%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU097+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 : n008.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 10:42:53 AM UTC 2026
% Result : Theorem 0.50s 0.32s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 121 ( 72 unt; 0 typ; 0 def)
% Number of atoms : 591 ( 170 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 867 ( 204 ~; 109 |; 20 &; 505 @)
% ( 0 <=>; 29 =>; 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 : 31 ( 28 usr; 7 con; 0-2 aty)
% Number of variables : 174 ( 0 ^; 168 !; 6 ?; 174 :)
% 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_SY21,type,
sK2_SY21: $i ).
thf(tp_sK3_SX0,type,
sK3_SX0: $i ).
thf(tp_sK4_SY27,type,
sK4_SY27: $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_symmetric_difference,type,
symmetric_difference: $i > $i > $i ).
thf(tp_transfinite_sequence,type,
transfinite_sequence: $i > $o ).
thf(5,axiom,
! [A: $i] :
( ( symmetric_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finset_1) ).
thf(21,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(38,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_finset_1) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(62,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(67,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(70,conjecture,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( symmetric_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finset_1) ).
thf(71,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( symmetric_difference @ A @ B ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[70]) ).
thf(72,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( symmetric_difference @ A @ B ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[71]) ).
thf(73,plain,
( ( ! [A: $i] :
( ( symmetric_difference @ A @ empty_set )
= A ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(75,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(76,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(77,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(82,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(83,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(84,plain,
( ( ! [SY21: $i] :
( ( ( finite @ sK1_A )
& ( finite @ SY21 ) )
=> ( finite @ ( symmetric_difference @ sK1_A @ SY21 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[72]) ).
thf(85,plain,
( ( ( ( finite @ sK1_A )
& ( finite @ sK2_SY21 ) )
=> ( finite @ ( symmetric_difference @ sK1_A @ sK2_SY21 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[84]) ).
thf(86,plain,
( ( finite @ sK1_A )
= $true ),
inference(standard_cnf,[status(thm)],[85]) ).
thf(87,plain,
( ( finite @ sK2_SY21 )
= $true ),
inference(standard_cnf,[status(thm)],[85]) ).
thf(88,plain,
( ( finite @ ( symmetric_difference @ sK1_A @ sK2_SY21 ) )
= $false ),
inference(standard_cnf,[status(thm)],[85]) ).
thf(89,plain,
( ( ~ ( finite @ ( symmetric_difference @ sK1_A @ sK2_SY21 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[88]) ).
thf(90,plain,
( ( ! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(91,plain,
( ( ! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(92,plain,
( ( ! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(95,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(97,plain,
( ( ? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(98,plain,
( ( ! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(100,plain,
( ( ! [A: $i] :
( ( symmetric_difference @ A @ empty_set )
= A ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(101,plain,
( ( finite @ sK2_SY21 )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(102,plain,
( ( finite @ sK1_A )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(103,plain,
( ( ~ ( finite @ ( symmetric_difference @ sK1_A @ sK2_SY21 ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(104,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( finite @ SX0 )
| ~ ( finite @ SX1 ) )
| ( finite @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(105,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( finite @ SX0 )
| ( finite @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(106,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(107,plain,
( ( ! [SX0: $i] :
( ~ ( finite @ SX0 )
| ! [SX1: $i] :
( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(108,plain,
( ( ! [SX0: $i] :
( ~ ( empty @ SX0 )
| ( finite @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(109,plain,
( ( ! [SX0: $i] :
( ~ ~ ( empty @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SX1 @ ( powerset @ SX0 ) )
| ~ ~ ( empty @ SX1 ) )
| ~ ( finite @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(110,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( finite @ SX0 )
| ( finite @ ( set_difference @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(111,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( finite @ SX0 )
| ~ ( finite @ SX1 ) )
| ( finite @ ( set_union2 @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(112,plain,
! [SV1: $i] :
( ( ! [SY22: $i] :
( ( symmetric_difference @ SV1 @ SY22 )
= ( symmetric_difference @ SY22 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(113,plain,
! [SV2: $i] :
( ( ! [SY23: $i] :
( ( symmetric_difference @ SV2 @ SY23 )
= ( set_union2 @ ( set_difference @ SV2 @ SY23 ) @ ( set_difference @ SY23 @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(114,plain,
! [SV3: $i] :
( ( ( symmetric_difference @ SV3 @ empty_set )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(115,plain,
( ( finite @ ( symmetric_difference @ sK1_A @ sK2_SY21 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV4: $i] :
( ( ! [SY24: $i] :
( ~ ~ ( ~ ( finite @ SV4 )
| ~ ( finite @ SY24 ) )
| ( finite @ ( set_union2 @ SV4 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV5: $i] :
( ( ! [SY25: $i] :
( ~ ( finite @ SV5 )
| ( finite @ ( set_difference @ SV5 @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(118,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ~ ( empty @ SX0 )
| ~ ( finite @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(119,plain,
! [SV6: $i] :
( ( ~ ( finite @ SV6 )
| ! [SY26: $i] :
( ~ ( element @ SY26 @ ( powerset @ SV6 ) )
| ( finite @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(120,plain,
! [SV7: $i] :
( ( ~ ( empty @ SV7 )
| ( finite @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV8: $i] :
( ( ~ ~ ( empty @ SV8 )
| ~ ! [SY27: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY27 @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ SY27 ) )
| ~ ( finite @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(122,plain,
! [SV9: $i] :
( ( ! [SY28: $i] :
( ~ ( finite @ SV9 )
| ( finite @ ( set_difference @ SV9 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV10: $i] :
( ( ! [SY29: $i] :
( ~ ~ ( ~ ( finite @ SV10 )
| ~ ( finite @ SY29 ) )
| ( finite @ ( set_union2 @ SV10 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV11: $i,SV1: $i] :
( ( ( symmetric_difference @ SV1 @ SV11 )
= ( symmetric_difference @ SV11 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(125,plain,
! [SV12: $i,SV2: $i] :
( ( ( symmetric_difference @ SV2 @ SV12 )
= ( set_union2 @ ( set_difference @ SV2 @ SV12 ) @ ( set_difference @ SV12 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(126,plain,
! [SV13: $i,SV4: $i] :
( ( ~ ~ ( ~ ( finite @ SV4 )
| ~ ( finite @ SV13 ) )
| ( finite @ ( set_union2 @ SV4 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV14: $i,SV5: $i] :
( ( ~ ( finite @ SV5 )
| ( finite @ ( set_difference @ SV5 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(128,plain,
( ( ~ ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[118]) ).
thf(129,plain,
! [SV6: $i] :
( ( ( ~ ( finite @ SV6 ) )
= $true )
| ( ( ! [SY26: $i] :
( ~ ( element @ SY26 @ ( powerset @ SV6 ) )
| ( finite @ SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(130,plain,
! [SV7: $i] :
( ( ( ~ ( empty @ SV7 ) )
= $true )
| ( ( finite @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV8: $i] :
( ( ( ~ ~ ( empty @ SV8 ) )
= $true )
| ( ( ~ ! [SY27: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY27 @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ SY27 ) )
| ~ ( finite @ SY27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV15: $i,SV9: $i] :
( ( ~ ( finite @ SV9 )
| ( finite @ ( set_difference @ SV9 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV16: $i,SV10: $i] :
( ( ~ ~ ( ~ ( finite @ SV10 )
| ~ ( finite @ SV16 ) )
| ( finite @ ( set_union2 @ SV10 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( finite @ SV4 )
| ~ ( finite @ SV13 ) ) )
= $true )
