sK2_SY12 )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(77,plain,
( ( ~ ( finite @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(78,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(79,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(80,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( element @ SX0 @ ( powerset @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ( element @ SX0 @ ( powerset @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(81,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(82,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(83,plain,
! [SV1: $i] :
( ( ! [SY13: $i] : ( subset @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(84,plain,
( ( finite @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV2: $i] :
( ( ~ ~ ( empty @ SV2 )
| ~ ! [SY14: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY14 @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ SY14 ) )
| ~ ( finite @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(86,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(87,plain,
! [SV3: $i] :
( ( ! [SY15: $i] :
~ ( ~ ( ~ ( element @ SV3 @ ( powerset @ SY15 ) )
| ( subset @ SV3 @ SY15 ) )
| ~ ( ~ ( subset @ SV3 @ SY15 )
| ( element @ SV3 @ ( powerset @ SY15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(88,plain,
! [SV4: $i] :
( ( ~ ( finite @ SV4 )
| ! [SY16: $i] :
( ~ ( element @ SY16 @ ( powerset @ SV4 ) )
| ( finite @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(89,plain,
! [SV5: $i] :
( ( ~ ( empty @ SV5 )
| ( finite @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV1: $i] :
( ( subset @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(91,plain,
! [SV2: $i] :
( ( ( ~ ~ ( empty @ SV2 ) )
= $true )
| ( ( ~ ! [SY14: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY14 @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ SY14 ) )
| ~ ( finite @ SY14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(92,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[86]) ).
thf(93,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( element @ SV3 @ ( powerset @ SV7 ) )
| ( subset @ SV3 @ SV7 ) )
| ~ ( ~ ( subset @ SV3 @ SV7 )
| ( element @ SV3 @ ( powerset @ SV7 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV4: $i] :
( ( ( ~ ( finite @ SV4 ) )
= $true )
| ( ( ! [SY16: $i] :
( ~ ( element @ SY16 @ ( powerset @ SV4 ) )
| ( finite @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV5: $i] :
( ( ( ~ ( empty @ SV5 ) )
= $true )
| ( ( finite @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ SV2 ) )
= $false )
| ( ( ~ ! [SY14: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY14 @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ SY14 ) )
| ~ ( finite @ SY14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(97,plain,
( ( ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(98,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( ~ ( element @ SV3 @ ( powerset @ SV7 ) )
| ( subset @ SV3 @ SV7 ) )
| ~ ( ~ ( subset @ SV3 @ SV7 )
| ( element @ SV3 @ ( powerset @ SV7 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV4: $i] :
( ( ( finite @ SV4 )
= $false )
| ( ( ! [SY16: $i] :
( ~ ( element @ SY16 @ ( powerset @ SV4 ) )
| ( finite @ SY16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV5: $i] :
( ( ( empty @ SV5 )
= $false )
| ( ( finite @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(101,plain,
! [SV2: $i] :
( ( ( empty @ SV2 )
= $true )
| ( ( ~ ! [SY14: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY14 @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ SY14 ) )
| ~ ( finite @ SY14 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(102,plain,
( ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( ~ ( element @ SV3 @ ( powerset @ SV7 ) )
| ( subset @ SV3 @ SV7 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(104,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( ~ ( subset @ SV3 @ SV7 )
| ( element @ SV3 @ ( powerset @ SV7 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(105,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( element @ SV8 @ ( powerset @ SV4 ) )
| ( finite @ SV8 ) )
= $true )
| ( ( finite @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(106,plain,
! [SV2: $i] :
( ( ( ! [SY14: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY14 @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ SY14 ) )
| ~ ( finite @ SY14 ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(107,plain,
( ( ~ ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(108,plain,
( ( ~ ( finite @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(109,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( element @ SV3 @ ( powerset @ SV7 ) )
| ( subset @ SV3 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(110,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ SV7 )
| ( element @ SV3 @ ( powerset @ SV7 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(111,plain,
! [SV4: $i,SV8: $i] :
( ( ( ~ ( element @ SV8 @ ( powerset @ SV4 ) ) )
= $true )
| ( ( finite @ SV8 )
= $true )
| ( ( finite @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(112,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK4_SY14 @ SV2 ) @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ ( sK4_SY14 @ SV2 ) ) )
| ~ ( finite @ ( sK4_SY14 @ SV2 ) ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[106]) ).
