%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET012+4 : TPTP v9.3.1. Released v2.2.0.
% 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 : n019.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 10:38:51 AM UTC 2026
% Result : Theorem 13.22s 2.45s
% Output : CNFRefutation 13.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 86 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 522 ( 129 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 1068 ( 256 ~; 155 |; 6 &; 634 @)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 202 ( 0 ^; 202 !; 0 ?; 202 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_difference,type,
difference: $i > $i > $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_equal_set,type,
equal_set: $i > $i > $o ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_power_set,type,
power_set: $i > $i ).
thf(tp_product,type,
product: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY10,type,
sK2_SY10: $i ).
thf(tp_sK3_SY19,type,
sK3_SY19: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_sum,type,
sum: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(5,axiom,
! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
thf(12,conjecture,
! [A: $i,E: $i] :
( ( subset @ A @ E )
=> ( equal_set @ ( difference @ E @ ( difference @ E @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI23) ).
thf(13,negated_conjecture,
( ( ! [A: $i,E: $i] :
( ( subset @ A @ E )
=> ( equal_set @ ( difference @ E @ ( difference @ E @ A ) ) @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [A: $i,E: $i] :
( ( subset @ A @ E )
=> ( equal_set @ ( difference @ E @ ( difference @ E @ A ) ) @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [SY10: $i] :
( ( subset @ sK1_A @ SY10 )
=> ( equal_set @ ( difference @ SY10 @ ( difference @ SY10 @ sK1_A ) ) @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(19,plain,
( ( ( subset @ sK1_A @ sK2_SY10 )
=> ( equal_set @ ( difference @ sK2_SY10 @ ( difference @ sK2_SY10 @ sK1_A ) ) @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(20,plain,
( ( subset @ sK1_A @ sK2_SY10 )
= $true ),
inference(standard_cnf,[status(thm)],[19]) ).
thf(21,plain,
( ( equal_set @ ( difference @ sK2_SY10 @ ( difference @ sK2_SY10 @ sK1_A ) ) @ sK1_A )
= $false ),
inference(standard_cnf,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ( equal_set @ ( difference @ sK2_SY10 @ ( difference @ sK2_SY10 @ sK1_A ) ) @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [X: $i] :
( ( member @ X @ A )
=> ( member @ X @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( equal_set @ A @ B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( ! [B: $i,A: $i,E: $i] :
( ( member @ B @ ( difference @ E @ A ) )
<=> ( ( member @ B @ E )
& ~ ( member @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(26,plain,
( ( subset @ sK1_A @ sK2_SY10 )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(27,plain,
( ( ~ ( equal_set @ ( difference @ sK2_SY10 @ ( difference @ sK2_SY10 @ sK1_A ) ) @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( equal_set @ SX0 @ SX1 )
| ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 ) )
| ( equal_set @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(29,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( member @ SX0 @ ( difference @ SX2 @ SX1 ) )
| ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ~ ( member @ SX0 @ SX1 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SX0 @ SX2 )
| ~ ~ ( member @ SX0 @ SX1 ) )
| ( member @ SX0 @ ( difference @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( member @ SX2 @ SX0 )
| ( member @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(31,plain,
( ( equal_set @ ( difference @ sK2_SY10 @ ( difference @ sK2_SY10 @ sK1_A ) ) @ sK1_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV1: $i] :
( ( ! [SY11: $i] :
~ ( ~ ( ~ ( equal_set @ SV1 @ SY11 )
| ~ ( ~ ( subset @ SV1 @ SY11 )
| ~ ( subset @ SY11 @ SV1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV1 @ SY11 )
| ~ ( subset @ SY11 @ SV1 ) )
| ( equal_set @ SV1 @ SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV2: $i] :
( ( ! [SY12: $i,SY13: $i] :
~ ( ~ ( ~ ( member @ SV2 @ ( difference @ SY13 @ SY12 ) )
| ~ ( ~ ( member @ SV2 @ SY13 )
| ~ ~ ( member @ SV2 @ SY12 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV2 @ SY13 )
| ~ ~ ( member @ SV2 @ SY12 ) )
| ( member @ SV2 @ ( difference @ SY13 @ SY12 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV3: $i] :
( ( ! [SY14: $i] :
~ ( ~ ( ~ ( subset @ SV3 @ SY14 )
| ! [SY15: $i] :
( ~ ( member @ SY15 @ SV3 )
| ( member @ SY15 @ SY14 ) ) )
| ~ ( ~ ! [SY16: $i] :
( ~ ( member @ SY16 @ SV3 )
| ( member @ SY16 @ SY14 ) )
| ( subset @ SV3 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ( equal_set @ SV1 @ SV4 )
| ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) )
| ( equal_set @ SV1 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY17: $i] :
~ ( ~ ( ~ ( member @ SV2 @ ( difference @ SY17 @ SV5 ) )
| ~ ( ~ ( member @ SV2 @ SY17 )
| ~ ~ ( member @ SV2 @ SV5 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV2 @ SY17 )