| ( ( finite @ ( set_union2 @ SV4 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(135,plain,
! [SV14: $i,SV5: $i] :
( ( ( ~ ( finite @ SV5 ) )
= $true )
| ( ( finite @ ( set_difference @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(136,plain,
( ( ~ ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(137,plain,
! [SV6: $i] :
( ( ( finite @ SV6 )
= $false )
| ( ( ! [SY26: $i] :
( ~ ( element @ SY26 @ ( powerset @ SV6 ) )
| ( finite @ SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(138,plain,
! [SV7: $i] :
( ( ( empty @ SV7 )
= $false )
| ( ( finite @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(139,plain,
! [SV8: $i] :
( ( ( ~ ( empty @ SV8 ) )
= $false )
| ( ( ~ ! [SY27: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY27 @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ SY27 ) )
| ~ ( finite @ SY27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(140,plain,
! [SV15: $i,SV9: $i] :
( ( ( ~ ( finite @ SV9 ) )
= $true )
| ( ( finite @ ( set_difference @ SV9 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(141,plain,
! [SV16: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( finite @ SV10 )
| ~ ( finite @ SV16 ) ) )
= $true )
| ( ( finite @ ( set_union2 @ SV10 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(142,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ( ~ ( finite @ SV4 )
| ~ ( finite @ SV13 ) ) )
= $false )
| ( ( finite @ ( set_union2 @ SV4 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(143,plain,
! [SV14: $i,SV5: $i] :
( ( ( finite @ SV5 )
= $false )
| ( ( finite @ ( set_difference @ SV5 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(144,plain,
( ( ~ ~ ( empty @ sK3_SX0 )
| ~ ( finite @ sK3_SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(145,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ ( powerset @ SV6 ) )
| ( finite @ SV17 ) )
= $true )
| ( ( finite @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(146,plain,
! [SV8: $i] :
( ( ( empty @ SV8 )
= $true )
| ( ( ~ ! [SY27: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY27 @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ SY27 ) )
| ~ ( finite @ SY27 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(147,plain,
! [SV15: $i,SV9: $i] :
( ( ( finite @ SV9 )
= $false )
| ( ( finite @ ( set_difference @ SV9 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(148,plain,
! [SV16: $i,SV10: $i] :
( ( ( ~ ( ~ ( finite @ SV10 )
| ~ ( finite @ SV16 ) ) )
= $false )
| ( ( finite @ ( set_union2 @ SV10 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(149,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ( finite @ SV4 )
| ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV4 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(150,plain,
( ( ~ ~ ( empty @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(151,plain,
( ( ~ ( finite @ sK3_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(152,plain,
! [SV6: $i,SV17: $i] :
( ( ( ~ ( element @ SV17 @ ( powerset @ SV6 ) ) )
= $true )
| ( ( finite @ SV17 )
= $true )
| ( ( finite @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(153,plain,
! [SV8: $i] :
( ( ( ! [SY27: $i] :
~ ~ ( ~ ~ ( ~ ( element @ SY27 @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ SY27 ) )
| ~ ( finite @ SY27 ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(154,plain,
! [SV16: $i,SV10: $i] :
( ( ( ~ ( finite @ SV10 )
| ~ ( finite @ SV16 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV10 @ SV16 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(155,plain,
! [SV13: $i,SV4: $i] :
( ( ( ~ ( finite @ SV4 ) )
= $true )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV4 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(156,plain,
( ( ~ ( empty @ sK3_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(157,plain,
( ( finite @ sK3_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(158,plain,
! [SV6: $i,SV17: $i] :
( ( ( element @ SV17 @ ( powerset @ SV6 ) )
= $false )
| ( ( finite @ SV17 )
= $true )
| ( ( finite @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(159,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( element @ ( sK4_SY27 @ SV8 ) @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ ( sK4_SY27 @ SV8 ) ) )
| ~ ( finite @ ( sK4_SY27 @ SV8 ) ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[153]) ).
