%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET019^4 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 Sep 30 08:22:51 AM UTC 2026
% Result : Theorem 5.09s 2.70s
% Output : Refutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 44
% Syntax : Number of formulae : 82 ( 13 unt; 0 typ; 8 def)
% Number of atoms : 462 ( 19 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 1079 ( 5 ~; 3 |; 17 &; 942 @)
% ( 0 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 10 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 3 con; 0-3 aty)
% Number of variables : 207 ( 107 ^; 96 !; 4 ?; 207 :)
% Comments :
%------------------------------------------------------------------------------
thf(mworld_type,type,
mworld: $tType ).
thf(mrel_decl,type,
mrel: mworld > mworld > $o ).
thf(mactual_decl,type,
mactual: mworld ).
thf(mlocal_decl,type,
mlocal: ( mworld > $o ) > $o ).
thf(mnot_decl,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(mand_decl,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mor_decl,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mimplies_decl,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mequiv_decl,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(eiw_di_decl,type,
eiw_di: $i > mworld > $o ).
thf(mforall_di_decl,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mexists_di_decl,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(qmltpeq_decl,type,
qmltpeq: $i > $i > mworld > $o ).
thf(equal_set_decl,type,
equal_set: $i > $i > mworld > $o ).
thf(member_decl,type,
member: $i > $i > mworld > $o ).
thf(subset_decl,type,
subset: $i > $i > mworld > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(product_decl,type,
product: $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(sum_decl,type,
sum: $i > $i ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(power_set_decl,type,
power_set: $i > $i ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [A: mworld > $o] : ( A @ mactual ) ) ) ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,B: mworld] :
~ ( A @ B ) ) ) ).
thf(mand_def,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(mor_def,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,C: mworld] :
( ( A @ C )
= ( B @ C ) ) ) ) ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
! [C: $i] :
( ( eiw_di @ C @ B )
=> ( A @ C @ B ) ) ) ) ).
thf(mexists_di_def,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,B: mworld] :
? [C: $i] :
( ( eiw_di @ C @ B )
& ( A @ C @ B ) ) ) ) ).
thf(33,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_2) ).
thf(115,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( subset @ C @ A @ mactual ) )
=> ( subset @ C @ B @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(6,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_substitution_1) ).
thf(52,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( equal_set @ A @ C @ mactual ) )
=> ( equal_set @ B @ C @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_1) ).
thf(74,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) @ ( equal_set @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI02) ).
thf(2,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) @ ( equal_set @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(38,plain,
~ ! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( ( subset @ A @ B @ mactual )
& ( subset @ B @ A @ mactual ) )
=> ( equal_set @ A @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set_substitution_1) ).
thf(80,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(37,axiom,
! [A: mworld,B: mworld,C: $i] :
( ( ( eiw_di @ C @ A )
& ( mrel @ B @ A ) )
=> ( eiw_di @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_decr) ).
thf(123,plain,
! [A: mworld,B: mworld,C: $i] :
( ( ( eiw_di @ C @ A )
& ( mrel @ B @ A ) )
=> ( eiw_di @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(25,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( member @ A @ ( unordered_pair @ B @ C ) ) @ ( mor @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_0) ).
thf(95,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ A @ ( unordered_pair @ B @ C ) @ mactual )
= ( ( qmltpeq @ A @ B @ mactual )
| ( qmltpeq @ A @ C @ mactual ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(13,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_substitution_1) ).
thf(69,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(22,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( member @ A @ ( sum @ B ) )
@ ( mexists_di
@ ^ [C: $i] : ( mand @ ( member @ C @ B ) @ ( member @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_0) ).
thf(88,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( member @ A @ ( sum @ B ) @ mactual )
= ( ? [C: $i] :
( ( eiw_di @ C @ mactual )
& ( member @ C @ B @ mactual )
& ( member @ A @ C @ mactual ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(24,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_substitution_2) ).
thf(93,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_0) ).
thf(57,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( equal_set @ A @ B @ mactual )
= ( ( subset @ A @ B @ mactual )
& ( subset @ B @ A @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_2) ).
thf(78,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( member @ C @ A @ mactual ) )
=> ( member @ C @ B @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(29,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( mnot @ ( member @ A @ empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_0) ).
thf(106,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ~ ( member @ A @ empty_set @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(36,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(121,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ B @ A @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(20,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set_substitution_2) ).
thf(84,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( equal_set @ C @ A @ mactual ) )
=> ( equal_set @ C @ B @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_substitution_2) ).
thf(60,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_1) ).
thf(117,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(3,axiom,
! [A: mworld] : ( mrel @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).
thf(45,plain,
! [A: mworld] : ( mrel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_1) ).
thf(64,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( subset @ A @ C @ mactual ) )
=> ( subset @ B @ C @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( subset @ A @ B )
@ ( mforall_di
@ ^ [C: $i] : ( mimplies @ ( member @ C @ A ) @ ( member @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_0) ).