| ~ ~ ( member @ SV2 @ SV5 ) )
| ( member @ SV2 @ ( difference @ SY17 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( ~ ( subset @ SV3 @ SV6 )
| ! [SY18: $i] :
( ~ ( member @ SY18 @ SV3 )
| ( member @ SY18 @ SV6 ) ) )
| ~ ( ~ ! [SY19: $i] :
( ~ ( member @ SY19 @ SV3 )
| ( member @ SY19 @ SV6 ) )
| ( subset @ SV3 @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( ~ ( equal_set @ SV1 @ SV4 )
| ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
| ~ ( ~ ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) )
| ( equal_set @ SV1 @ SV4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
| ~ ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) )
| ( member @ SV2 @ ( difference @ SV7 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( subset @ SV3 @ SV6 )
| ! [SY18: $i] :
( ~ ( member @ SY18 @ SV3 )
| ( member @ SY18 @ SV6 ) ) )
| ~ ( ~ ! [SY19: $i] :
( ~ ( member @ SY19 @ SV3 )
| ( member @ SY19 @ SV6 ) )
| ( subset @ SV3 @ SV6 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( ~ ( equal_set @ SV1 @ SV4 )
| ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(42,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( ~ ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) )
| ( equal_set @ SV1 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ~ ( ~ ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
| ~ ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) ) )
| ~ ( ~ ~ ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) )
| ( member @ SV2 @ ( difference @ SV7 @ SV5 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ( subset @ SV3 @ SV6 )
| ! [SY18: $i] :
( ~ ( member @ SY18 @ SV3 )
| ( member @ SY18 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( ~ ! [SY19: $i] :
( ~ ( member @ SY19 @ SV3 )
| ( member @ SY19 @ SV6 ) )
| ( subset @ SV3 @ SV6 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ( equal_set @ SV1 @ SV4 )
| ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(47,plain,
! [SV4: $i,SV1: $i] :
( ( ~ ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) )
| ( equal_set @ SV1 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(48,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ~ ( ~ ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
| ~ ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(49,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ~ ( ~ ~ ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) )
| ( member @ SV2 @ ( difference @ SV7 @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[43]) ).
thf(50,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ( subset @ SV3 @ SV6 )
| ! [SY18: $i] :
( ~ ( member @ SY18 @ SV3 )
| ( member @ SY18 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(51,plain,
! [SV6: $i,SV3: $i] :
( ( ~ ! [SY19: $i] :
( ~ ( member @ SY19 @ SV3 )
| ( member @ SY19 @ SV6 ) )
| ( subset @ SV3 @ SV6 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( equal_set @ SV1 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
= $true )
| ( ( equal_set @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ~ ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
| ~ ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(55,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ~ ~ ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) )
| ( member @ SV2 @ ( difference @ SV7 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(56,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( subset @ SV3 @ SV6 ) )
= $true )
| ( ( ! [SY18: $i] :
( ~ ( member @ SY18 @ SV3 )
| ( member @ SY18 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ! [SY19: $i] :
( ~ ( member @ SY19 @ SV3 )
| ( member @ SY19 @ SV6 ) ) )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV4: $i,SV1: $i] :
( ( ( equal_set @ SV1 @ SV4 )
= $false )
| ( ( ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) ) )
= $false )
| ( ( equal_set @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ ( difference @ SV7 @ SV5 ) ) )
= $true )
| ( ( ~ ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) ) )
= $true )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV6: $i,SV3: $i] :
( ( ( subset @ SV3 @ SV6 )
= $false )
| ( ( ! [SY18: $i] :
( ~ ( member @ SY18 @ SV3 )
| ( member @ SY18 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV6: $i,SV3: $i] :
( ( ( ! [SY19: $i] :
( ~ ( member @ SY19 @ SV3 )
| ( member @ SY19 @ SV6 ) ) )
= $false )
| ( ( subset @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(64,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) )
= $false )
| ( ( equal_set @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( subset @ SV1 @ SV4 )
| ~ ( subset @ SV4 @ SV1 ) )
= $true )
| ( ( equal_set @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(66,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $false )
| ( ( ~ ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) ) )
= $false )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV3 )
| ( member @ SV8 @ SV6 ) )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK3_SY19 @ SV6 @ SV3 ) @ SV3 )