thf(113,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(114,plain,
( ( finite @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(115,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( element @ SV3 @ ( powerset @ SV7 ) ) )
= $true )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(116,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV7 ) )
= $true )
| ( ( element @ SV3 @ ( powerset @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(117,plain,
! [SV4: $i,SV8: $i] :
( ( ( element @ SV8 @ ( powerset @ SV4 ) )
= $false )
| ( ( finite @ SV8 )
= $true )
| ( ( finite @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(118,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK4_SY14 @ SV2 ) @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ ( sK4_SY14 @ SV2 ) ) )
| ~ ( finite @ ( sK4_SY14 @ SV2 ) ) ) )
= $true )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(119,plain,
( ( empty @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(120,plain,
! [SV7: $i,SV3: $i] :
( ( ( element @ SV3 @ ( powerset @ SV7 ) )
= $false )
| ( ( subset @ SV3 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(121,plain,
! [SV7: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV7 )
= $false )
| ( ( element @ SV3 @ ( powerset @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(122,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK4_SY14 @ SV2 ) @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ ( sK4_SY14 @ SV2 ) ) )
| ~ ( finite @ ( sK4_SY14 @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(123,plain,
! [SV2: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK4_SY14 @ SV2 ) @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ ( sK4_SY14 @ SV2 ) ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(124,plain,
! [SV2: $i] :
( ( ( ~ ( finite @ ( sK4_SY14 @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[122]) ).
thf(125,plain,
! [SV2: $i] :
( ( ( ~ ( ~ ( element @ ( sK4_SY14 @ SV2 ) @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ ( sK4_SY14 @ SV2 ) ) ) )
= $true )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[123]) ).
thf(126,plain,
! [SV2: $i] :
( ( ( finite @ ( sK4_SY14 @ SV2 ) )
= $true )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(127,plain,
! [SV2: $i] :
( ( ( ~ ( element @ ( sK4_SY14 @ SV2 ) @ ( powerset @ SV2 ) )
| ~ ~ ( empty @ ( sK4_SY14 @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(128,plain,
! [SV2: $i] :
( ( ( ~ ( element @ ( sK4_SY14 @ SV2 ) @ ( powerset @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(129,plain,
! [SV2: $i] :
( ( ( ~ ~ ( empty @ ( sK4_SY14 @ SV2 ) ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(130,plain,
! [SV2: $i] :
( ( ( element @ ( sK4_SY14 @ SV2 ) @ ( powerset @ SV2 ) )
= $true )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(131,plain,
! [SV2: $i] :
( ( ( ~ ( empty @ ( sK4_SY14 @ SV2 ) ) )
= $true )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(132,plain,
! [SV2: $i] :
( ( ( empty @ ( sK4_SY14 @ SV2 ) )
= $false )
| ( ( empty @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(133,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[75,132,130,126,121,120,119,117,114,100,90,84,76]) ).
thf(134,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU294+3 : 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
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 15:15:02 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.30
% 0.45/0.30 No.of.Axioms: 6
% 0.45/0.30
% 0.45/0.30 Length.of.Defs: 0
% 0.45/0.30
% 0.45/0.30 Contains.Choice.Funs: false
% 0.45/0.30 ..
% 0.45/0.30
% 0.45/0.30 ********************************
% 0.45/0.30 * All subproblems solved! *
% 0.45/0.30 ********************************
% 0.45/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,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:133,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.45/0.30
% 0.45/0.30 %**** Beginning of derivation protocol ****
% 0.45/0.30 % SZS output start CNFRefutation
% See solution above
% 0.45/0.30
% 0.45/0.30 %**** End of derivation protocol ****
% 0.45/0.30 %**** no. of clauses in derivation: 87 ****
% 0.45/0.30 %**** clause counter: 133 ****
% 0.45/0.30
% 0.45/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,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:133,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------