thf(71,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( subset @ A @ B @ mactual )
= ( ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ C @ A @ mactual )
=> ( member @ C @ B @ mactual ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( member @ A @ ( difference @ C @ B ) ) @ ( mand @ ( member @ A @ C ) @ ( mnot @ ( member @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_0) ).
thf(54,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ A @ ( difference @ C @ B ) @ mactual )
= ( ( member @ A @ C @ mactual )
& ~ ( member @ A @ B @ mactual ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mequiv @ ( member @ A @ ( product @ B ) )
@ ( mforall_di
@ ^ [C: $i] : ( mimplies @ ( member @ C @ B ) @ ( member @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_0) ).
thf(49,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( member @ A @ ( product @ B ) @ mactual )
= ( ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ C @ B @ mactual )
=> ( member @ A @ C @ mactual ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] : ( qmltpeq @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(86,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ( qmltpeq @ A @ A @ mactual ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(32,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_2) ).
thf(113,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(16,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_1) ).
thf(76,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( member @ A @ C @ mactual ) )
=> ( member @ B @ C @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(26,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution_1) ).
thf(98,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( product @ A ) @ ( product @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(28,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( member @ A @ ( union @ B @ C ) ) @ ( mor @ ( member @ A @ B ) @ ( member @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_0) ).
thf(103,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ A @ ( union @ B @ C ) @ mactual )
= ( ( member @ A @ B @ mactual )
| ( member @ A @ C @ mactual ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(23,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_substitution_1) ).
thf(91,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(12,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( member @ A @ ( singleton @ B ) ) @ ( qmltpeq @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_0) ).
thf(66,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( member @ A @ ( singleton @ B ) @ mactual )
= ( qmltpeq @ A @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(30,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mequiv @ ( member @ A @ ( power_set @ B ) ) @ ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set_0) ).
thf(108,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( member @ A @ ( power_set @ B ) @ mactual )
= ( subset @ A @ B @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(35,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_1) ).
thf(119,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(19,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_substitution_2) ).
thf(82,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution_1) ).
thf(47,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ( ( qmltpeq @ A @ B @ mactual )
=> ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) @ mactual ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ B @ C ) ) @ ( qmltpeq @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(62,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( ( qmltpeq @ A @ B @ mactual )
& ( qmltpeq @ B @ C @ mactual ) )
=> ( qmltpeq @ A @ C @ mactual ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,axiom,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_nonempty) ).
thf(111,plain,
! [A: mworld] :
? [B: $i] : ( eiw_di @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(27,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mequiv @ ( member @ A @ ( intersection @ B @ C ) ) @ ( mand @ ( member @ A @ B ) @ ( member @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_0) ).
thf(100,plain,
! [A: $i] :
( ( eiw_di @ A @ mactual )
=> ! [B: $i] :
( ( eiw_di @ B @ mactual )
=> ! [C: $i] :
( ( eiw_di @ C @ mactual )
=> ( ( member @ A @ ( intersection @ B @ C ) @ mactual )
= ( ( member @ A @ B @ mactual )
& ( member @ A @ C @ mactual ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(125,plain,
$false,
inference(e,[status(thm)],[115,52,74,38,80,123,95,69,88,93,57,78,106,121,84,60,117,45,64,71,54,49,86,113,76,98,103,91,66,108,119,82,47,62,111,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET019^4 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.23 % Computer : n002.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 13:38:07 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.00/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.07 % [INFO] Parsing done (263ms).
% 1.47/1.08 % [INFO] Running in sequential loop mode.
% 2.18/1.46 % [INFO] eprover registered as external prover.
% 2.18/1.47 % [INFO] Scanning for conjecture ...
% 2.55/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 35 axioms. Running axiom selection ...
% 2.55/1.70 % [INFO] Axiom selection finished. Selected 35 axioms (removed 0 axioms).
% 2.73/1.75 % [INFO] Problem is higher-order (TPTP THF).
% 2.73/1.76 % [INFO] Type checking passed.
% 2.73/1.77 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.09/2.70 % External prover 'e' found a proof!
% 5.09/2.70 % [INFO] Killing All external provers ...
% 5.09/2.70 % Time passed: 2319ms (effective reasoning time: 1610ms)
% 5.09/2.70 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 5.09/2.70 % Axioms used in derivation (35): product_substitution_1, intersection_substitution_1, singleton_0, power_set_0, unordered_pair_0, difference_substitution_1, transitivity, member_substitution_2, member_substitution_1, sum_substitution_1, subset_substitution_2, empty_set_0, mrel_reflexive, unordered_pair_substitution_2, intersection_0, intersection_substitution_2, sum_0, equal_set_0, union_substitution_2, difference_0, reflexivity, product_0, subset_0, equal_set_substitution_2, union_0, unordered_pair_substitution_1, difference_substitution_2, power_set_substitution_1, eiw_di_nonempty, subset_substitution_1, equal_set_substitution_1, union_substitution_1, singleton_substitution_1, symmetry, eiw_di_decr
% 5.09/2.70 % No. of inferences in proof: 74
% 5.09/2.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2319 ms resp. 1610 ms w/o parsing
% 5.38/2.84 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.38/2.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------