thf(160,plain,
! [SV16: $i,SV10: $i] :
( ( ( ~ ( finite @ SV10 ) )
= $true )
| ( ( ~ ( finite @ SV16 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV10 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(161,plain,
! [SV13: $i,SV4: $i] :
( ( ( finite @ SV4 )
= $false )
| ( ( ~ ( finite @ SV13 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV4 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(162,plain,
( ( empty @ sK3_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(163,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ( element @ ( sK4_SY27 @ SV8 ) @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ ( sK4_SY27 @ SV8 ) ) )
| ~ ( finite @ ( sK4_SY27 @ SV8 ) ) ) )
= $true )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(164,plain,
! [SV16: $i,SV10: $i] :
( ( ( finite @ SV10 )
= $false )
| ( ( ~ ( finite @ SV16 ) )
= $true )
| ( ( finite @ ( set_union2 @ SV10 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(165,plain,
! [SV4: $i,SV13: $i] :
( ( ( finite @ SV13 )
= $false )
| ( ( finite @ SV4 )
= $false )
| ( ( finite @ ( set_union2 @ SV4 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(166,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK4_SY27 @ SV8 ) @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ ( sK4_SY27 @ SV8 ) ) )
| ~ ( finite @ ( sK4_SY27 @ SV8 ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(167,plain,
! [SV10: $i,SV16: $i] :
( ( ( finite @ SV16 )
= $false )
| ( ( finite @ SV10 )
= $false )
| ( ( finite @ ( set_union2 @ SV10 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(168,plain,
! [SV8: $i] :
( ( ( ~ ~ ( ~ ( element @ ( sK4_SY27 @ SV8 ) @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ ( sK4_SY27 @ SV8 ) ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(169,plain,
! [SV8: $i] :
( ( ( ~ ( finite @ ( sK4_SY27 @ SV8 ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(170,plain,
! [SV8: $i] :
( ( ( ~ ( ~ ( element @ ( sK4_SY27 @ SV8 ) @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ ( sK4_SY27 @ SV8 ) ) ) )
= $true )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(171,plain,
! [SV8: $i] :
( ( ( finite @ ( sK4_SY27 @ SV8 ) )
= $true )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(172,plain,
! [SV8: $i] :
( ( ( ~ ( element @ ( sK4_SY27 @ SV8 ) @ ( powerset @ SV8 ) )
| ~ ~ ( empty @ ( sK4_SY27 @ SV8 ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(173,plain,
! [SV8: $i] :
( ( ( ~ ( element @ ( sK4_SY27 @ SV8 ) @ ( powerset @ SV8 ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(174,plain,
! [SV8: $i] :
( ( ( ~ ~ ( empty @ ( sK4_SY27 @ SV8 ) ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[172]) ).
thf(175,plain,
! [SV8: $i] :
( ( ( element @ ( sK4_SY27 @ SV8 ) @ ( powerset @ SV8 ) )
= $true )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(176,plain,
! [SV8: $i] :
( ( ( ~ ( empty @ ( sK4_SY27 @ SV8 ) ) )
= $true )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(177,plain,
! [SV8: $i] :
( ( ( empty @ ( sK4_SY27 @ SV8 ) )
= $false )
| ( ( empty @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(178,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[101,177,175,171,167,165,162,158,157,147,143,138,125,124,115,114,102]) ).
thf(179,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU097+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 : n008.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 15:00:54 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
% 0.50/0.32
% 0.50/0.32 No.of.Axioms: 11
% 0.50/0.32
% 0.50/0.32 Length.of.Defs: 0
% 0.50/0.32
% 0.50/0.32 Contains.Choice.Funs: false
% 0.50/0.32 ...
% 0.50/0.32
% 0.50/0.32 ********************************
% 0.50/0.32 * All subproblems solved! *
% 0.50/0.32 ********************************
% 0.50/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:13,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:178,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.50/0.32
% 0.50/0.32 %**** Beginning of derivation protocol ****
% 0.50/0.32 % SZS output start CNFRefutation
% See solution above
% 0.50/0.32
% 0.50/0.32 %**** End of derivation protocol ****
% 0.50/0.32 %**** no. of clauses in derivation: 121 ****
% 0.50/0.32 %**** clause counter: 178 ****
% 0.50/0.32
% 0.50/0.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:13,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:178,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------