| ( member @ ( sK3_SY19 @ SV6 @ SV3 ) @ SV6 ) )
= $false )
| ( ( subset @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(70,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( subset @ SV1 @ SV4 ) )
= $false )
| ( ( equal_set @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(71,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( subset @ SV4 @ SV1 ) )
= $false )
| ( ( equal_set @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(72,plain,
! [SV4: $i,SV1: $i] :
( ( ( ~ ( subset @ SV1 @ SV4 ) )
= $true )
| ( ( ~ ( subset @ SV4 @ SV1 ) )
= $true )
| ( ( equal_set @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(73,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) )
= $false )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(74,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV7 )
| ~ ~ ( member @ SV2 @ SV5 ) )
= $true )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(75,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ SV3 ) )
= $true )
| ( ( member @ SV8 @ SV6 )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(76,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( member @ ( sK3_SY19 @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( subset @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(77,plain,
! [SV3: $i,SV6: $i] :
( ( ( member @ ( sK3_SY19 @ SV6 @ SV3 ) @ SV6 )
= $false )
| ( ( subset @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(78,plain,
! [SV4: $i,SV1: $i] :
( ( ( subset @ SV1 @ SV4 )
= $true )
| ( ( equal_set @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(79,plain,
! [SV1: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV1 )
= $true )
| ( ( equal_set @ SV1 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(80,plain,
! [SV4: $i,SV1: $i] :
( ( ( subset @ SV1 @ SV4 )
= $false )
| ( ( ~ ( subset @ SV4 @ SV1 ) )
= $true )
| ( ( equal_set @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV7 ) )
= $false )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(82,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( ~ ~ ( member @ SV2 @ SV5 ) )
= $false )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(83,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV7 ) )
= $true )
| ( ( ~ ~ ( member @ SV2 @ SV5 ) )
= $true )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( member @ SV8 @ SV3 )
= $false )
| ( ( member @ SV8 @ SV6 )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV3: $i,SV6: $i] :
( ( ( member @ ( sK3_SY19 @ SV6 @ SV3 ) @ SV3 )
= $true )
| ( ( subset @ SV3 @ SV6 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(86,plain,
! [SV1: $i,SV4: $i] :
( ( ( subset @ SV4 @ SV1 )
= $false )
| ( ( subset @ SV1 @ SV4 )
= $false )
| ( ( equal_set @ SV1 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( member @ SV2 @ SV7 )
= $true )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(88,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV5 ) )
= $true )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[82]) ).
thf(89,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( member @ SV2 @ SV7 )
= $false )
| ( ( ~ ~ ( member @ SV2 @ SV5 ) )
= $true )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(90,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( member @ SV2 @ SV5 )
= $false )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(91,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( ~ ( member @ SV2 @ SV5 ) )
= $false )
| ( ( member @ SV2 @ SV7 )
= $false )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(92,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( member @ SV2 @ SV5 )
= $true )
| ( ( member @ SV2 @ SV7 )
= $false )
| ( ( member @ SV2 @ ( difference @ SV7 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(93,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,92,90,87,86,85,84,79,78,77,31]) ).
thf(94,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012+4 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.07/0.19 % Computer : n019.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % 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 14:26:01 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.22/2.45
% 13.22/2.45 No.of.Axioms: 3
% 13.22/2.45
% 13.22/2.45 Length.of.Defs: 0
% 13.22/2.45
% 13.22/2.45 Contains.Choice.Funs: false
% 13.22/2.45 ..
% 13.22/2.45
% 13.22/2.45 ********************************
% 13.22/2.45 * All subproblems solved! *
% 13.22/2.45 ********************************
% 13.22/2.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:93,loop_count:0,foatp_calls:1,translation:fof_full)
% 13.22/2.45
% 13.22/2.45 %**** Beginning of derivation protocol ****
% 13.22/2.45 % SZS output start CNFRefutation
% See solution above
% 13.22/2.45
% 13.22/2.45 %**** End of derivation protocol ****
% 13.22/2.45 %**** no. of clauses in derivation: 86 ****
% 13.22/2.45 %**** clause counter: 93 ****
% 13.22/2.45
% 13.22/2.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:4,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:93,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------